Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 68.6% → 91.2%

Time: 20.3s

Alternatives: 24

Speedup: 0.8×

Specification

Math

\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.6% accurate, 1.0× speedup

Math

\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq \frac{-4602094425247529}{23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{t - a} \cdot \left(y - x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
  (if (<=
       t_1
       -4602094425247529/23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648)
    (134-z0z1z2z3z4 (/ -1 (- t a)) (- z t) (- y x) (- t a) x)
    (if (<= t_1 0)
      (+ y (* -1 (/ (- (* z (- y x)) (* a (- y x))) t)))
      (+ x (* (/ (- t z) (- t a)) (- y x)))))))

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-295

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   if -2.0000000000000001e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      2. lower-*.f64 N/A

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{\color{blue}{t}} \]

      4. lower--.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      5. lower-*.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      6. lower--.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      7. lower-*.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      8. lower--.f64 45.7%

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

   10. Applied rewrites 45.7%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot \left(z - t\right)}}{a - t} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      6. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(z - t\right)\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      8. sub-negate-rev N/A

         \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t - z}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      11. lift--.f64 N/A

          \[\leadsto x + \frac{t - z}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)} \cdot \left(y - x\right) \]

      12. sub-negate-rev N/A

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

      13. lower--.f64 84.4%

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

   3. Applied rewrites 84.4%

      \[\leadsto x + \color{blue}{\frac{t - z}{t - a} \cdot \left(y - x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t - z}{t - a} \cdot \left(y - x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq \frac{-4602094425247529}{23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (/ (- t z) (- t a)) (- y x))))
       (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
  (if (<=
       t_2
       -4602094425247529/23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648)
    t_1
    (if (<= t_2 0)
      (+ y (* -1 (/ (- (* z (- y x)) (* a (- y x))) t)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - z) / (t - a)) * (y - x));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-295) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (-1.0 * (((z * (y - x)) - (a * (y - x))) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((t - z) / (t - a)) * (y - x))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-2d-295)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = y + ((-1.0d0) * (((z * (y - x)) - (a * (y - x))) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - z) / (t - a)) * (y - x));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-295) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (-1.0 * (((z * (y - x)) - (a * (y - x))) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - z) / (t - a)) * (y - x))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -2e-295:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = y + (-1.0 * (((z * (y - x)) - (a * (y - x))) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - z) / Float64(t - a)) * Float64(y - x)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-295)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(-1.0 * Float64(Float64(Float64(z * Float64(y - x)) - Float64(a * Float64(y - x))) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - z) / (t - a)) * (y - x));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-295)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = y + (-1.0 * (((z * (y - x)) - (a * (y - x))) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4602094425247529/23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648], t$95$1, If[LessEqual[t$95$2, 0], N[(y + N[(-1 * N[(N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot \left(z - t\right)}}{a - t} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      6. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(z - t\right)\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      8. sub-negate-rev N/A

         \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t - z}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      11. lift--.f64 N/A

          \[\leadsto x + \frac{t - z}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)} \cdot \left(y - x\right) \]

      12. sub-negate-rev N/A

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

      13. lower--.f64 84.4%

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

   3. Applied rewrites 84.4%

      \[\leadsto x + \color{blue}{\frac{t - z}{t - a} \cdot \left(y - x\right)} \]

   if -2.0000000000000001e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      2. lower-*.f64 N/A

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{\color{blue}{t}} \]

      4. lower--.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      5. lower-*.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      6. lower--.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      7. lower-*.f64 N/A

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

      8. lower--.f64 45.7%

         \[\leadsto y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t} \]

   10. Applied rewrites 45.7%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \mathbf{if}\;t \leq -3199999999999999843658535884555242257084531347579589343829306844983523751599986938649084124535148872990680143605484242146223441040176797789643435496408465278006517292279496000248715692233307591802880:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 47999999999999996758420028465010248540784950903205898777505147341473406437850717603188489528757242548373800041820977301682092317158153014221734479178139712973821722381169998168064:\\ \;\;\;\;x + \frac{t - z}{t - a} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* y (- (/ z (- a t)) (/ t (- a t))))))
  (if (<=
       t
       -3199999999999999843658535884555242257084531347579589343829306844983523751599986938649084124535148872990680143605484242146223441040176797789643435496408465278006517292279496000248715692233307591802880)
    t_1
    (if (<=
         t
         47999999999999996758420028465010248540784950903205898777505147341473406437850717603188489528757242548373800041820977301682092317158153014221734479178139712973821722381169998168064)
      (+ x (* (/ (- t z) (- t a)) (- y x)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z / (a - t)) - (t / (a - t)));
	double tmp;
	if (t <= -3.2e+198) {
		tmp = t_1;
	} else if (t <= 4.8e+178) {
		tmp = x + (((t - z) / (t - a)) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z / (a - t)) - (t / (a - t)))
    if (t <= (-3.2d+198)) then
        tmp = t_1
    else if (t <= 4.8d+178) then
        tmp = x + (((t - z) / (t - a)) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z / (a - t)) - (t / (a - t)));
	double tmp;
	if (t <= -3.2e+198) {
		tmp = t_1;
	} else if (t <= 4.8e+178) {
		tmp = x + (((t - z) / (t - a)) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z / (a - t)) - (t / (a - t)))
	tmp = 0
	if t <= -3.2e+198:
		tmp = t_1
	elif t <= 4.8e+178:
		tmp = x + (((t - z) / (t - a)) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z / Float64(a - t)) - Float64(t / Float64(a - t))))
	tmp = 0.0
	if (t <= -3.2e+198)
		tmp = t_1;
	elseif (t <= 4.8e+178)
		tmp = Float64(x + Float64(Float64(Float64(t - z) / Float64(t - a)) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z / (a - t)) - (t / (a - t)));
	tmp = 0.0;
	if (t <= -3.2e+198)
		tmp = t_1;
	elseif (t <= 4.8e+178)
		tmp = x + (((t - z) / (t - a)) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3199999999999999843658535884555242257084531347579589343829306844983523751599986938649084124535148872990680143605484242146223441040176797789643435496408465278006517292279496000248715692233307591802880], t$95$1, If[LessEqual[t, 47999999999999996758420028465010248540784950903205898777505147341473406437850717603188489528757242548373800041820977301682092317158153014221734479178139712973821722381169998168064], N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1999999999999998e198 or 4.7999999999999997e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{z}{a - t} - \color{blue}{\frac{t}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{z}{a - t} - \frac{\color{blue}{t}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{z}{a - t} - \frac{t}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto y \cdot \left(\frac{z}{a - t} - \frac{t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 51.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]

   if -3.1999999999999998e198 < t < 4.7999999999999997e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot \left(z - t\right)}}{a - t} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      6. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(z - t\right)\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      8. sub-negate-rev N/A

         \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t - z}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      11. lift--.f64 N/A

          \[\leadsto x + \frac{t - z}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)} \cdot \left(y - x\right) \]

      12. sub-negate-rev N/A

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

      13. lower--.f64 84.4%

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

   3. Applied rewrites 84.4%

      \[\leadsto x + \color{blue}{\frac{t - z}{t - a} \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), z, y, t, y\right)\\ \mathbf{if}\;t \leq -3199999999999999843658535884555242257084531347579589343829306844983523751599986938649084124535148872990680143605484242146223441040176797789643435496408465278006517292279496000248715692233307591802880:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 47999999999999996758420028465010248540784950903205898777505147341473406437850717603188489528757242548373800041820977301682092317158153014221734479178139712973821722381169998168064:\\ \;\;\;\;x + \frac{t - z}{t - a} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (134-z0z1z2z3z4 (/ -1 (- t a)) z y t y)))
  (if (<=
       t
       -3199999999999999843658535884555242257084531347579589343829306844983523751599986938649084124535148872990680143605484242146223441040176797789643435496408465278006517292279496000248715692233307591802880)
    t_1
    (if (<=
         t
         47999999999999996758420028465010248540784950903205898777505147341473406437850717603188489528757242548373800041820977301682092317158153014221734479178139712973821722381169998168064)
      (+ x (* (/ (- t z) (- t a)) (- y x)))
      t_1))))

Derivation

1. Split input into 2 regimes

2. if t < -3.1999999999999998e198 or 4.7999999999999997e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} \]

      4. lower--.f64 39.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - \color{blue}{t}} \]

   10. Applied rewrites 39.7%

       \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   11. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

       2. mult-flip N/A

          \[\leadsto \left(y \cdot \left(z - t\right)\right) \cdot \color{blue}{\frac{1}{a - t}} \]

       3. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(y \cdot \left(z - t\right)\right)} \]

       4. lift-*.f64 N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(y \cdot \color{blue}{\left(z - t\right)}\right) \]

       5. lift--.f64 N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(y \cdot \left(z - \color{blue}{t}\right)\right) \]

       6. sub-flip N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(y \cdot \left(z + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

       7. distribute-rgt-in N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(z \cdot y + \color{blue}{\left(\mathsf{neg}\left(t\right)\right) \cdot y}\right) \]

       8. fp-cancel-sub-sign N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(z \cdot y - \color{blue}{t \cdot y}\right) \]

       9. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \color{blue}{z}, y, t, y\right) \]

       10. frac-2neg N/A

           \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), z, y, t, y\right) \]

       11. metadata-eval N/A

           \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), z, y, t, y\right) \]

       12. lower-/.f64 N/A

           \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), z, y, t, y\right) \]

       13. lift--.f64 N/A

           \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), z, y, t, y\right) \]

       14. sub-negate-rev N/A

           \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), z, y, t, y\right) \]

       15. lower--.f64 51.9%

           \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), z, y, t, y\right) \]

   12. Applied rewrites 51.9%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \color{blue}{z}, y, t, y\right) \]

   if -3.1999999999999998e198 < t < 4.7999999999999997e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot \left(z - t\right)}}{a - t} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      6. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(z - t\right)\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      8. sub-negate-rev N/A

         \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t - z}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      11. lift--.f64 N/A

          \[\leadsto x + \frac{t - z}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)} \cdot \left(y - x\right) \]

      12. sub-negate-rev N/A

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

      13. lower--.f64 84.4%

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

   3. Applied rewrites 84.4%

      \[\leadsto x + \color{blue}{\frac{t - z}{t - a} \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t - z}{t - a} \cdot \left(y - x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq \frac{-4602094425247529}{23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (/ (- t z) (- t a)) (- y x))))
       (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
  (if (<=
       t_2
       -4602094425247529/23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648)
    t_1
    (if (<= t_2 0) (* x (/ (- z a) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - z) / (t - a)) * (y - x));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-295) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((t - z) / (t - a)) * (y - x))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-2d-295)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = x * ((z - a) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - z) / (t - a)) * (y - x));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-295) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - z) / (t - a)) * (y - x))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -2e-295:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = x * ((z - a) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - z) / Float64(t - a)) * Float64(y - x)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-295)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - z) / (t - a)) * (y - x));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-295)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = x * ((z - a) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4602094425247529/23010472126237643618935106442099516590310105330461524130999050388189782503104123280986685097268164610703374576623538349780325090408245327679084471121852687920354290358382782115366684108959500047289994617866880738411283287339835248828660878149225886356908865367627046174713247480125403687018925610191900689563648], t$95$1, If[LessEqual[t$95$2, 0], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot \left(z - t\right)}}{a - t} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

      6. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(z - t\right)\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      8. sub-negate-rev N/A

         \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t - z}{\mathsf{neg}\left(\left(a - t\right)\right)}} \cdot \left(y - x\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \frac{\color{blue}{t - z}}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(y - x\right) \]

      11. lift--.f64 N/A

          \[\leadsto x + \frac{t - z}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)} \cdot \left(y - x\right) \]

      12. sub-negate-rev N/A

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

      13. lower--.f64 84.4%

          \[\leadsto x + \frac{t - z}{\color{blue}{t - a}} \cdot \left(y - x\right) \]

   3. Applied rewrites 84.4%

      \[\leadsto x + \color{blue}{\frac{t - z}{t - a} \cdot \left(y - x\right)} \]

   if -2.0000000000000001e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around -inf

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{z - a}{t} \]

      2. lower--.f64 23.0%

         \[\leadsto x \cdot \frac{z - a}{t} \]

   7. Applied rewrites 23.0%

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x - \frac{t - z}{t - a} \cdot x\\ \mathbf{if}\;x \leq -30000000000000000606566373814678409657282889696430732234133305686240120149944929280760934825984:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 229999999999999994953556542904221181187001180058745893459291421216394549673437691904:\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (* (/ (- t z) (- t a)) x))))
  (if (<=
       x
       -30000000000000000606566373814678409657282889696430732234133305686240120149944929280760934825984)
    t_1
    (if (<=
         x
         229999999999999994953556542904221181187001180058745893459291421216394549673437691904)
      (- x (* y (/ (- t z) (- a t))))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - z) / (t - a)) * x);
	double tmp;
	if (x <= -3e+94) {
		tmp = t_1;
	} else if (x <= 2.3e+83) {
		tmp = x - (y * ((t - z) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - z) / (t - a)) * x)
    if (x <= (-3d+94)) then
        tmp = t_1
    else if (x <= 2.3d+83) then
        tmp = x - (y * ((t - z) / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - z) / (t - a)) * x);
	double tmp;
	if (x <= -3e+94) {
		tmp = t_1;
	} else if (x <= 2.3e+83) {
		tmp = x - (y * ((t - z) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - z) / (t - a)) * x)
	tmp = 0
	if x <= -3e+94:
		tmp = t_1
	elif x <= 2.3e+83:
		tmp = x - (y * ((t - z) / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - z) / Float64(t - a)) * x))
	tmp = 0.0
	if (x <= -3e+94)
		tmp = t_1;
	elseif (x <= 2.3e+83)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - z) / (t - a)) * x);
	tmp = 0.0;
	if (x <= -3e+94)
		tmp = t_1;
	elseif (x <= 2.3e+83)
		tmp = x - (y * ((t - z) / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -30000000000000000606566373814678409657282889696430732234133305686240120149944929280760934825984], t$95$1, If[LessEqual[x, 229999999999999994953556542904221181187001180058745893459291421216394549673437691904], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000001e94 or 2.2999999999999999e83 < x

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \frac{z - t}{a - t}\right) \cdot x} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto 1 \cdot x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{z - t}{a - t}\right)\right) \cdot x} \]

      5. *-lft-identity N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{z - t}{a - t}\right)\right)} \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{z - t}{a - t}\right)\right) \cdot x} \]

      7. lower-*.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{z - t}{a - t}\right)\right) \cdot \color{blue}{x} \]

      8. lift-*.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{z - t}{a - t}\right)\right) \cdot x \]

      9. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right)\right)\right) \cdot x \]

      10. lift-/.f64 N/A

          \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right)\right)\right) \cdot x \]

      11. distribute-neg-frac2 N/A

          \[\leadsto x - \left(\mathsf{neg}\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)\right) \cdot x \]

      12. lift--.f64 N/A

          \[\leadsto x - \left(\mathsf{neg}\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)\right) \cdot x \]

      13. sub-negate-rev N/A

          \[\leadsto x - \left(\mathsf{neg}\left(\frac{z - t}{t - a}\right)\right) \cdot x \]

      14. lift--.f64 N/A

          \[\leadsto x - \left(\mathsf{neg}\left(\frac{z - t}{t - a}\right)\right) \cdot x \]

      15. distribute-frac-neg N/A

          \[\leadsto x - \frac{\mathsf{neg}\left(\left(z - t\right)\right)}{t - a} \cdot x \]

      16. lower-/.f64 N/A

          \[\leadsto x - \frac{\mathsf{neg}\left(\left(z - t\right)\right)}{t - a} \cdot x \]

      17. lift--.f64 N/A

          \[\leadsto x - \frac{\mathsf{neg}\left(\left(z - t\right)\right)}{t - a} \cdot x \]

      18. sub-negate-rev N/A

          \[\leadsto x - \frac{t - z}{t - a} \cdot x \]

      19. lower--.f64 43.2%

          \[\leadsto x - \frac{t - z}{t - a} \cdot x \]

   6. Applied rewrites 43.2%

      \[\leadsto x - \color{blue}{\frac{t - z}{t - a} \cdot x} \]

   if -3.0000000000000001e94 < x < 2.2999999999999999e83

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -23000:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq \frac{-8107084883601233}{386051661123868214325895970762095083331216144111904370034983364157543830047598546775742309000849007597326427200921653578548066591998660043462778854257084865420374725869305346230443778499781067545394454342790117394565596548890481374012190543459242928201313126587598361115137891035519604744312911050121319319358268243968}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 55000000000000003204716691456:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;\frac{z}{t - a} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176)
    t_1
    (if (<= t -23000)
      (- x (* y (/ t (- a t))))
      (if (<=
           t
           -8107084883601233/386051661123868214325895970762095083331216144111904370034983364157543830047598546775742309000849007597326427200921653578548066591998660043462778854257084865420374725869305346230443778499781067545394454342790117394565596548890481374012190543459242928201313126587598361115137891035519604744312911050121319319358268243968)
        (+ x (/ (* z (- y x)) (- a t)))
        (if (<= t 55000000000000003204716691456)
          (+ x (* (- z t) (/ (- y x) a)))
          (if (<=
               t
               95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
            (* (/ z (- t a)) (- x y))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -23000.0) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= -2.1e-302) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 5.5e+28) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-8.8d+149)) then
        tmp = t_1
    else if (t <= (-23000.0d0)) then
        tmp = x - (y * (t / (a - t)))
    else if (t <= (-2.1d-302)) then
        tmp = x + ((z * (y - x)) / (a - t))
    else if (t <= 5.5d+28) then
        tmp = x + ((z - t) * ((y - x) / a))
    else if (t <= 9.5d+178) then
        tmp = (z / (t - a)) * (x - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -23000.0) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= -2.1e-302) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 5.5e+28) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -8.8e+149:
		tmp = t_1
	elif t <= -23000.0:
		tmp = x - (y * (t / (a - t)))
	elif t <= -2.1e-302:
		tmp = x + ((z * (y - x)) / (a - t))
	elif t <= 5.5e+28:
		tmp = x + ((z - t) * ((y - x) / a))
	elif t <= 9.5e+178:
		tmp = (z / (t - a)) * (x - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -23000.0)
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	elseif (t <= -2.1e-302)
		tmp = Float64(x + Float64(Float64(z * Float64(y - x)) / Float64(a - t)));
	elseif (t <= 5.5e+28)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)));
	elseif (t <= 9.5e+178)
		tmp = Float64(Float64(z / Float64(t - a)) * Float64(x - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -23000.0)
		tmp = x - (y * (t / (a - t)));
	elseif (t <= -2.1e-302)
		tmp = x + ((z * (y - x)) / (a - t));
	elseif (t <= 5.5e+28)
		tmp = x + ((z - t) * ((y - x) / a));
	elseif (t <= 9.5e+178)
		tmp = (z / (t - a)) * (x - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176], t$95$1, If[LessEqual[t, -23000], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8107084883601233/386051661123868214325895970762095083331216144111904370034983364157543830047598546775742309000849007597326427200921653578548066591998660043462778854257084865420374725869305346230443778499781067545394454342790117394565596548890481374012190543459242928201313126587598361115137891035519604744312911050121319319358268243968], N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 55000000000000003204716691456], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.8e149 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -8.8e149 < t < -23000

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in z around 0

      \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

       \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]

   if -23000 < t < -2.1000000000000001e-302

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a - t} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x + \frac{z \cdot \color{blue}{\left(y - x\right)}}{a - t} \]

      2. lower--.f64 55.5%

         \[\leadsto x + \frac{z \cdot \left(y - \color{blue}{x}\right)}{a - t} \]

   4. Applied rewrites 55.5%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a - t} \]

   if -2.1000000000000001e-302 < t < 5.5000000000000003e28

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{\color{blue}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 46.6%

      \[\leadsto x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{\color{blue}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right)\right)} \cdot \frac{1}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\left(\left(z - t\right) \cdot \left(y - x\right)\right)} \cdot \frac{1}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y - x}{a}} \]

      8. lower-/.f64 52.2%

         \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y - x}{a}} \]

   6. Applied rewrites 52.2%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a}} \]

   if 5.5000000000000003e28 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      3. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      5. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - x \cdot \color{blue}{\frac{1}{a - t}}\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      7. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(y - \color{blue}{x}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      9. lower-/.f64 42.8%

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(\color{blue}{y} - x\right)\right) \]

   6. Applied rewrites 42.8%

      \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{1}{a - t} \cdot \left(y - x\right)\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \color{blue}{\left(y - x\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) \]

      5. mult-flip-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\color{blue}{y} - x\right) \]

      6. lift--.f64 N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(y - \color{blue}{x}\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\frac{z}{a - t} \cdot \left(x - y\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{z}{a - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \color{blue}{\left(x - y\right)} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(x - y\right) \]

      14. sub-negate-rev N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      15. lower--.f64 N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      16. lower--.f64 44.0%

          \[\leadsto \frac{z}{t - a} \cdot \left(x - \color{blue}{y}\right) \]

   8. Applied rewrites 44.0%

      \[\leadsto \frac{z}{t - a} \cdot \color{blue}{\left(x - y\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -800000:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 55000000000000003204716691456:\\ \;\;\;\;\frac{z - t}{a} \cdot \left(y - x\right) + x\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;\frac{z}{t - a} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176)
    t_1
    (if (<= t -800000)
      (- x (* y (/ t (- a t))))
      (if (<= t 55000000000000003204716691456)
        (+ (* (/ (- z t) a) (- y x)) x)
        (if (<=
             t
             95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
          (* (/ z (- t a)) (- x y))
          t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -800000.0) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 5.5e+28) {
		tmp = (((z - t) / a) * (y - x)) + x;
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-8.8d+149)) then
        tmp = t_1
    else if (t <= (-800000.0d0)) then
        tmp = x - (y * (t / (a - t)))
    else if (t <= 5.5d+28) then
        tmp = (((z - t) / a) * (y - x)) + x
    else if (t <= 9.5d+178) then
        tmp = (z / (t - a)) * (x - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -800000.0) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 5.5e+28) {
		tmp = (((z - t) / a) * (y - x)) + x;
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -8.8e+149:
		tmp = t_1
	elif t <= -800000.0:
		tmp = x - (y * (t / (a - t)))
	elif t <= 5.5e+28:
		tmp = (((z - t) / a) * (y - x)) + x
	elif t <= 9.5e+178:
		tmp = (z / (t - a)) * (x - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -800000.0)
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	elseif (t <= 5.5e+28)
		tmp = Float64(Float64(Float64(Float64(z - t) / a) * Float64(y - x)) + x);
	elseif (t <= 9.5e+178)
		tmp = Float64(Float64(z / Float64(t - a)) * Float64(x - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -800000.0)
		tmp = x - (y * (t / (a - t)));
	elseif (t <= 5.5e+28)
		tmp = (((z - t) / a) * (y - x)) + x;
	elseif (t <= 9.5e+178)
		tmp = (z / (t - a)) * (x - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176], t$95$1, If[LessEqual[t, -800000], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 55000000000000003204716691456], N[(N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.8e149 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -8.8e149 < t < -8e5

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in z around 0

      \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

       \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]

   if -8e5 < t < 5.5000000000000003e28

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{\color{blue}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 46.6%

      \[\leadsto x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{\color{blue}{a}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a} + x} \]

      3. lower-+.f64 46.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a} + x} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(y - x\right) \cdot \left(z - t\right)}}{a} + x \]

      6. associate-/l* N/A

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a}} + x \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z - t}{a} \cdot \left(y - x\right)} + x \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z - t}{a} \cdot \left(y - x\right)} + x \]

      9. lower-/.f64 53.6%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot \left(y - x\right) + x \]

   6. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\frac{z - t}{a} \cdot \left(y - x\right) + x} \]

   if 5.5000000000000003e28 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      3. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      5. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - x \cdot \color{blue}{\frac{1}{a - t}}\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      7. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(y - \color{blue}{x}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      9. lower-/.f64 42.8%

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(\color{blue}{y} - x\right)\right) \]

   6. Applied rewrites 42.8%

      \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{1}{a - t} \cdot \left(y - x\right)\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \color{blue}{\left(y - x\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) \]

      5. mult-flip-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\color{blue}{y} - x\right) \]

      6. lift--.f64 N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(y - \color{blue}{x}\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\frac{z}{a - t} \cdot \left(x - y\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{z}{a - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \color{blue}{\left(x - y\right)} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(x - y\right) \]

      14. sub-negate-rev N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      15. lower--.f64 N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      16. lower--.f64 44.0%

          \[\leadsto \frac{z}{t - a} \cdot \left(x - \color{blue}{y}\right) \]

   8. Applied rewrites 44.0%

      \[\leadsto \frac{z}{t - a} \cdot \color{blue}{\left(x - y\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-501766766966939}{696898287454081973172991196020261297061888}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 55000000000000003204716691456:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;\frac{z}{t - a} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176)
    t_1
    (if (<=
         t
         -501766766966939/696898287454081973172991196020261297061888)
      (- x (* y (/ t (- a t))))
      (if (<= t 55000000000000003204716691456)
        (+ x (* (- z t) (/ (- y x) a)))
        (if (<=
             t
             95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
          (* (/ z (- t a)) (- x y))
          t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -7.2e-28) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 5.5e+28) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-8.8d+149)) then
        tmp = t_1
    else if (t <= (-7.2d-28)) then
        tmp = x - (y * (t / (a - t)))
    else if (t <= 5.5d+28) then
        tmp = x + ((z - t) * ((y - x) / a))
    else if (t <= 9.5d+178) then
        tmp = (z / (t - a)) * (x - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -7.2e-28) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 5.5e+28) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -8.8e+149:
		tmp = t_1
	elif t <= -7.2e-28:
		tmp = x - (y * (t / (a - t)))
	elif t <= 5.5e+28:
		tmp = x + ((z - t) * ((y - x) / a))
	elif t <= 9.5e+178:
		tmp = (z / (t - a)) * (x - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -7.2e-28)
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	elseif (t <= 5.5e+28)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)));
	elseif (t <= 9.5e+178)
		tmp = Float64(Float64(z / Float64(t - a)) * Float64(x - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -7.2e-28)
		tmp = x - (y * (t / (a - t)));
	elseif (t <= 5.5e+28)
		tmp = x + ((z - t) * ((y - x) / a));
	elseif (t <= 9.5e+178)
		tmp = (z / (t - a)) * (x - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176], t$95$1, If[LessEqual[t, -501766766966939/696898287454081973172991196020261297061888], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 55000000000000003204716691456], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.8e149 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -8.8e149 < t < -7.1999999999999997e-28

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in z around 0

      \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

       \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]

   if -7.1999999999999997e-28 < t < 5.5000000000000003e28

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{\color{blue}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 46.6%

      \[\leadsto x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{\color{blue}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right)\right)} \cdot \frac{1}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\left(\left(z - t\right) \cdot \left(y - x\right)\right)} \cdot \frac{1}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y - x}{a}} \]

      8. lower-/.f64 52.2%

         \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y - x}{a}} \]

   6. Applied rewrites 52.2%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a}} \]

   if 5.5000000000000003e28 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      3. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      5. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - x \cdot \color{blue}{\frac{1}{a - t}}\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      7. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(y - \color{blue}{x}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      9. lower-/.f64 42.8%

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(\color{blue}{y} - x\right)\right) \]

   6. Applied rewrites 42.8%

      \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{1}{a - t} \cdot \left(y - x\right)\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \color{blue}{\left(y - x\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) \]

      5. mult-flip-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\color{blue}{y} - x\right) \]

      6. lift--.f64 N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(y - \color{blue}{x}\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\frac{z}{a - t} \cdot \left(x - y\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{z}{a - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \color{blue}{\left(x - y\right)} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(x - y\right) \]

      14. sub-negate-rev N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      15. lower--.f64 N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      16. lower--.f64 44.0%

          \[\leadsto \frac{z}{t - a} \cdot \left(x - \color{blue}{y}\right) \]

   8. Applied rewrites 44.0%

      \[\leadsto \frac{z}{t - a} \cdot \color{blue}{\left(x - y\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -880000:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 77999999999999997188138598400:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;\frac{z}{t - a} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176)
    t_1
    (if (<= t -880000)
      (- x (* y (/ t (- a t))))
      (if (<= t 77999999999999997188138598400)
        (+ x (* (- y x) (/ z a)))
        (if (<=
             t
             95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
          (* (/ z (- t a)) (- x y))
          t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -880000.0) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 7.8e+28) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-8.8d+149)) then
        tmp = t_1
    else if (t <= (-880000.0d0)) then
        tmp = x - (y * (t / (a - t)))
    else if (t <= 7.8d+28) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= 9.5d+178) then
        tmp = (z / (t - a)) * (x - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -880000.0) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 7.8e+28) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -8.8e+149:
		tmp = t_1
	elif t <= -880000.0:
		tmp = x - (y * (t / (a - t)))
	elif t <= 7.8e+28:
		tmp = x + ((y - x) * (z / a))
	elif t <= 9.5e+178:
		tmp = (z / (t - a)) * (x - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -880000.0)
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	elseif (t <= 7.8e+28)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= 9.5e+178)
		tmp = Float64(Float64(z / Float64(t - a)) * Float64(x - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -880000.0)
		tmp = x - (y * (t / (a - t)));
	elseif (t <= 7.8e+28)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= 9.5e+178)
		tmp = (z / (t - a)) * (x - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176], t$95$1, If[LessEqual[t, -880000], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 77999999999999997188138598400], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.8e149 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -8.8e149 < t < -8.8e5

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in z around 0

      \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

       \[\leadsto x - y \cdot \frac{\color{blue}{t}}{a - t} \]

   if -8.8e5 < t < 7.7999999999999997e28

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

      3. lower--.f64 44.1%

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

   4. Applied rewrites 44.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \color{blue}{\frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{\color{blue}{1}}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{\color{blue}{1}}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

      8. lower-/.f64 48.9%

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

   6. Applied rewrites 48.9%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{z}{a}} \]

   if 7.7999999999999997e28 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      3. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      5. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - x \cdot \color{blue}{\frac{1}{a - t}}\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      7. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(y - \color{blue}{x}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      9. lower-/.f64 42.8%

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(\color{blue}{y} - x\right)\right) \]

   6. Applied rewrites 42.8%

      \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{1}{a - t} \cdot \left(y - x\right)\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \color{blue}{\left(y - x\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) \]

      5. mult-flip-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\color{blue}{y} - x\right) \]

      6. lift--.f64 N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(y - \color{blue}{x}\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\frac{z}{a - t} \cdot \left(x - y\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{z}{a - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \color{blue}{\left(x - y\right)} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(x - y\right) \]

      14. sub-negate-rev N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      15. lower--.f64 N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      16. lower--.f64 44.0%

          \[\leadsto \frac{z}{t - a} \cdot \left(x - \color{blue}{y}\right) \]

   8. Applied rewrites 44.0%

      \[\leadsto \frac{z}{t - a} \cdot \color{blue}{\left(x - y\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2050000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 77999999999999997188138598400:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;\frac{z}{t - a} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - \left(x + -1 \cdot x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= t -2050000)
  (* (- z t) (/ y (- a t)))
  (if (<= t 77999999999999997188138598400)
    (+ x (* (- y x) (/ z a)))
    (if (<=
         t
         95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
      (* (/ z (- t a)) (- x y))
      (- y (+ x (* -1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2050000.0) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 7.8e+28) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = y - (x + (-1.0 * x));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2050000.0d0)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 7.8d+28) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= 9.5d+178) then
        tmp = (z / (t - a)) * (x - y)
    else
        tmp = y - (x + ((-1.0d0) * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2050000.0) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 7.8e+28) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 9.5e+178) {
		tmp = (z / (t - a)) * (x - y);
	} else {
		tmp = y - (x + (-1.0 * x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2050000.0:
		tmp = (z - t) * (y / (a - t))
	elif t <= 7.8e+28:
		tmp = x + ((y - x) * (z / a))
	elif t <= 9.5e+178:
		tmp = (z / (t - a)) * (x - y)
	else:
		tmp = y - (x + (-1.0 * x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2050000.0)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 7.8e+28)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= 9.5e+178)
		tmp = Float64(Float64(z / Float64(t - a)) * Float64(x - y));
	else
		tmp = Float64(y - Float64(x + Float64(-1.0 * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2050000.0)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 7.8e+28)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= 9.5e+178)
		tmp = (z / (t - a)) * (x - y);
	else
		tmp = y - (x + (-1.0 * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2050000], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 77999999999999997188138598400], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.05e6

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} \]

      4. lower--.f64 39.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - \color{blue}{t}} \]

   10. Applied rewrites 39.7%

       \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   11. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

       3. *-commutative N/A

          \[\leadsto \frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t} \]

       4. associate-/l* N/A

          \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

       5. lift-/.f64 N/A

          \[\leadsto \left(z - t\right) \cdot \frac{y}{\color{blue}{a - t}} \]

       6. lower-*.f64 46.3%

          \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   12. Applied rewrites 46.3%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   if -2.05e6 < t < 7.7999999999999997e28

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

      3. lower--.f64 44.1%

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

   4. Applied rewrites 44.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \color{blue}{\frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{\color{blue}{1}}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{\color{blue}{1}}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

      8. lower-/.f64 48.9%

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

   6. Applied rewrites 48.9%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{z}{a}} \]

   if 7.7999999999999997e28 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      3. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      5. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - x \cdot \color{blue}{\frac{1}{a - t}}\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      7. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(y - \color{blue}{x}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      9. lower-/.f64 42.8%

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(\color{blue}{y} - x\right)\right) \]

   6. Applied rewrites 42.8%

      \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{1}{a - t} \cdot \left(y - x\right)\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \color{blue}{\left(y - x\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) \]

      5. mult-flip-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\color{blue}{y} - x\right) \]

      6. lift--.f64 N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(y - \color{blue}{x}\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\frac{z}{a - t} \cdot \left(x - y\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{z}{a - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \color{blue}{\left(x - y\right)} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(x - y\right) \]

      14. sub-negate-rev N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      15. lower--.f64 N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      16. lower--.f64 44.0%

          \[\leadsto \frac{z}{t - a} \cdot \left(x - \color{blue}{y}\right) \]

   8. Applied rewrites 44.0%

      \[\leadsto \frac{z}{t - a} \cdot \color{blue}{\left(x - y\right)} \]

   if 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 56.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot \left(x - y\right)\\ \mathbf{if}\;t \leq -195000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq \frac{-6166959734027569}{9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 19999999999999999166239473664:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - \left(x + -1 \cdot x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ z (- t a)) (- x y))))
  (if (<= t -195000)
    (* (- z t) (/ y (- a t)))
    (if (<=
         t
         -6166959734027569/9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248)
      t_1
      (if (<= t 19999999999999999166239473664)
        (+ x (* y (/ z a)))
        (if (<=
             t
             95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
          t_1
          (- y (+ x (* -1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / (t - a)) * (x - y);
	double tmp;
	if (t <= -195000.0) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= -6.6e-181) {
		tmp = t_1;
	} else if (t <= 2e+28) {
		tmp = x + (y * (z / a));
	} else if (t <= 9.5e+178) {
		tmp = t_1;
	} else {
		tmp = y - (x + (-1.0 * x));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / (t - a)) * (x - y)
    if (t <= (-195000.0d0)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= (-6.6d-181)) then
        tmp = t_1
    else if (t <= 2d+28) then
        tmp = x + (y * (z / a))
    else if (t <= 9.5d+178) then
        tmp = t_1
    else
        tmp = y - (x + ((-1.0d0) * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / (t - a)) * (x - y);
	double tmp;
	if (t <= -195000.0) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= -6.6e-181) {
		tmp = t_1;
	} else if (t <= 2e+28) {
		tmp = x + (y * (z / a));
	} else if (t <= 9.5e+178) {
		tmp = t_1;
	} else {
		tmp = y - (x + (-1.0 * x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / (t - a)) * (x - y)
	tmp = 0
	if t <= -195000.0:
		tmp = (z - t) * (y / (a - t))
	elif t <= -6.6e-181:
		tmp = t_1
	elif t <= 2e+28:
		tmp = x + (y * (z / a))
	elif t <= 9.5e+178:
		tmp = t_1
	else:
		tmp = y - (x + (-1.0 * x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / Float64(t - a)) * Float64(x - y))
	tmp = 0.0
	if (t <= -195000.0)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= -6.6e-181)
		tmp = t_1;
	elseif (t <= 2e+28)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 9.5e+178)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(x + Float64(-1.0 * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / (t - a)) * (x - y);
	tmp = 0.0;
	if (t <= -195000.0)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= -6.6e-181)
		tmp = t_1;
	elseif (t <= 2e+28)
		tmp = x + (y * (z / a));
	elseif (t <= 9.5e+178)
		tmp = t_1;
	else
		tmp = y - (x + (-1.0 * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -195000], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6166959734027569/9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248], t$95$1, If[LessEqual[t, 19999999999999999166239473664], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], t$95$1, N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -195000

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} \]

      4. lower--.f64 39.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - \color{blue}{t}} \]

   10. Applied rewrites 39.7%

       \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   11. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

       3. *-commutative N/A

          \[\leadsto \frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t} \]

       4. associate-/l* N/A

          \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

       5. lift-/.f64 N/A

          \[\leadsto \left(z - t\right) \cdot \frac{y}{\color{blue}{a - t}} \]

       6. lower-*.f64 46.3%

          \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   12. Applied rewrites 46.3%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   if -195000 < t < -6.6000000000000002e-181 or 1.9999999999999999e28 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      3. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      5. mult-flip N/A

         \[\leadsto z \cdot \left(y \cdot \frac{1}{a - t} - x \cdot \color{blue}{\frac{1}{a - t}}\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      7. lift--.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(y - \color{blue}{x}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      9. lower-/.f64 42.8%

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \left(\color{blue}{y} - x\right)\right) \]

   6. Applied rewrites 42.8%

      \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{1}{a - t} \cdot \left(y - x\right)\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\frac{1}{a - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \color{blue}{\left(y - x\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(z \cdot \frac{1}{a - t}\right) \cdot \left(y - x\right) \]

      5. mult-flip-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\color{blue}{y} - x\right) \]

      6. lift--.f64 N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(y - \color{blue}{x}\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{z}{a - t} \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\frac{z}{a - t} \cdot \left(x - y\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{z}{a - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      10. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \color{blue}{\left(x - y\right)} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(\color{blue}{x} - y\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{z}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot \left(x - y\right) \]

      14. sub-negate-rev N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      15. lower--.f64 N/A

          \[\leadsto \frac{z}{t - a} \cdot \left(x - y\right) \]

      16. lower--.f64 44.0%

          \[\leadsto \frac{z}{t - a} \cdot \left(x - \color{blue}{y}\right) \]

   8. Applied rewrites 44.0%

      \[\leadsto \frac{z}{t - a} \cdot \color{blue}{\left(x - y\right)} \]

   if -6.6000000000000002e-181 < t < 1.9999999999999999e28

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

      3. lower--.f64 44.1%

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

   4. Applied rewrites 44.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \color{blue}{\frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{\color{blue}{1}}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{\color{blue}{1}}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

      8. lower-/.f64 48.9%

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

   6. Applied rewrites 48.9%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{z}{a}} \]

   7. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \frac{\color{blue}{z}}{a} \]
   8. Step-by-step derivation

   9. Applied rewrites 41.2%

      \[\leadsto x + y \cdot \frac{\color{blue}{z}}{a} \]

   if 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 55.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -2050000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{3314649325744685}{144115188075855872}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (- z t) (/ y (- a t)))))
  (if (<= t -2050000)
    t_1
    (if (<= t 3314649325744685/144115188075855872)
      (+ x (* y (/ z a)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -2050000.0) {
		tmp = t_1;
	} else if (t <= 0.023) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / (a - t))
    if (t <= (-2050000.0d0)) then
        tmp = t_1
    else if (t <= 0.023d0) then
        tmp = x + (y * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -2050000.0) {
		tmp = t_1;
	} else if (t <= 0.023) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (a - t))
	tmp = 0
	if t <= -2050000.0:
		tmp = t_1
	elif t <= 0.023:
		tmp = x + (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t <= -2050000.0)
		tmp = t_1;
	elseif (t <= 0.023)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (a - t));
	tmp = 0.0;
	if (t <= -2050000.0)
		tmp = t_1;
	elseif (t <= 0.023)
		tmp = x + (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2050000], t$95$1, If[LessEqual[t, 3314649325744685/144115188075855872], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05e6 or 0.023 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} \]

      4. lower--.f64 39.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - \color{blue}{t}} \]

   10. Applied rewrites 39.7%

       \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   11. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

       3. *-commutative N/A

          \[\leadsto \frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t} \]

       4. associate-/l* N/A

          \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

       5. lift-/.f64 N/A

          \[\leadsto \left(z - t\right) \cdot \frac{y}{\color{blue}{a - t}} \]

       6. lower-*.f64 46.3%

          \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   12. Applied rewrites 46.3%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   if -2.05e6 < t < 0.023

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

      3. lower--.f64 44.1%

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

   4. Applied rewrites 44.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \color{blue}{\frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{\color{blue}{1}}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{\color{blue}{1}}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

      8. lower-/.f64 48.9%

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

   6. Applied rewrites 48.9%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{z}{a}} \]

   7. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \frac{\color{blue}{z}}{a} \]
   8. Step-by-step derivation

   9. Applied rewrites 41.2%

      \[\leadsto x + y \cdot \frac{\color{blue}{z}}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 51.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -2050000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1049999999999999924343677575419984678682242318336:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<= t -2050000)
    t_1
    (if (<= t 1049999999999999924343677575419984678682242318336)
      (+ x (* y (/ z a)))
      (if (<=
           t
           3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952)
        (* x (/ (- z a) t))
        t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -2050000.0) {
		tmp = t_1;
	} else if (t <= 1.05e+48) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.6e+210) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-2050000.0d0)) then
        tmp = t_1
    else if (t <= 1.05d+48) then
        tmp = x + (y * (z / a))
    else if (t <= 3.6d+210) then
        tmp = x * ((z - a) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -2050000.0) {
		tmp = t_1;
	} else if (t <= 1.05e+48) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.6e+210) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -2050000.0:
		tmp = t_1
	elif t <= 1.05e+48:
		tmp = x + (y * (z / a))
	elif t <= 3.6e+210:
		tmp = x * ((z - a) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -2050000.0)
		tmp = t_1;
	elseif (t <= 1.05e+48)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 3.6e+210)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -2050000.0)
		tmp = t_1;
	elseif (t <= 1.05e+48)
		tmp = x + (y * (z / a));
	elseif (t <= 3.6e+210)
		tmp = x * ((z - a) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2050000], t$95$1, If[LessEqual[t, 1049999999999999924343677575419984678682242318336], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e6 or 3.6000000000000003e210 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -2.05e6 < t < 1.0499999999999999e48

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in t around 0

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

      3. lower--.f64 44.1%

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{a} \]

   4. Applied rewrites 44.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \color{blue}{\frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{\color{blue}{1}}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{\color{blue}{1}}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

      8. lower-/.f64 48.9%

         \[\leadsto x + \left(y - x\right) \cdot \frac{z}{\color{blue}{a}} \]

   6. Applied rewrites 48.9%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{z}{a}} \]

   7. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \frac{\color{blue}{z}}{a} \]
   8. Step-by-step derivation

   9. Applied rewrites 41.2%

      \[\leadsto x + y \cdot \frac{\color{blue}{z}}{a} \]

   if 1.0499999999999999e48 < t < 3.6000000000000003e210

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around -inf

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{z - a}{t} \]

      2. lower--.f64 23.0%

         \[\leadsto x \cdot \frac{z - a}{t} \]

   7. Applied rewrites 23.0%

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 40.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-1067993517960455}{266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072}:\\ \;\;\;\;x - y \cdot -1\\ \mathbf{elif}\;t \leq \frac{-2588678114201735}{5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1049999999999999924343677575419984678682242318336:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t \leq 3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528)
    t_1
    (if (<=
         t
         -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072)
      (- x (* y -1))
      (if (<=
           t
           -2588678114201735/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912)
        (* z (/ (- y x) a))
        (if (<= t 1049999999999999924343677575419984678682242318336)
          (* x 1)
          (if (<=
               t
               3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952)
            (* x (/ (- z a) t))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.5e-295) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 3.6e+210) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-1.8d+144)) then
        tmp = t_1
    else if (t <= (-4d-81)) then
        tmp = x - (y * (-1.0d0))
    else if (t <= (-4.5d-295)) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.05d+48) then
        tmp = x * 1.0d0
    else if (t <= 3.6d+210) then
        tmp = x * ((z - a) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.5e-295) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 3.6e+210) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -1.8e+144:
		tmp = t_1
	elif t <= -4e-81:
		tmp = x - (y * -1.0)
	elif t <= -4.5e-295:
		tmp = z * ((y - x) / a)
	elif t <= 1.05e+48:
		tmp = x * 1.0
	elif t <= 3.6e+210:
		tmp = x * ((z - a) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = Float64(x - Float64(y * -1.0));
	elseif (t <= -4.5e-295)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.05e+48)
		tmp = Float64(x * 1.0);
	elseif (t <= 3.6e+210)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = x - (y * -1.0);
	elseif (t <= -4.5e-295)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.05e+48)
		tmp = x * 1.0;
	elseif (t <= 3.6e+210)
		tmp = x * ((z - a) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528], t$95$1, If[LessEqual[t, -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2588678114201735/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1049999999999999924343677575419984678682242318336], N[(x * 1), $MachinePrecision], If[LessEqual[t, 3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7999999999999999e144 or 3.6000000000000003e210 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -1.7999999999999999e144 < t < -3.9999999999999998e-81

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]

   if -3.9999999999999998e-81 < t < -4.5000000000000002e-295

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto z \cdot \frac{y}{a - \color{blue}{t}} \]

      2. lower--.f64 23.7%

         \[\leadsto z \cdot \frac{y}{a - t} \]

   7. Applied rewrites 23.7%

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]

   8. Taylor expanded in a around inf

      \[\leadsto z \cdot \frac{y - x}{\color{blue}{a}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto z \cdot \frac{y - x}{a} \]

      2. lower--.f64 25.9%

         \[\leadsto z \cdot \frac{y - x}{a} \]

   10. Applied rewrites 25.9%

       \[\leadsto z \cdot \frac{y - x}{\color{blue}{a}} \]

   if -4.5000000000000002e-295 < t < 1.0499999999999999e48

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   if 1.0499999999999999e48 < t < 3.6000000000000003e210

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around -inf

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{z - a}{t} \]

      2. lower--.f64 23.0%

         \[\leadsto x \cdot \frac{z - a}{t} \]

   7. Applied rewrites 23.0%

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 39.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-1067993517960455}{266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072}:\\ \;\;\;\;x - y \cdot -1\\ \mathbf{elif}\;t \leq \frac{-2588678114201735}{5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{a}\\ \mathbf{elif}\;t \leq 1049999999999999924343677575419984678682242318336:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t \leq 3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528)
    t_1
    (if (<=
         t
         -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072)
      (- x (* y -1))
      (if (<=
           t
           -2588678114201735/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912)
        (/ (* z (- y x)) a)
        (if (<= t 1049999999999999924343677575419984678682242318336)
          (* x 1)
          (if (<=
               t
               3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952)
            (* x (/ (- z a) t))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.5e-295) {
		tmp = (z * (y - x)) / a;
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 3.6e+210) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-1.8d+144)) then
        tmp = t_1
    else if (t <= (-4d-81)) then
        tmp = x - (y * (-1.0d0))
    else if (t <= (-4.5d-295)) then
        tmp = (z * (y - x)) / a
    else if (t <= 1.05d+48) then
        tmp = x * 1.0d0
    else if (t <= 3.6d+210) then
        tmp = x * ((z - a) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.5e-295) {
		tmp = (z * (y - x)) / a;
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 3.6e+210) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -1.8e+144:
		tmp = t_1
	elif t <= -4e-81:
		tmp = x - (y * -1.0)
	elif t <= -4.5e-295:
		tmp = (z * (y - x)) / a
	elif t <= 1.05e+48:
		tmp = x * 1.0
	elif t <= 3.6e+210:
		tmp = x * ((z - a) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = Float64(x - Float64(y * -1.0));
	elseif (t <= -4.5e-295)
		tmp = Float64(Float64(z * Float64(y - x)) / a);
	elseif (t <= 1.05e+48)
		tmp = Float64(x * 1.0);
	elseif (t <= 3.6e+210)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = x - (y * -1.0);
	elseif (t <= -4.5e-295)
		tmp = (z * (y - x)) / a;
	elseif (t <= 1.05e+48)
		tmp = x * 1.0;
	elseif (t <= 3.6e+210)
		tmp = x * ((z - a) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528], t$95$1, If[LessEqual[t, -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2588678114201735/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1049999999999999924343677575419984678682242318336], N[(x * 1), $MachinePrecision], If[LessEqual[t, 3600000000000000263202775859717469256018174328535138252152055447988004720056054266751308276517886685603398476798911472512056500497788749608139688697102507805581500737953993050408248616802767716133203854546173952], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7999999999999999e144 or 3.6000000000000003e210 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -1.7999999999999999e144 < t < -3.9999999999999998e-81

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]

   if -3.9999999999999998e-81 < t < -4.5000000000000002e-295

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto z \cdot \frac{y}{a - \color{blue}{t}} \]

      2. lower--.f64 23.7%

         \[\leadsto z \cdot \frac{y}{a - t} \]

   7. Applied rewrites 23.7%

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]

   8. Taylor expanded in a around inf

      \[\leadsto \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - x\right)}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - x\right)}{a} \]

      3. lower--.f64 23.7%

         \[\leadsto \frac{z \cdot \left(y - x\right)}{a} \]

   10. Applied rewrites 23.7%

       \[\leadsto \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

   if -4.5000000000000002e-295 < t < 1.0499999999999999e48

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   if 1.0499999999999999e48 < t < 3.6000000000000003e210

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around -inf

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{z - a}{t} \]

      2. lower--.f64 23.0%

         \[\leadsto x \cdot \frac{z - a}{t} \]

   7. Applied rewrites 23.0%

      \[\leadsto x \cdot \frac{z - a}{\color{blue}{t}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 17: 39.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-1067993517960455}{266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072}:\\ \;\;\;\;x - y \cdot -1\\ \mathbf{elif}\;t \leq \frac{-2588678114201735}{5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{a}\\ \mathbf{elif}\;t \leq 1049999999999999924343677575419984678682242318336:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528)
    t_1
    (if (<=
         t
         -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072)
      (- x (* y -1))
      (if (<=
           t
           -2588678114201735/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912)
        (/ (* z (- y x)) a)
        (if (<= t 1049999999999999924343677575419984678682242318336)
          (* x 1)
          (if (<=
               t
               95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
            (* x (/ z t))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.5e-295) {
		tmp = (z * (y - x)) / a;
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-1.8d+144)) then
        tmp = t_1
    else if (t <= (-4d-81)) then
        tmp = x - (y * (-1.0d0))
    else if (t <= (-4.5d-295)) then
        tmp = (z * (y - x)) / a
    else if (t <= 1.05d+48) then
        tmp = x * 1.0d0
    else if (t <= 9.5d+178) then
        tmp = x * (z / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.5e-295) {
		tmp = (z * (y - x)) / a;
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -1.8e+144:
		tmp = t_1
	elif t <= -4e-81:
		tmp = x - (y * -1.0)
	elif t <= -4.5e-295:
		tmp = (z * (y - x)) / a
	elif t <= 1.05e+48:
		tmp = x * 1.0
	elif t <= 9.5e+178:
		tmp = x * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = Float64(x - Float64(y * -1.0));
	elseif (t <= -4.5e-295)
		tmp = Float64(Float64(z * Float64(y - x)) / a);
	elseif (t <= 1.05e+48)
		tmp = Float64(x * 1.0);
	elseif (t <= 9.5e+178)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = x - (y * -1.0);
	elseif (t <= -4.5e-295)
		tmp = (z * (y - x)) / a;
	elseif (t <= 1.05e+48)
		tmp = x * 1.0;
	elseif (t <= 9.5e+178)
		tmp = x * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528], t$95$1, If[LessEqual[t, -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2588678114201735/5752618031559410904733776610524879147577526332615381032749762597047445625776030820246671274317041152675843644155884587445081272602061331919771117780463171980088572589595695528841671027239875011822498654466720184602820821834958812207165219537306471589227216341906761543678311870031350921754731402547975172390912], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1049999999999999924343677575419984678682242318336], N[(x * 1), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7999999999999999e144 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -1.7999999999999999e144 < t < -3.9999999999999998e-81

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]

   if -3.9999999999999998e-81 < t < -4.5000000000000002e-295

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto z \cdot \frac{y}{a - \color{blue}{t}} \]

      2. lower--.f64 23.7%

         \[\leadsto z \cdot \frac{y}{a - t} \]

   7. Applied rewrites 23.7%

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]

   8. Taylor expanded in a around inf

      \[\leadsto \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - x\right)}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - x\right)}{a} \]

      3. lower--.f64 23.7%

         \[\leadsto \frac{z \cdot \left(y - x\right)}{a} \]

   10. Applied rewrites 23.7%

       \[\leadsto \frac{z \cdot \left(y - x\right)}{\color{blue}{a}} \]

   if -4.5000000000000002e-295 < t < 1.0499999999999999e48

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   if 1.0499999999999999e48 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   11. Taylor expanded in a around 0

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
   12. Step-by-step derivation

       1. lower-/.f64 19.1%

          \[\leadsto x \cdot \frac{z}{t} \]

   13. Applied rewrites 19.1%

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 18: 38.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-6521557777124079}{6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057152}:\\ \;\;\;\;x - y \cdot -1\\ \mathbf{elif}\;t \leq \frac{-3949107279145325}{270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 1049999999999999924343677575419984678682242318336:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176)
    t_1
    (if (<=
         t
         -6521557777124079/6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057152)
      (- x (* y -1))
      (if (<=
           t
           -3949107279145325/270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032)
        (/ (* y z) (- a t))
        (if (<= t 1049999999999999924343677575419984678682242318336)
          (* x 1)
          (if (<=
               t
               95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
            (* x (/ z t))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -9.5e-142) {
		tmp = x - (y * -1.0);
	} else if (t <= -1.46e-257) {
		tmp = (y * z) / (a - t);
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-8.8d+149)) then
        tmp = t_1
    else if (t <= (-9.5d-142)) then
        tmp = x - (y * (-1.0d0))
    else if (t <= (-1.46d-257)) then
        tmp = (y * z) / (a - t)
    else if (t <= 1.05d+48) then
        tmp = x * 1.0d0
    else if (t <= 9.5d+178) then
        tmp = x * (z / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -8.8e+149) {
		tmp = t_1;
	} else if (t <= -9.5e-142) {
		tmp = x - (y * -1.0);
	} else if (t <= -1.46e-257) {
		tmp = (y * z) / (a - t);
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -8.8e+149:
		tmp = t_1
	elif t <= -9.5e-142:
		tmp = x - (y * -1.0)
	elif t <= -1.46e-257:
		tmp = (y * z) / (a - t)
	elif t <= 1.05e+48:
		tmp = x * 1.0
	elif t <= 9.5e+178:
		tmp = x * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -9.5e-142)
		tmp = Float64(x - Float64(y * -1.0));
	elseif (t <= -1.46e-257)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t <= 1.05e+48)
		tmp = Float64(x * 1.0);
	elseif (t <= 9.5e+178)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -8.8e+149)
		tmp = t_1;
	elseif (t <= -9.5e-142)
		tmp = x - (y * -1.0);
	elseif (t <= -1.46e-257)
		tmp = (y * z) / (a - t);
	elseif (t <= 1.05e+48)
		tmp = x * 1.0;
	elseif (t <= 9.5e+178)
		tmp = x * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -879999999999999997672099117657027450690821770106771224993052246681969304369041136631928238650233080250998827309506196002949420576786954145137401266176], t$95$1, If[LessEqual[t, -6521557777124079/6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057152], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3949107279145325/270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1049999999999999924343677575419984678682242318336], N[(x * 1), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.8e149 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -8.8e149 < t < -9.4999999999999997e-142

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]

   if -9.4999999999999997e-142 < t < -1.4600000000000001e-257

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{y \cdot z}{\color{blue}{a - t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot z}{a - \color{blue}{t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot z}{a - t} \]

      3. lower--.f64 21.4%

         \[\leadsto \frac{y \cdot z}{a - t} \]

   7. Applied rewrites 21.4%

      \[\leadsto \frac{y \cdot z}{\color{blue}{a - t}} \]

   if -1.4600000000000001e-257 < t < 1.0499999999999999e48

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   if 1.0499999999999999e48 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   11. Taylor expanded in a around 0

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
   12. Step-by-step derivation

       1. lower-/.f64 19.1%

          \[\leadsto x \cdot \frac{z}{t} \]

   13. Applied rewrites 19.1%

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 19: 38.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-1067993517960455}{266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072}:\\ \;\;\;\;x - y \cdot -1\\ \mathbf{elif}\;t \leq \frac{-4254389501031255}{8863311460481781141746416676937941075153709659930434578989576454853657824757125219971944776154496375261537574471193391385403783592849407838528338558092085276740615608975052082196989118065224509657855008735367281473086766641604185629827373864344704645943910512054824309490712576}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1049999999999999924343677575419984678682242318336:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528)
    t_1
    (if (<=
         t
         -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072)
      (- x (* y -1))
      (if (<=
           t
           -4254389501031255/8863311460481781141746416676937941075153709659930434578989576454853657824757125219971944776154496375261537574471193391385403783592849407838528338558092085276740615608975052082196989118065224509657855008735367281473086766641604185629827373864344704645943910512054824309490712576)
        (* z (/ y a))
        (if (<= t 1049999999999999924343677575419984678682242318336)
          (* x 1)
          (if (<=
               t
               95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
            (* x (/ z t))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.8e-262) {
		tmp = z * (y / a);
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-1.8d+144)) then
        tmp = t_1
    else if (t <= (-4d-81)) then
        tmp = x - (y * (-1.0d0))
    else if (t <= (-4.8d-262)) then
        tmp = z * (y / a)
    else if (t <= 1.05d+48) then
        tmp = x * 1.0d0
    else if (t <= 9.5d+178) then
        tmp = x * (z / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -1.8e+144) {
		tmp = t_1;
	} else if (t <= -4e-81) {
		tmp = x - (y * -1.0);
	} else if (t <= -4.8e-262) {
		tmp = z * (y / a);
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -1.8e+144:
		tmp = t_1
	elif t <= -4e-81:
		tmp = x - (y * -1.0)
	elif t <= -4.8e-262:
		tmp = z * (y / a)
	elif t <= 1.05e+48:
		tmp = x * 1.0
	elif t <= 9.5e+178:
		tmp = x * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = Float64(x - Float64(y * -1.0));
	elseif (t <= -4.8e-262)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 1.05e+48)
		tmp = Float64(x * 1.0);
	elseif (t <= 9.5e+178)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -1.8e+144)
		tmp = t_1;
	elseif (t <= -4e-81)
		tmp = x - (y * -1.0);
	elseif (t <= -4.8e-262)
		tmp = z * (y / a);
	elseif (t <= 1.05e+48)
		tmp = x * 1.0;
	elseif (t <= 9.5e+178)
		tmp = x * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1799999999999999869449922363021060919684697761148896472674919768617891425020663242208887992937348489434422362932188577849477458618078907521302528], t$95$1, If[LessEqual[t, -1067993517960455/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4254389501031255/8863311460481781141746416676937941075153709659930434578989576454853657824757125219971944776154496375261537574471193391385403783592849407838528338558092085276740615608975052082196989118065224509657855008735367281473086766641604185629827373864344704645943910512054824309490712576], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1049999999999999924343677575419984678682242318336], N[(x * 1), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7999999999999999e144 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -1.7999999999999999e144 < t < -3.9999999999999998e-81

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]

   if -3.9999999999999998e-81 < t < -4.8000000000000001e-262

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \color{blue}{\frac{x}{a - t}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{\color{blue}{x}}{a - t}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{\color{blue}{a - t}}\right) \]

      6. lower--.f64 42.4%

         \[\leadsto z \cdot \left(\frac{y}{a - t} - \frac{x}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 42.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto z \cdot \frac{y}{a - \color{blue}{t}} \]

      2. lower--.f64 23.7%

         \[\leadsto z \cdot \frac{y}{a - t} \]

   7. Applied rewrites 23.7%

      \[\leadsto z \cdot \frac{y}{\color{blue}{a - t}} \]

   8. Taylor expanded in t around 0

      \[\leadsto z \cdot \frac{y}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 18.1%

       \[\leadsto z \cdot \frac{y}{a} \]

   if -4.8000000000000001e-262 < t < 1.0499999999999999e48

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   if 1.0499999999999999e48 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   11. Taylor expanded in a around 0

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
   12. Step-by-step derivation

       1. lower-/.f64 19.1%

          \[\leadsto x \cdot \frac{z}{t} \]

   13. Applied rewrites 19.1%

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 20: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -32999999999999999224551649921188376054309610847698636434518172229497721989585267143685755563589344485225679296183401740245116370550784000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-2980834737217361}{12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352918515131554298200329449113635639808166799244402122285052787558602103993549731750007142774830528462848}:\\ \;\;\;\;x - y \cdot -1\\ \mathbf{elif}\;t \leq \frac{-3949107279145325}{270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1049999999999999924343677575419984678682242318336:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t \leq 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -32999999999999999224551649921188376054309610847698636434518172229497721989585267143685755563589344485225679296183401740245116370550784000)
    t_1
    (if (<=
         t
         -2980834737217361/12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352918515131554298200329449113635639808166799244402122285052787558602103993549731750007142774830528462848)
      (- x (* y -1))
      (if (<=
           t
           -3949107279145325/270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032)
        (/ (* y z) a)
        (if (<= t 1049999999999999924343677575419984678682242318336)
          (* x 1)
          (if (<=
               t
               95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696)
            (* x (/ z t))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -3.3e+136) {
		tmp = t_1;
	} else if (t <= -2.4e-217) {
		tmp = x - (y * -1.0);
	} else if (t <= -1.46e-257) {
		tmp = (y * z) / a;
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-3.3d+136)) then
        tmp = t_1
    else if (t <= (-2.4d-217)) then
        tmp = x - (y * (-1.0d0))
    else if (t <= (-1.46d-257)) then
        tmp = (y * z) / a
    else if (t <= 1.05d+48) then
        tmp = x * 1.0d0
    else if (t <= 9.5d+178) then
        tmp = x * (z / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -3.3e+136) {
		tmp = t_1;
	} else if (t <= -2.4e-217) {
		tmp = x - (y * -1.0);
	} else if (t <= -1.46e-257) {
		tmp = (y * z) / a;
	} else if (t <= 1.05e+48) {
		tmp = x * 1.0;
	} else if (t <= 9.5e+178) {
		tmp = x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -3.3e+136:
		tmp = t_1
	elif t <= -2.4e-217:
		tmp = x - (y * -1.0)
	elif t <= -1.46e-257:
		tmp = (y * z) / a
	elif t <= 1.05e+48:
		tmp = x * 1.0
	elif t <= 9.5e+178:
		tmp = x * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -3.3e+136)
		tmp = t_1;
	elseif (t <= -2.4e-217)
		tmp = Float64(x - Float64(y * -1.0));
	elseif (t <= -1.46e-257)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= 1.05e+48)
		tmp = Float64(x * 1.0);
	elseif (t <= 9.5e+178)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -3.3e+136)
		tmp = t_1;
	elseif (t <= -2.4e-217)
		tmp = x - (y * -1.0);
	elseif (t <= -1.46e-257)
		tmp = (y * z) / a;
	elseif (t <= 1.05e+48)
		tmp = x * 1.0;
	elseif (t <= 9.5e+178)
		tmp = x * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -32999999999999999224551649921188376054309610847698636434518172229497721989585267143685755563589344485225679296183401740245116370550784000], t$95$1, If[LessEqual[t, -2980834737217361/12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352918515131554298200329449113635639808166799244402122285052787558602103993549731750007142774830528462848], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3949107279145325/270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1049999999999999924343677575419984678682242318336], N[(x * 1), $MachinePrecision], If[LessEqual[t, 95000000000000003182055734695818400232785698392689640252499456490754934189858100161564057624839499224276609604404512829410417062553420770158150408427907518478854544725081845661696], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.2999999999999999e136 or 9.5000000000000003e178 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -3.2999999999999999e136 < t < -2.3999999999999999e-217

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]

   if -2.3999999999999999e-217 < t < -1.4600000000000001e-257

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} \]

      4. lower--.f64 39.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - \color{blue}{t}} \]

   10. Applied rewrites 39.7%

       \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   11. Taylor expanded in t around 0

       \[\leadsto \frac{y \cdot z}{\color{blue}{a}} \]
   12. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{y \cdot z}{a} \]

       2. lower-*.f64 16.3%

          \[\leadsto \frac{y \cdot z}{a} \]

   13. Applied rewrites 16.3%

       \[\leadsto \frac{y \cdot z}{\color{blue}{a}} \]

   if -1.4600000000000001e-257 < t < 1.0499999999999999e48

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   if 1.0499999999999999e48 < t < 9.5000000000000003e178

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   11. Taylor expanded in a around 0

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
   12. Step-by-step derivation

       1. lower-/.f64 19.1%

          \[\leadsto x \cdot \frac{z}{t} \]

   13. Applied rewrites 19.1%

       \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 21: 37.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq -32999999999999999224551649921188376054309610847698636434518172229497721989585267143685755563589344485225679296183401740245116370550784000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{-2980834737217361}{12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352918515131554298200329449113635639808166799244402122285052787558602103993549731750007142774830528462848}:\\ \;\;\;\;x - y \cdot -1\\ \mathbf{elif}\;t \leq \frac{-3949107279145325}{270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1060000000000000025165824:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<=
       t
       -32999999999999999224551649921188376054309610847698636434518172229497721989585267143685755563589344485225679296183401740245116370550784000)
    t_1
    (if (<=
         t
         -2980834737217361/12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352918515131554298200329449113635639808166799244402122285052787558602103993549731750007142774830528462848)
      (- x (* y -1))
      (if (<=
           t
           -3949107279145325/270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032)
        (/ (* y z) a)
        (if (<= t 1060000000000000025165824) (* x 1) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -3.3e+136) {
		tmp = t_1;
	} else if (t <= -2.4e-217) {
		tmp = x - (y * -1.0);
	} else if (t <= -1.46e-257) {
		tmp = (y * z) / a;
	} else if (t <= 1.06e+24) {
		tmp = x * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-3.3d+136)) then
        tmp = t_1
    else if (t <= (-2.4d-217)) then
        tmp = x - (y * (-1.0d0))
    else if (t <= (-1.46d-257)) then
        tmp = (y * z) / a
    else if (t <= 1.06d+24) then
        tmp = x * 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -3.3e+136) {
		tmp = t_1;
	} else if (t <= -2.4e-217) {
		tmp = x - (y * -1.0);
	} else if (t <= -1.46e-257) {
		tmp = (y * z) / a;
	} else if (t <= 1.06e+24) {
		tmp = x * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -3.3e+136:
		tmp = t_1
	elif t <= -2.4e-217:
		tmp = x - (y * -1.0)
	elif t <= -1.46e-257:
		tmp = (y * z) / a
	elif t <= 1.06e+24:
		tmp = x * 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -3.3e+136)
		tmp = t_1;
	elseif (t <= -2.4e-217)
		tmp = Float64(x - Float64(y * -1.0));
	elseif (t <= -1.46e-257)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= 1.06e+24)
		tmp = Float64(x * 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -3.3e+136)
		tmp = t_1;
	elseif (t <= -2.4e-217)
		tmp = x - (y * -1.0);
	elseif (t <= -1.46e-257)
		tmp = (y * z) / a;
	elseif (t <= 1.06e+24)
		tmp = x * 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -32999999999999999224551649921188376054309610847698636434518172229497721989585267143685755563589344485225679296183401740245116370550784000], t$95$1, If[LessEqual[t, -2980834737217361/12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352918515131554298200329449113635639808166799244402122285052787558602103993549731750007142774830528462848], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3949107279145325/270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1060000000000000025165824], N[(x * 1), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.2999999999999999e136 or 1.06e24 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -3.2999999999999999e136 < t < -2.3999999999999999e-217

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]

   if -2.3999999999999999e-217 < t < -1.4600000000000001e-257

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a - t}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{\color{blue}{a} - t} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} \]

      4. lower--.f64 39.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - \color{blue}{t}} \]

   10. Applied rewrites 39.7%

       \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   11. Taylor expanded in t around 0

       \[\leadsto \frac{y \cdot z}{\color{blue}{a}} \]
   12. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{y \cdot z}{a} \]

       2. lower-*.f64 16.3%

          \[\leadsto \frac{y \cdot z}{a} \]

   13. Applied rewrites 16.3%

       \[\leadsto \frac{y \cdot z}{\color{blue}{a}} \]

   if -1.4600000000000001e-257 < t < 1.06e24

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 22: 37.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := y - \left(x + -1 \cdot x\right)\\ \mathbf{if}\;t \leq \frac{-4842270319348757}{2305843009213693952}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1060000000000000025165824:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- y (+ x (* -1 x)))))
  (if (<= t -4842270319348757/2305843009213693952)
    t_1
    (if (<= t 1060000000000000025165824) (* x 1) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -0.0021) {
		tmp = t_1;
	} else if (t <= 1.06e+24) {
		tmp = x * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x + ((-1.0d0) * x))
    if (t <= (-0.0021d0)) then
        tmp = t_1
    else if (t <= 1.06d+24) then
        tmp = x * 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x + (-1.0 * x));
	double tmp;
	if (t <= -0.0021) {
		tmp = t_1;
	} else if (t <= 1.06e+24) {
		tmp = x * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x + (-1.0 * x))
	tmp = 0
	if t <= -0.0021:
		tmp = t_1
	elif t <= 1.06e+24:
		tmp = x * 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x + Float64(-1.0 * x)))
	tmp = 0.0
	if (t <= -0.0021)
		tmp = t_1;
	elseif (t <= 1.06e+24)
		tmp = Float64(x * 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x + (-1.0 * x));
	tmp = 0.0;
	if (t <= -0.0021)
		tmp = t_1;
	elseif (t <= 1.06e+24)
		tmp = x * 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x + N[(-1 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4842270319348757/2305843009213693952], t$95$1, If[LessEqual[t, 1060000000000000025165824], N[(x * 1), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0020999999999999999 or 1.06e24 < t

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   4. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto y - \color{blue}{\left(x + -1 \cdot x\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto y - \left(x + \color{blue}{-1 \cdot x}\right) \]

      3. lower-*.f64 24.9%

         \[\leadsto y - \left(x + -1 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 24.9%

      \[\leadsto \color{blue}{y - \left(x + -1 \cdot x\right)} \]

   if -0.0020999999999999999 < t < 1.06e24

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 34.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -40999999999999999722058895648826747034930046119706624:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot -1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -40999999999999999722058895648826747034930046119706624)
  (* x 1)
  (- x (* y -1))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+52) {
		tmp = x * 1.0;
	} else {
		tmp = x - (y * -1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.1d+52)) then
        tmp = x * 1.0d0
    else
        tmp = x - (y * (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+52) {
		tmp = x * 1.0;
	} else {
		tmp = x - (y * -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.1e+52:
		tmp = x * 1.0
	else:
		tmp = x - (y * -1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.1e+52)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(x - Float64(y * -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.1e+52)
		tmp = x * 1.0;
	else
		tmp = x - (y * -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -40999999999999999722058895648826747034930046119706624], N[(x * 1), $MachinePrecision], N[(x - N[(y * -1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1e52

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot \left(1 + -1\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 2.8%

      \[\leadsto x \cdot \left(1 + -1\right) \]

   8. Taylor expanded in a around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 25.0%

       \[\leadsto x \cdot 1 \]

   if -4.1e52 < a

   1. Initial program 68.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(x \cdot \left(a - t\right) + \left(y - x\right) \cdot \left(z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) + x \cdot \left(a - t\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right) + \color{blue}{\left(a - t\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - t\right) - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(y - x\right) \cdot \left(z - t\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      10. *-commutative N/A

          \[\leadsto \frac{1}{a - t} \cdot \left(\color{blue}{\left(z - t\right) \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(\left(a - t\right)\right)\right) \cdot x\right) \]

      11. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - t}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right)} \]

      12. frac-2neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      14. lower-/.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(a - t\right)\right)}\right)}, \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{t - a}}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right), x\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - t\right)}\right)\right), x\right) \]

      19. sub-negate-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

      20. lower--.f64 85.3%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \color{blue}{\left(t - a\right)}, x\right) \]

   3. Applied rewrites 85.3%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{t - a}\right), \left(z - t\right), \left(y - x\right), \left(t - a\right), x\right)} \]

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \frac{t - z}{a - t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.3%

      \[\leadsto x - \color{blue}{y} \cdot \frac{t - z}{a - t} \]

   9. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto x - y \cdot \color{blue}{-1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 25.0% accurate, 4.8× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (* x 1))

C

double code(double x, double y, double z, double t, double a) {
	return x * 1.0;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x * 1.0;
}

Python

def code(x, y, z, t, a):
	return x * 1.0

Julia

function code(x, y, z, t, a)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x * 1), $MachinePrecision]

Derivation

1. Initial program 68.6%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{z - t}{a - t}}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{z - t}{a - t}}\right) \]

   4. lower-/.f64 N/A

      \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a - t}}\right) \]

   5. lower--.f64 N/A

      \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{\color{blue}{a} - t}\right) \]

   6. lower--.f64 43.2%

      \[\leadsto x \cdot \left(1 + -1 \cdot \frac{z - t}{a - \color{blue}{t}}\right) \]

4. Applied rewrites 43.2%

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

5. Taylor expanded in t around inf

   \[\leadsto x \cdot \left(1 + -1\right) \]
6. Step-by-step derivation

7. Applied rewrites 2.8%

   \[\leadsto x \cdot \left(1 + -1\right) \]

8. Taylor expanded in a around inf

   \[\leadsto x \cdot 1 \]
9. Step-by-step derivation

10. Applied rewrites 25.0%

    \[\leadsto x \cdot 1 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y x) (- z t)) (- a t))))