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

Percentage Accurate: 67.6% → 91.5%

Time: 31.5s

Alternatives: 25

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

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 - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -1200000000000000010626946991786816693270672485690848906838016:\\ \;\;\;\;x - \frac{z - y}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq \frac{7926335344172073}{288230376151711744}:\\ \;\;\;\;x \cdot \left(-1 \cdot \frac{a - y}{z - a} + \frac{t \cdot \left(z - y\right)}{x \cdot \left(z - a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - a}\right), \left(z - y\right), \left(x - t\right), \left(z - a\right), x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     t
     -1200000000000000010626946991786816693270672485690848906838016)
  (- x (* (/ (- z y) (- a z)) (- t x)))
  (if (<= t 7926335344172073/288230376151711744)
    (*
     x
     (+ (* -1 (/ (- a y) (- z a))) (/ (* t (- z y)) (* x (- z a)))))
    (134-z0z1z2z3z4 (/ -1 (- z a)) (- z y) (- x t) (- z a) x))))

Derivation

1. Split input into 3 regimes

2. if t < -1.2e60

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower--.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. div-sub N/A

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

      13. sub-negate N/A

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

      14. div-sub N/A

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

      15. frac-2neg-rev N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower-*.f64 N/A

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

   3. Applied rewrites 83.6%

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

   if -1.2e60 < t < 0.0275

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. add-to-fraction N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

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

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

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

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower-134-z0z1z2z3z4 N/A

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

   3. Applied rewrites 84.5%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 75.1%

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

   6. Applied rewrites 75.1%

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

   if 0.0275 < t

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. add-to-fraction N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

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

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

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

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower-134-z0z1z2z3z4 N/A

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

   3. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - a}\right), \left(z - y\right), \left(x - t\right), \left(z - a\right), x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - a}\right), \left(z - y\right), \left(x - t\right), \left(z - a\right), x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq \frac{-5617791046444737}{11235582092889474423308157442431404585112356118389416079589380072358292237843810195794279832650471001320007117491962084853674360550901038905802964414967132773610493339054092829768888725077880882465817684505312860552384417646403930092119569408801702322709406917786643639996702871154982269052209770601514008576}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (134-z0z1z2z3z4 (/ -1 (- z a)) (- z y) (- x t) (- z a) x))
       (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
  (if (<=
       t_2
       -5617791046444737/11235582092889474423308157442431404585112356118389416079589380072358292237843810195794279832650471001320007117491962084853674360550901038905802964414967132773610493339054092829768888725077880882465817684505312860552384417646403930092119569408801702322709406917786643639996702871154982269052209770601514008576)
    t_1
    (if (<= t_2 0)
      (+ t (* -1 (/ (- (* y (- t x)) (* a (- t x))) z)))
      t_1))))

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.9999999999999998e-292 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. add-to-fraction N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

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

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

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

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower-134-z0z1z2z3z4 N/A

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

   3. Applied rewrites 84.5%

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

   if -4.9999999999999998e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]

   8. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.4%

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

   10. Applied rewrites 46.4%

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

Alternative 3: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{x - t}{z - a} \cdot \left(y - z\right)\\ \mathbf{elif}\;t\_1 \leq \frac{-5617791046444737}{11235582092889474423308157442431404585112356118389416079589380072358292237843810195794279832650471001320007117491962084853674360550901038905802964414967132773610493339054092829768888725077880882465817684505312860552384417646403930092119569408801702322709406917786643639996702871154982269052209770601514008576}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{1}{a - z} \cdot \left(z - y\right)\right) \cdot \left(t - x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
  (if (<= t_1 (- INFINITY))
    (+ x (* (/ (- x t) (- z a)) (- y z)))
    (if (<=
         t_1
         -5617791046444737/11235582092889474423308157442431404585112356118389416079589380072358292237843810195794279832650471001320007117491962084853674360550901038905802964414967132773610493339054092829768888725077880882465817684505312860552384417646403930092119569408801702322709406917786643639996702871154982269052209770601514008576)
      t_1
      (if (<= t_1 0)
        (+ t (* -1 (/ (- (* y (- t x)) (* a (- t x))) z)))
        (- x (* (* (/ 1 (- a z)) (- z y)) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (((x - t) / (z - a)) * (y - z));
	} else if (t_1 <= -5e-292) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (((x - t) / (z - a)) * (y - z));
	} else if (t_1 <= -5e-292) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (((x - t) / (z - a)) * (y - z))
	elif t_1 <= -5e-292:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z))
	else:
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(Float64(x - t) / Float64(z - a)) * Float64(y - z)));
	elseif (t_1 <= -5e-292)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = Float64(x - Float64(Float64(Float64(1.0 / Float64(a - z)) * Float64(z - y)) * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (((x - t) / (z - a)) * (y - z));
	elseif (t_1 <= -5e-292)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	else
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5617791046444737/11235582092889474423308157442431404585112356118389416079589380072358292237843810195794279832650471001320007117491962084853674360550901038905802964414967132773610493339054092829768888725077880882465817684505312860552384417646403930092119569408801702322709406917786643639996702871154982269052209770601514008576], t$95$1, If[LessEqual[t$95$1, 0], N[(t + N[(-1 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(1 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0

   1. Initial program 67.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. frac-2neg N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower--.f64 79.6%

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

   3. Applied rewrites 79.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.9999999999999998e-292

   1. Initial program 67.6%

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

   if -4.9999999999999998e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]

   8. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.4%

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

   10. Applied rewrites 46.4%

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

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

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower--.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. div-sub N/A

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

      13. sub-negate N/A

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

      14. div-sub N/A

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

      15. frac-2neg-rev N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower-*.f64 N/A

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

   3. Applied rewrites 83.6%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval 83.5%

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

   5. Applied rewrites 83.5%

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

Alternative 4: 87.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{x - t}{z - a} \cdot \left(y - z\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \frac{-2291112313477997}{57277807836949922408837567867349676981443478344341305058882899404622128010705808318690568531649256750858719018437999440148793721514146753400890052083129159241025748615958424204533602522957957552490080016463490494951861107213475167230717574212948590592}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;-1 \cdot \frac{x \cdot \left(a - y\right)}{z - a}\\ \mathbf{elif}\;t\_2 \leq 50000000000000003960719125422883827062840959584985546704194967116721787948758551386272267278602882264876081416647209031203419106557526049419390978660438178426771560410745940876447333535260291112887354734608898565252528592034690824272687386622186778733613155375371021108230826846322688:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (/ (- x t) (- z a)) (- y z))))
       (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
  (if (<= t_2 (- INFINITY))
    t_1
    (if (<=
         t_2
         -2291112313477997/57277807836949922408837567867349676981443478344341305058882899404622128010705808318690568531649256750858719018437999440148793721514146753400890052083129159241025748615958424204533602522957957552490080016463490494951861107213475167230717574212948590592)
      t_2
      (if (<= t_2 0)
        (* -1 (/ (* x (- a y)) (- z a)))
        (if (<=
             t_2
             50000000000000003960719125422883827062840959584985546704194967116721787948758551386272267278602882264876081416647209031203419106557526049419390978660438178426771560410745940876447333535260291112887354734608898565252528592034690824272687386622186778733613155375371021108230826846322688)
          t_2
          t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - t) / (z - a)) * (y - z));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-236) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 * ((x * (a - y)) / (z - a));
	} else if (t_2 <= 5e+283) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - t) / (z - a)) * (y - z));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-236) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 * ((x * (a - y)) / (z - a));
	} else if (t_2 <= 5e+283) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((x - t) / (z - a)) * (y - z))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-236:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = -1.0 * ((x * (a - y)) / (z - a))
	elif t_2 <= 5e+283:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - t) / Float64(z - a)) * Float64(y - z)))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-236)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(-1.0 * Float64(Float64(x * Float64(a - y)) / Float64(z - a)));
	elseif (t_2 <= 5e+283)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((x - t) / (z - a)) * (y - z));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-236)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = -1.0 * ((x * (a - y)) / (z - a));
	elseif (t_2 <= 5e+283)
		tmp = t_2;
	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[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2291112313477997/57277807836949922408837567867349676981443478344341305058882899404622128010705808318690568531649256750858719018437999440148793721514146753400890052083129159241025748615958424204533602522957957552490080016463490494951861107213475167230717574212948590592], t$95$2, If[LessEqual[t$95$2, 0], N[(-1 * N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 50000000000000003960719125422883827062840959584985546704194967116721787948758551386272267278602882264876081416647209031203419106557526049419390978660438178426771560410745940876447333535260291112887354734608898565252528592034690824272687386622186778733613155375371021108230826846322688], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.0000000000000004e283 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 67.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. frac-2neg N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower--.f64 79.6%

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

   3. Applied rewrites 79.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.0000000000000002e-236 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000004e283

   1. Initial program 67.6%

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

   if -4.0000000000000002e-236 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. add-to-fraction N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

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

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

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

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower-134-z0z1z2z3z4 N/A

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

   3. Applied rewrites 84.5%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 39.0%

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

   6. Applied rewrites 39.0%

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

Alternative 5: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056:\\ \;\;\;\;x - \left(\frac{1}{a - z} \cdot \left(z - y\right)\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056)
  (- x (* (* (/ 1 (- a z)) (- z y)) (- t x)))
  (* t (- (/ y (- a z)) (/ z (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	} else {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	}
	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 (z <= 1.35d+165) then
        tmp = x - (((1.0d0 / (a - z)) * (z - y)) * (t - x))
    else
        tmp = t * ((y / (a - z)) - (z / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	} else {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.35e+165:
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x))
	else:
		tmp = t * ((y / (a - z)) - (z / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.35e+165)
		tmp = Float64(x - Float64(Float64(Float64(1.0 / Float64(a - z)) * Float64(z - y)) * Float64(t - x)));
	else
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - Float64(z / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.35e+165)
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	else
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056], N[(x - N[(N[(N[(1 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35e165

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower--.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. div-sub N/A

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

      13. sub-negate N/A

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

      14. div-sub N/A

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

      15. frac-2neg-rev N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower-*.f64 N/A

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

   3. Applied rewrites 83.6%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval 83.5%

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

   5. Applied rewrites 83.5%

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

   if 1.35e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   7. Applied rewrites 52.4%

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

Alternative 6: 83.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056:\\ \;\;\;\;x - \left(\frac{1}{a - z} \cdot \left(z - y\right)\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056)
  (- x (* (* (/ 1 (- a z)) (- z y)) (- t x)))
  (* t (/ z (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	} else {
		tmp = t * (z / (z - a));
	}
	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 (z <= 1.35d+165) then
        tmp = x - (((1.0d0 / (a - z)) * (z - y)) * (t - x))
    else
        tmp = t * (z / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.35e+165:
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.35e+165)
		tmp = Float64(x - Float64(Float64(Float64(1.0 / Float64(a - z)) * Float64(z - y)) * Float64(t - x)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.35e+165)
		tmp = x - (((1.0 / (a - z)) * (z - y)) * (t - x));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056], N[(x - N[(N[(N[(1 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35e165

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower--.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. div-sub N/A

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

      13. sub-negate N/A

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

      14. div-sub N/A

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

      15. frac-2neg-rev N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower-*.f64 N/A

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

   3. Applied rewrites 83.6%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval 83.5%

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

   5. Applied rewrites 83.5%

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

   if 1.35e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   9. Applied rewrites 52.4%

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

   10. Taylor expanded in y around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 30.6%

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

   12. Applied rewrites 30.6%

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

Alternative 7: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056:\\ \;\;\;\;x - \frac{z - y}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056)
  (- x (* (/ (- z y) (- a z)) (- t x)))
  (* t (/ z (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x - (((z - y) / (a - z)) * (t - x));
	} else {
		tmp = t * (z / (z - a));
	}
	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 (z <= 1.35d+165) then
        tmp = x - (((z - y) / (a - z)) * (t - x))
    else
        tmp = t * (z / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x - (((z - y) / (a - z)) * (t - x));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.35e+165:
		tmp = x - (((z - y) / (a - z)) * (t - x))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.35e+165)
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(a - z)) * Float64(t - x)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.35e+165)
		tmp = x - (((z - y) / (a - z)) * (t - x));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35e165

   1. Initial program 67.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower--.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. lift--.f64 N/A

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

      12. div-sub N/A

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

      13. sub-negate N/A

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

      14. div-sub N/A

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

      15. frac-2neg-rev N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower-*.f64 N/A

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

   3. Applied rewrites 83.6%

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

   if 1.35e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   9. Applied rewrites 52.4%

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

   10. Taylor expanded in y around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 30.6%

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

   12. Applied rewrites 30.6%

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

Alternative 8: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056:\\ \;\;\;\;x + \frac{x - t}{z - a} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056)
  (+ x (* (/ (- x t) (- z a)) (- y z)))
  (* t (/ z (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x + (((x - t) / (z - a)) * (y - z));
	} else {
		tmp = t * (z / (z - a));
	}
	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 (z <= 1.35d+165) then
        tmp = x + (((x - t) / (z - a)) * (y - z))
    else
        tmp = t * (z / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = x + (((x - t) / (z - a)) * (y - z));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.35e+165:
		tmp = x + (((x - t) / (z - a)) * (y - z))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.35e+165)
		tmp = Float64(x + Float64(Float64(Float64(x - t) / Float64(z - a)) * Float64(y - z)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.35e+165)
		tmp = x + (((x - t) / (z - a)) * (y - z));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1349999999999999976834158306405081433468564668098450424901954640185304620606950559836587471378818037322790513692856978439889183474863931657115851209179973310853677056], N[(x + N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35e165

   1. Initial program 67.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. frac-2neg N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower--.f64 79.6%

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

   3. Applied rewrites 79.6%

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

   if 1.35e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   9. Applied rewrites 52.4%

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

   10. Taylor expanded in y around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 30.6%

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

   12. Applied rewrites 30.6%

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

Alternative 9: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := x - \frac{t}{z - a} \cdot \left(y - z\right)\\ \mathbf{if}\;z \leq -18499999999999999558625001472:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{6859310779502913}{381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864:\\ \;\;\;\;\frac{y}{\frac{z - a}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (* (/ t (- z a)) (- y z)))))
  (if (<= z -18499999999999999558625001472)
    t_1
    (if (<=
         z
         6859310779502913/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928)
      (+ x (/ (* y (- t x)) (- a z)))
      (if (<=
           z
           8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176)
        t_1
        (if (<=
             z
             6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864)
          (/ y (/ (- z a) (- x t)))
          (* t (/ z (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t / (z - a)) * (y - z));
	double tmp;
	if (z <= -1.85e+28) {
		tmp = t_1;
	} else if (z <= 1.8e-125) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 9e+120) {
		tmp = t_1;
	} else if (z <= 6.6e+165) {
		tmp = y / ((z - a) / (x - t));
	} else {
		tmp = t * (z / (z - a));
	}
	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 - a)) * (y - z))
    if (z <= (-1.85d+28)) then
        tmp = t_1
    else if (z <= 1.8d-125) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 9d+120) then
        tmp = t_1
    else if (z <= 6.6d+165) then
        tmp = y / ((z - a) / (x - t))
    else
        tmp = t * (z / (z - a))
    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 - a)) * (y - z));
	double tmp;
	if (z <= -1.85e+28) {
		tmp = t_1;
	} else if (z <= 1.8e-125) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 9e+120) {
		tmp = t_1;
	} else if (z <= 6.6e+165) {
		tmp = y / ((z - a) / (x - t));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t / (z - a)) * (y - z))
	tmp = 0
	if z <= -1.85e+28:
		tmp = t_1
	elif z <= 1.8e-125:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 9e+120:
		tmp = t_1
	elif z <= 6.6e+165:
		tmp = y / ((z - a) / (x - t))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t / Float64(z - a)) * Float64(y - z)))
	tmp = 0.0
	if (z <= -1.85e+28)
		tmp = t_1;
	elseif (z <= 1.8e-125)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 9e+120)
		tmp = t_1;
	elseif (z <= 6.6e+165)
		tmp = Float64(y / Float64(Float64(z - a) / Float64(x - t)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t / (z - a)) * (y - z));
	tmp = 0.0;
	if (z <= -1.85e+28)
		tmp = t_1;
	elseif (z <= 1.8e-125)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 9e+120)
		tmp = t_1;
	elseif (z <= 6.6e+165)
		tmp = y / ((z - a) / (x - t));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -18499999999999999558625001472], t$95$1, If[LessEqual[z, 6859310779502913/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176], t$95$1, If[LessEqual[z, 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864], N[(y / N[(N[(z - a), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.85e28 or 1.8000000000000001e-125 < z < 8.9999999999999995e120

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   if -1.85e28 < z < 1.8000000000000001e-125

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 54.7%

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

   4. Applied rewrites 54.7%

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

   if 8.9999999999999995e120 < z < 6.5999999999999997e165

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 37.7%

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

   6. Applied rewrites 37.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-/r/ N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. frac-2neg N/A

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

      13. lift-/.f64 N/A

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

      14. lower-/.f64 41.9%

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

   8. Applied rewrites 41.9%

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

   if 6.5999999999999997e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   9. Applied rewrites 52.4%

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

   10. Taylor expanded in y around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 30.6%

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

   12. Applied rewrites 30.6%

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

Alternative 10: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x - \frac{t}{z - a} \cdot \left(y - z\right)\\ \mathbf{if}\;z \leq -18499999999999999558625001472:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{6859310779502913}{381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (* (/ t (- z a)) (- y z)))))
  (if (<= z -18499999999999999558625001472)
    t_1
    (if (<=
         z
         6859310779502913/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928)
      (+ x (/ (* y (- t x)) (- a z)))
      (if (<=
           z
           8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176)
        t_1
        (if (<=
             z
             6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864)
          (* (/ y (- z a)) (- x t))
          (* t (/ z (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t / (z - a)) * (y - z));
	double tmp;
	if (z <= -1.85e+28) {
		tmp = t_1;
	} else if (z <= 1.8e-125) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 9e+120) {
		tmp = t_1;
	} else if (z <= 6.6e+165) {
		tmp = (y / (z - a)) * (x - t);
	} else {
		tmp = t * (z / (z - a));
	}
	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 - a)) * (y - z))
    if (z <= (-1.85d+28)) then
        tmp = t_1
    else if (z <= 1.8d-125) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 9d+120) then
        tmp = t_1
    else if (z <= 6.6d+165) then
        tmp = (y / (z - a)) * (x - t)
    else
        tmp = t * (z / (z - a))
    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 - a)) * (y - z));
	double tmp;
	if (z <= -1.85e+28) {
		tmp = t_1;
	} else if (z <= 1.8e-125) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 9e+120) {
		tmp = t_1;
	} else if (z <= 6.6e+165) {
		tmp = (y / (z - a)) * (x - t);
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t / (z - a)) * (y - z))
	tmp = 0
	if z <= -1.85e+28:
		tmp = t_1
	elif z <= 1.8e-125:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 9e+120:
		tmp = t_1
	elif z <= 6.6e+165:
		tmp = (y / (z - a)) * (x - t)
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t / Float64(z - a)) * Float64(y - z)))
	tmp = 0.0
	if (z <= -1.85e+28)
		tmp = t_1;
	elseif (z <= 1.8e-125)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 9e+120)
		tmp = t_1;
	elseif (z <= 6.6e+165)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t / (z - a)) * (y - z));
	tmp = 0.0;
	if (z <= -1.85e+28)
		tmp = t_1;
	elseif (z <= 1.8e-125)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 9e+120)
		tmp = t_1;
	elseif (z <= 6.6e+165)
		tmp = (y / (z - a)) * (x - t);
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -18499999999999999558625001472], t$95$1, If[LessEqual[z, 6859310779502913/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176], t$95$1, If[LessEqual[z, 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.85e28 or 1.8000000000000001e-125 < z < 8.9999999999999995e120

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   if -1.85e28 < z < 1.8000000000000001e-125

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 54.7%

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

   4. Applied rewrites 54.7%

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

   if 8.9999999999999995e120 < z < 6.5999999999999997e165

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 37.7%

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

   6. Applied rewrites 37.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-lft-neg-out N/A

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

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

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 43.0%

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

   8. Applied rewrites 43.0%

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

   if 6.5999999999999997e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   9. Applied rewrites 52.4%

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

   10. Taylor expanded in y around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 30.6%

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

   12. Applied rewrites 30.6%

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

Alternative 11: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3399999999999999750280910337709527728652288:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{4001264621376699}{190536410541747572716161940294993060653600960856016305594430966774009505543198585212421026798308836130360530463953040948208494609331560382464}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* t (/ z (- z a)))))
  (if (<= z -3399999999999999750280910337709527728652288)
    t_1
    (if (<=
         z
         4001264621376699/190536410541747572716161940294993060653600960856016305594430966774009505543198585212421026798308836130360530463953040948208494609331560382464)
      (+ x (/ (* y (- t x)) (- a z)))
      (if (<=
           z
           8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176)
        (+ x (/ (* (- y z) t) (- a z)))
        (if (<=
             z
             6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864)
          (* (/ y (- z a)) (- x t))
          t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -3.4e+42) {
		tmp = t_1;
	} else if (z <= 2.1e-125) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 9e+120) {
		tmp = x + (((y - z) * t) / (a - z));
	} else if (z <= 6.6e+165) {
		tmp = (y / (z - a)) * (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) :: tmp
    t_1 = t * (z / (z - a))
    if (z <= (-3.4d+42)) then
        tmp = t_1
    else if (z <= 2.1d-125) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 9d+120) then
        tmp = x + (((y - z) * t) / (a - z))
    else if (z <= 6.6d+165) then
        tmp = (y / (z - a)) * (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 = t * (z / (z - a));
	double tmp;
	if (z <= -3.4e+42) {
		tmp = t_1;
	} else if (z <= 2.1e-125) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 9e+120) {
		tmp = x + (((y - z) * t) / (a - z));
	} else if (z <= 6.6e+165) {
		tmp = (y / (z - a)) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	tmp = 0
	if z <= -3.4e+42:
		tmp = t_1
	elif z <= 2.1e-125:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 9e+120:
		tmp = x + (((y - z) * t) / (a - z))
	elif z <= 6.6e+165:
		tmp = (y / (z - a)) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.4e+42)
		tmp = t_1;
	elseif (z <= 2.1e-125)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 9e+120)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	elseif (z <= 6.6e+165)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -3.4e+42)
		tmp = t_1;
	elseif (z <= 2.1e-125)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 9e+120)
		tmp = x + (((y - z) * t) / (a - z));
	elseif (z <= 6.6e+165)
		tmp = (y / (z - a)) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3399999999999999750280910337709527728652288], t$95$1, If[LessEqual[z, 4001264621376699/190536410541747572716161940294993060653600960856016305594430966774009505543198585212421026798308836130360530463953040948208494609331560382464], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999998e42 or 6.5999999999999997e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   9. Applied rewrites 52.4%

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

   10. Taylor expanded in y around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 30.6%

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

   12. Applied rewrites 30.6%

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

   if -3.3999999999999998e42 < z < 2.1e-125

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 54.7%

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

   4. Applied rewrites 54.7%

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

   if 2.1e-125 < z < 8.9999999999999995e120

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

   if 8.9999999999999995e120 < z < 6.5999999999999997e165

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 37.7%

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

   6. Applied rewrites 37.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-lft-neg-out N/A

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

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

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 43.0%

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

   8. Applied rewrites 43.0%

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

Alternative 12: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3399999999999999750280910337709527728652288:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* t (/ z (- z a)))))
  (if (<= z -3399999999999999750280910337709527728652288)
    t_1
    (if (<=
         z
         8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176)
      (+ x (/ (* y (- t x)) (- a z)))
      (if (<=
           z
           6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864)
        (* (/ y (- z a)) (- x t))
        t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -3.4e+42) {
		tmp = t_1;
	} else if (z <= 9e+120) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 6.6e+165) {
		tmp = (y / (z - a)) * (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) :: tmp
    t_1 = t * (z / (z - a))
    if (z <= (-3.4d+42)) then
        tmp = t_1
    else if (z <= 9d+120) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 6.6d+165) then
        tmp = (y / (z - a)) * (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 = t * (z / (z - a));
	double tmp;
	if (z <= -3.4e+42) {
		tmp = t_1;
	} else if (z <= 9e+120) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 6.6e+165) {
		tmp = (y / (z - a)) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	tmp = 0
	if z <= -3.4e+42:
		tmp = t_1
	elif z <= 9e+120:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 6.6e+165:
		tmp = (y / (z - a)) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.4e+42)
		tmp = t_1;
	elseif (z <= 9e+120)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 6.6e+165)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -3.4e+42)
		tmp = t_1;
	elseif (z <= 9e+120)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 6.6e+165)
		tmp = (y / (z - a)) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3399999999999999750280910337709527728652288], t$95$1, If[LessEqual[z, 8999999999999999533343888127788871683666634823312209064127211160441811264448253605817745403309330949040665537863982514176], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999998e42 or 6.5999999999999997e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

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

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

   6. Applied rewrites 64.3%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 52.4%

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

   9. Applied rewrites 52.4%

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

   10. Taylor expanded in y around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 30.6%

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

   12. Applied rewrites 30.6%

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

   if -3.3999999999999998e42 < z < 8.9999999999999995e120

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 54.7%

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

   4. Applied rewrites 54.7%

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

   if 8.9999999999999995e120 < z < 6.5999999999999997e165

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 37.7%

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

   6. Applied rewrites 37.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-lft-neg-out N/A

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

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

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 43.0%

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

   8. Applied rewrites 43.0%

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

Alternative 13: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(x - t\right)\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -5400000000000000067330389781411646144512:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq \frac{-5648671608315113}{20173827172553973356686868531273530268200826506478308693989526222973809547006571833044104322501076808092993531037089792}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{8418548055909837}{59285549689505892056868344324448208820874232148807968788202283012051522375647232}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ y (- z a)) (- x t))) (t_2 (* t (/ z (- z a)))))
  (if (<= z -5400000000000000067330389781411646144512)
    t_2
    (if (<=
         z
         -5648671608315113/20173827172553973356686868531273530268200826506478308693989526222973809547006571833044104322501076808092993531037089792)
      t_1
      (if (<=
           z
           8418548055909837/59285549689505892056868344324448208820874232148807968788202283012051522375647232)
        (+ x (/ (* y (- t x)) a))
        (if (<=
             z
             6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864)
          t_1
          t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (x - t);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -5.4e+39) {
		tmp = t_2;
	} else if (z <= -2.8e-103) {
		tmp = t_1;
	} else if (z <= 1.42e-64) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 6.6e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (y / (z - a)) * (x - t)
    t_2 = t * (z / (z - a))
    if (z <= (-5.4d+39)) then
        tmp = t_2
    else if (z <= (-2.8d-103)) then
        tmp = t_1
    else if (z <= 1.42d-64) then
        tmp = x + ((y * (t - x)) / a)
    else if (z <= 6.6d+165) then
        tmp = t_1
    else
        tmp = t_2
    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)) * (x - t);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -5.4e+39) {
		tmp = t_2;
	} else if (z <= -2.8e-103) {
		tmp = t_1;
	} else if (z <= 1.42e-64) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 6.6e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * (x - t)
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -5.4e+39:
		tmp = t_2
	elif z <= -2.8e-103:
		tmp = t_1
	elif z <= 1.42e-64:
		tmp = x + ((y * (t - x)) / a)
	elif z <= 6.6e+165:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(x - t))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -5.4e+39)
		tmp = t_2;
	elseif (z <= -2.8e-103)
		tmp = t_1;
	elseif (z <= 1.42e-64)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (z <= 6.6e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * (x - t);
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -5.4e+39)
		tmp = t_2;
	elseif (z <= -2.8e-103)
		tmp = t_1;
	elseif (z <= 1.42e-64)
		tmp = x + ((y * (t - x)) / a);
	elseif (z <= 6.6e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5400000000000000067330389781411646144512], t$95$2, If[LessEqual[z, -5648671608315113/20173827172553973356686868531273530268200826506478308693989526222973809547006571833044104322501076808092993531037089792], t$95$1, If[LessEqual[z, 8418548055909837/59285549689505892056868344324448208820874232148807968788202283012051522375647232], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6599999999999999704889740170416960896224666331392471398596109016291223173895571176082550059814524022285304048837069830656864667679330832033829908917913588779255332864], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000001e39 or 6.5999999999999997e165 < z

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.5%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-flip N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      8. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(z - a\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)} \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      12. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      13. lift-*.f64 N/A

          \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      14. associate-/l* N/A

          \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      15. *-commutative N/A

          \[\leadsto x + \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

      16. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{t}{a - z}\right)\right) \cdot \left(y - z\right)} \]

   6. Applied rewrites 64.3%

      \[\leadsto \color{blue}{x - \frac{t}{z - a} \cdot \left(y - z\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 52.4%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   9. Applied rewrites 52.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   10. Taylor expanded in y around 0

       \[\leadsto t \cdot \frac{z}{\color{blue}{z - a}} \]
   11. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto t \cdot \frac{z}{z - \color{blue}{a}} \]

       2. lower--.f64 30.6%

          \[\leadsto t \cdot \frac{z}{z - a} \]

   12. Applied rewrites 30.6%

       \[\leadsto t \cdot \frac{z}{\color{blue}{z - a}} \]

   if -5.4000000000000001e39 < z < -2.8000000000000002e-103 or 1.4200000000000001e-64 < z < 6.5999999999999997e165

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      4. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      10. lower-*.f64 37.7%

          \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a} - z} \]

   6. Applied rewrites 37.7%

      \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{a - z} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a} - z} \]

      4. associate-/l* N/A

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto \frac{y}{a - z} \cdot \color{blue}{\left(t - x\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{y}{a - z} \cdot \left(t - x\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(t - x\right) \]

      8. lift--.f64 N/A

         \[\leadsto \frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(t - x\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{y}{z - a}\right)\right) \cdot \left(\color{blue}{t} - x\right) \]

      10. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{neg}\left(\frac{y}{z - a} \cdot \left(t - x\right)\right) \]

      11. distribute-rgt-neg-out N/A

          \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)} \]

      12. sub-negate-rev N/A

          \[\leadsto \frac{y}{z - a} \cdot \left(x - \color{blue}{t}\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{y}{z - a} \cdot \left(x - \color{blue}{t}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(x - t\right)} \]

      15. lower-/.f64 43.0%

          \[\leadsto \frac{y}{z - a} \cdot \left(\color{blue}{x} - t\right) \]

   8. Applied rewrites 43.0%

      \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(x - t\right)} \]

   if -2.8000000000000002e-103 < z < 1.4200000000000001e-64

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]

   8. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{a} \]

      3. lower--.f64 43.6%

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{a} \]

   10. Applied rewrites 43.6%

       \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq \frac{-8330559332786147}{1461501637330902918203684832716283019655932542976}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 305000000000000013664634946977792:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{a - z} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     y
     -8330559332786147/1461501637330902918203684832716283019655932542976)
  (* (/ y (- z a)) (- x t))
  (if (<= y 305000000000000013664634946977792)
    (+ t x)
    (* (/ (- t x) (- a z)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.7e-33) {
		tmp = (y / (z - a)) * (x - t);
	} else if (y <= 3.05e+32) {
		tmp = t + x;
	} else {
		tmp = ((t - x) / (a - z)) * y;
	}
	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 (y <= (-5.7d-33)) then
        tmp = (y / (z - a)) * (x - t)
    else if (y <= 3.05d+32) then
        tmp = t + x
    else
        tmp = ((t - x) / (a - z)) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.7e-33) {
		tmp = (y / (z - a)) * (x - t);
	} else if (y <= 3.05e+32) {
		tmp = t + x;
	} else {
		tmp = ((t - x) / (a - z)) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.7e-33:
		tmp = (y / (z - a)) * (x - t)
	elif y <= 3.05e+32:
		tmp = t + x
	else:
		tmp = ((t - x) / (a - z)) * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.7e-33)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	elseif (y <= 3.05e+32)
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(Float64(t - x) / Float64(a - z)) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.7e-33)
		tmp = (y / (z - a)) * (x - t);
	elseif (y <= 3.05e+32)
		tmp = t + x;
	else
		tmp = ((t - x) / (a - z)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8330559332786147/1461501637330902918203684832716283019655932542976], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 305000000000000013664634946977792], N[(t + x), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7000000000000003e-33

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      4. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      10. lower-*.f64 37.7%

          \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a} - z} \]

   6. Applied rewrites 37.7%

      \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{a - z} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a} - z} \]

      4. associate-/l* N/A

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto \frac{y}{a - z} \cdot \color{blue}{\left(t - x\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{y}{a - z} \cdot \left(t - x\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(t - x\right) \]

      8. lift--.f64 N/A

         \[\leadsto \frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(t - x\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{y}{z - a}\right)\right) \cdot \left(\color{blue}{t} - x\right) \]

      10. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{neg}\left(\frac{y}{z - a} \cdot \left(t - x\right)\right) \]

      11. distribute-rgt-neg-out N/A

          \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)} \]

      12. sub-negate-rev N/A

          \[\leadsto \frac{y}{z - a} \cdot \left(x - \color{blue}{t}\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{y}{z - a} \cdot \left(x - \color{blue}{t}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(x - t\right)} \]

      15. lower-/.f64 43.0%

          \[\leadsto \frac{y}{z - a} \cdot \left(\color{blue}{x} - t\right) \]

   8. Applied rewrites 43.0%

      \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(x - t\right)} \]

   if -5.7000000000000003e-33 < y < 3.0500000000000001e32

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]

   if 3.0500000000000001e32 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.6%

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. lift--.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      9. lower-/.f64 41.9%

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

   6. Applied rewrites 41.9%

      \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 56.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq \frac{-8330559332786147}{1461501637330902918203684832716283019655932542976}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 305000000000000013664634946977792:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ y (- z a)) (- x t))))
  (if (<=
       y
       -8330559332786147/1461501637330902918203684832716283019655932542976)
    t_1
    (if (<= y 305000000000000013664634946977792) (+ t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (x - t);
	double tmp;
	if (y <= -5.7e-33) {
		tmp = t_1;
	} else if (y <= 3.05e+32) {
		tmp = t + 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)) * (x - t)
    if (y <= (-5.7d-33)) then
        tmp = t_1
    else if (y <= 3.05d+32) then
        tmp = t + 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)) * (x - t);
	double tmp;
	if (y <= -5.7e-33) {
		tmp = t_1;
	} else if (y <= 3.05e+32) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * (x - t)
	tmp = 0
	if y <= -5.7e-33:
		tmp = t_1
	elif y <= 3.05e+32:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(x - t))
	tmp = 0.0
	if (y <= -5.7e-33)
		tmp = t_1;
	elseif (y <= 3.05e+32)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * (x - t);
	tmp = 0.0;
	if (y <= -5.7e-33)
		tmp = t_1;
	elseif (y <= 3.05e+32)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8330559332786147/1461501637330902918203684832716283019655932542976], t$95$1, If[LessEqual[y, 305000000000000013664634946977792], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7000000000000003e-33 or 3.0500000000000001e32 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      4. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      7. lift--.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      10. lower-*.f64 37.7%

          \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a} - z} \]

   6. Applied rewrites 37.7%

      \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a - z}} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{a - z} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(t - x\right) \cdot y}{\color{blue}{a} - z} \]

      4. associate-/l* N/A

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto \frac{y}{a - z} \cdot \color{blue}{\left(t - x\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \frac{y}{a - z} \cdot \left(t - x\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(t - x\right) \]

      8. lift--.f64 N/A

         \[\leadsto \frac{y}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot \left(t - x\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{y}{z - a}\right)\right) \cdot \left(\color{blue}{t} - x\right) \]

      10. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{neg}\left(\frac{y}{z - a} \cdot \left(t - x\right)\right) \]

      11. distribute-rgt-neg-out N/A

          \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)} \]

      12. sub-negate-rev N/A

          \[\leadsto \frac{y}{z - a} \cdot \left(x - \color{blue}{t}\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{y}{z - a} \cdot \left(x - \color{blue}{t}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(x - t\right)} \]

      15. lower-/.f64 43.0%

          \[\leadsto \frac{y}{z - a} \cdot \left(\color{blue}{x} - t\right) \]

   8. Applied rewrites 43.0%

      \[\leadsto \frac{y}{z - a} \cdot \color{blue}{\left(x - t\right)} \]

   if -5.7000000000000003e-33 < y < 3.0500000000000001e32

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 46.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -1320000000000000000:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq \frac{4282608696416015}{594806763391113225119224999259960224052504080663757783622308743726376262864161749418067325798462540235919489516077189220181834098217962283116332232440957850313188336178983949577074563933719094748095678312940574882427099482751152035262839576139463233204818042181657565129506139525873664}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;a \leq 21999999999999999317033377606233706984290011770878336524836782038285013611044653717164210203423579837854736449536:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -1320000000000000000)
  (+ t x)
  (if (<=
       a
       4282608696416015/594806763391113225119224999259960224052504080663757783622308743726376262864161749418067325798462540235919489516077189220181834098217962283116332232440957850313188336178983949577074563933719094748095678312940574882427099482751152035262839576139463233204818042181657565129506139525873664)
    (/ (* t (- z y)) (- z a))
    (if (<=
         a
         21999999999999999317033377606233706984290011770878336524836782038285013611044653717164210203423579837854736449536)
      (* t (- 1 (/ y z)))
      (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.32e+18) {
		tmp = t + x;
	} else if (a <= 7.2e-270) {
		tmp = (t * (z - y)) / (z - a);
	} else if (a <= 2.2e+112) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t + 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 (a <= (-1.32d+18)) then
        tmp = t + x
    else if (a <= 7.2d-270) then
        tmp = (t * (z - y)) / (z - a)
    else if (a <= 2.2d+112) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = t + 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 (a <= -1.32e+18) {
		tmp = t + x;
	} else if (a <= 7.2e-270) {
		tmp = (t * (z - y)) / (z - a);
	} else if (a <= 2.2e+112) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.32e+18:
		tmp = t + x
	elif a <= 7.2e-270:
		tmp = (t * (z - y)) / (z - a)
	elif a <= 2.2e+112:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.32e+18)
		tmp = Float64(t + x);
	elseif (a <= 7.2e-270)
		tmp = Float64(Float64(t * Float64(z - y)) / Float64(z - a));
	elseif (a <= 2.2e+112)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.32e+18)
		tmp = t + x;
	elseif (a <= 7.2e-270)
		tmp = (t * (z - y)) / (z - a);
	elseif (a <= 2.2e+112)
		tmp = t * (1.0 - (y / z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1320000000000000000], N[(t + x), $MachinePrecision], If[LessEqual[a, 4282608696416015/594806763391113225119224999259960224052504080663757783622308743726376262864161749418067325798462540235919489516077189220181834098217962283116332232440957850313188336178983949577074563933719094748095678312940574882427099482751152035262839576139463233204818042181657565129506139525873664], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 21999999999999999317033377606233706984290011770878336524836782038285013611044653717164210203423579837854736449536], N[(t * N[(1 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.32e18 or 2.1999999999999999e112 < a

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]

   if -1.32e18 < a < 7.1999999999999996e-270

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(a - z\right) + \left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(a - z\right) + \left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - z} \cdot \left(x \cdot \left(a - z\right) + \left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{1}{a - z} \cdot \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right) + x \cdot \left(a - z\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right) + \color{blue}{\left(a - z\right) \cdot x}\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{a - z} \cdot \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right) - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{a - z} \cdot \left(\color{blue}{\left(y - z\right) \cdot \left(t - x\right)} - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right) \]

      10. lift--.f64 N/A

          \[\leadsto \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \color{blue}{\left(t - x\right)} - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right) \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - t\right)\right)\right)} - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right) \]

      12. distribute-rgt-neg-out N/A

          \[\leadsto \frac{1}{a - z} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(y - z\right) \cdot \left(x - t\right)\right)\right)} - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right) \]

      13. distribute-lft-neg-in N/A

          \[\leadsto \frac{1}{a - z} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right) \cdot \left(x - t\right)} - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right) \]

      14. lift--.f64 N/A

          \[\leadsto \frac{1}{a - z} \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right) \cdot \left(x - t\right) - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right) \]

      15. sub-negate-rev N/A

          \[\leadsto \frac{1}{a - z} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(x - t\right) - \left(\mathsf{neg}\left(\left(a - z\right)\right)\right) \cdot x\right) \]

      16. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a - z}\right), \left(z - y\right), \left(x - t\right), \left(\mathsf{neg}\left(\left(a - z\right)\right)\right), x\right)} \]

   3. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - a}\right), \left(z - y\right), \left(x - t\right), \left(z - a\right), x\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(z - y\right)}{z - a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot \left(z - y\right)}{\color{blue}{z - a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot \left(z - y\right)}{\color{blue}{z} - a} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{t \cdot \left(z - y\right)}{z - a} \]

      4. lower--.f64 39.9%

         \[\leadsto \frac{t \cdot \left(z - y\right)}{z - \color{blue}{a}} \]

   6. Applied rewrites 39.9%

      \[\leadsto \color{blue}{\frac{t \cdot \left(z - y\right)}{z - a}} \]

   if 7.1999999999999996e-270 < a < 2.1999999999999999e112

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 55.5%

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot t}{a - z}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)} \]

      3. sub-flip N/A

         \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(a - z\right)\right)}}\right)\right) \]

      6. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}\right)\right) \]

      7. sub-negate-rev N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      8. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(z - a\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)} \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      12. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      13. lift-*.f64 N/A

          \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      14. associate-/l* N/A

          \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      15. *-commutative N/A

          \[\leadsto x + \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

      16. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{t}{a - z}\right)\right) \cdot \left(y - z\right)} \]

   6. Applied rewrites 64.3%

      \[\leadsto \color{blue}{x - \frac{t}{z - a} \cdot \left(y - z\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 52.4%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   9. Applied rewrites 52.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   10. Taylor expanded in a around 0

       \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]
   11. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto t \cdot \left(1 - \frac{y}{\color{blue}{z}}\right) \]

       2. lower-/.f64 37.4%

          \[\leadsto t \cdot \left(1 - \frac{y}{z}\right) \]

   12. Applied rewrites 37.4%

       \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 45.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -1320000000000000000:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 21999999999999999317033377606233706984290011770878336524836782038285013611044653717164210203423579837854736449536:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -1320000000000000000)
  (+ t x)
  (if (<=
       a
       21999999999999999317033377606233706984290011770878336524836782038285013611044653717164210203423579837854736449536)
    (* t (- 1 (/ y z)))
    (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.32e+18) {
		tmp = t + x;
	} else if (a <= 2.2e+112) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t + 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 (a <= (-1.32d+18)) then
        tmp = t + x
    else if (a <= 2.2d+112) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = t + 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 (a <= -1.32e+18) {
		tmp = t + x;
	} else if (a <= 2.2e+112) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.32e+18:
		tmp = t + x
	elif a <= 2.2e+112:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.32e+18)
		tmp = Float64(t + x);
	elseif (a <= 2.2e+112)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.32e+18)
		tmp = t + x;
	elseif (a <= 2.2e+112)
		tmp = t * (1.0 - (y / z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1320000000000000000], N[(t + x), $MachinePrecision], If[LessEqual[a, 21999999999999999317033377606233706984290011770878336524836782038285013611044653717164210203423579837854736449536], N[(t * N[(1 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.32e18 or 2.1999999999999999e112 < a

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]

   if -1.32e18 < a < 2.1999999999999999e112

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 55.5%

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot t}{a - z}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)} \]

      3. sub-flip N/A

         \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(a - z\right)\right)}}\right)\right) \]

      6. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}\right)\right) \]

      7. sub-negate-rev N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      8. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(z - a\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)} \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      12. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      13. lift-*.f64 N/A

          \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      14. associate-/l* N/A

          \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      15. *-commutative N/A

          \[\leadsto x + \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

      16. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{t}{a - z}\right)\right) \cdot \left(y - z\right)} \]

   6. Applied rewrites 64.3%

      \[\leadsto \color{blue}{x - \frac{t}{z - a} \cdot \left(y - z\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 52.4%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   9. Applied rewrites 52.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   10. Taylor expanded in a around 0

       \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]
   11. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto t \cdot \left(1 - \frac{y}{\color{blue}{z}}\right) \]

       2. lower-/.f64 37.4%

          \[\leadsto t \cdot \left(1 - \frac{y}{z}\right) \]

   12. Applied rewrites 37.4%

       \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 305000000000000013664634946977792:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     y
     -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528)
  (* y (/ t (- a z)))
  (if (<= y 305000000000000013664634946977792)
    (+ t x)
    (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e+147) {
		tmp = y * (t / (a - z));
	} else if (y <= 3.05e+32) {
		tmp = t + x;
	} else {
		tmp = y * ((x - t) / z);
	}
	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 (y <= (-1.3d+147)) then
        tmp = y * (t / (a - z))
    else if (y <= 3.05d+32) then
        tmp = t + x
    else
        tmp = y * ((x - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e+147) {
		tmp = y * (t / (a - z));
	} else if (y <= 3.05e+32) {
		tmp = t + x;
	} else {
		tmp = y * ((x - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.3e+147:
		tmp = y * (t / (a - z))
	elif y <= 3.05e+32:
		tmp = t + x
	else:
		tmp = y * ((x - t) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.3e+147)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= 3.05e+32)
		tmp = Float64(t + x);
	else
		tmp = Float64(y * Float64(Float64(x - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.3e+147)
		tmp = y * (t / (a - z));
	elseif (y <= 3.05e+32)
		tmp = t + x;
	else
		tmp = y * ((x - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 305000000000000013664634946977792], N[(t + x), $MachinePrecision], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e147

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto y \cdot \frac{t}{a - \color{blue}{z}} \]

      2. lower--.f64 23.4%

         \[\leadsto y \cdot \frac{t}{a - z} \]

   7. Applied rewrites 23.4%

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]

   if -1.2999999999999999e147 < y < 3.0500000000000001e32

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]

   if 3.0500000000000001e32 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      3. lift-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      4. sub-div N/A

         \[\leadsto y \cdot \frac{t - x}{\color{blue}{a - z}} \]

      5. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\color{blue}{a} - z} \]

      6. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \]

      7. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - \color{blue}{z}} \]

      8. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \]

      9. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \]

      10. frac-2neg-rev N/A

          \[\leadsto y \cdot \frac{x - t}{\color{blue}{z - a}} \]

      11. div-flip N/A

          \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z - a}{x - t}}} \]

      12. metadata-eval N/A

          \[\leadsto y \cdot \frac{\mathsf{neg}\left(-1\right)}{\frac{\color{blue}{z - a}}{x - t}} \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto y \cdot \frac{\mathsf{neg}\left(-1\right)}{\color{blue}{\frac{z - a}{x - t}}} \]

      14. metadata-eval N/A

          \[\leadsto y \cdot \frac{1}{\frac{\color{blue}{z - a}}{x - t}} \]

      15. lower-unsound-/.f64 41.7%

          \[\leadsto y \cdot \frac{1}{\frac{z - a}{\color{blue}{x - t}}} \]

   6. Applied rewrites 41.7%

      \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z - a}{x - t}}} \]

   7. Taylor expanded in z around inf

      \[\leadsto y \cdot \frac{x - t}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto y \cdot \frac{x - t}{z} \]

      2. lower--.f64 25.6%

         \[\leadsto y \cdot \frac{x - t}{z} \]

   9. Applied rewrites 25.6%

      \[\leadsto y \cdot \frac{x - t}{\color{blue}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 42.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 94999999999999994488169700123549150507398221570116778180359052610744099441334856712192:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     y
     -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528)
  (* y (/ t (- a z)))
  (if (<=
       y
       94999999999999994488169700123549150507398221570116778180359052610744099441334856712192)
    (+ t x)
    (* y (/ x (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e+147) {
		tmp = y * (t / (a - z));
	} else if (y <= 9.5e+85) {
		tmp = t + x;
	} else {
		tmp = y * (x / (z - a));
	}
	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 (y <= (-1.3d+147)) then
        tmp = y * (t / (a - z))
    else if (y <= 9.5d+85) then
        tmp = t + x
    else
        tmp = y * (x / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e+147) {
		tmp = y * (t / (a - z));
	} else if (y <= 9.5e+85) {
		tmp = t + x;
	} else {
		tmp = y * (x / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.3e+147:
		tmp = y * (t / (a - z))
	elif y <= 9.5e+85:
		tmp = t + x
	else:
		tmp = y * (x / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.3e+147)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= 9.5e+85)
		tmp = Float64(t + x);
	else
		tmp = Float64(y * Float64(x / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.3e+147)
		tmp = y * (t / (a - z));
	elseif (y <= 9.5e+85)
		tmp = t + x;
	else
		tmp = y * (x / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 94999999999999994488169700123549150507398221570116778180359052610744099441334856712192], N[(t + x), $MachinePrecision], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e147

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto y \cdot \frac{t}{a - \color{blue}{z}} \]

      2. lower--.f64 23.4%

         \[\leadsto y \cdot \frac{t}{a - z} \]

   7. Applied rewrites 23.4%

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]

   if -1.2999999999999999e147 < y < 9.4999999999999994e85

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]

   if 9.4999999999999994e85 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      3. lift-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      4. sub-div N/A

         \[\leadsto y \cdot \frac{t - x}{\color{blue}{a - z}} \]

      5. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\color{blue}{a} - z} \]

      6. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \]

      7. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - \color{blue}{z}} \]

      8. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \]

      9. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \]

      10. frac-2neg-rev N/A

          \[\leadsto y \cdot \frac{x - t}{\color{blue}{z - a}} \]

      11. div-flip N/A

          \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z - a}{x - t}}} \]

      12. metadata-eval N/A

          \[\leadsto y \cdot \frac{\mathsf{neg}\left(-1\right)}{\frac{\color{blue}{z - a}}{x - t}} \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto y \cdot \frac{\mathsf{neg}\left(-1\right)}{\color{blue}{\frac{z - a}{x - t}}} \]

      14. metadata-eval N/A

          \[\leadsto y \cdot \frac{1}{\frac{\color{blue}{z - a}}{x - t}} \]

      15. lower-unsound-/.f64 41.7%

          \[\leadsto y \cdot \frac{1}{\frac{z - a}{\color{blue}{x - t}}} \]

   6. Applied rewrites 41.7%

      \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z - a}{x - t}}} \]

   7. Taylor expanded in x around inf

      \[\leadsto y \cdot \frac{x}{\color{blue}{z - a}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto y \cdot \frac{x}{z - \color{blue}{a}} \]

      2. lower--.f64 22.9%

         \[\leadsto y \cdot \frac{x}{z - a} \]

   9. Applied rewrites 22.9%

      \[\leadsto y \cdot \frac{x}{\color{blue}{z - a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 42.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 920000000000000017773994917407618219622006784:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* y (/ t (- a z)))))
  (if (<=
       y
       -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528)
    t_1
    (if (<= y 920000000000000017773994917407618219622006784)
      (+ t x)
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (y <= -1.3e+147) {
		tmp = t_1;
	} else if (y <= 9.2e+44) {
		tmp = t + 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 * (t / (a - z))
    if (y <= (-1.3d+147)) then
        tmp = t_1
    else if (y <= 9.2d+44) then
        tmp = t + 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 * (t / (a - z));
	double tmp;
	if (y <= -1.3e+147) {
		tmp = t_1;
	} else if (y <= 9.2e+44) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if y <= -1.3e+147:
		tmp = t_1
	elif y <= 9.2e+44:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.3e+147)
		tmp = t_1;
	elseif (y <= 9.2e+44)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (y <= -1.3e+147)
		tmp = t_1;
	elseif (y <= 9.2e+44)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528], t$95$1, If[LessEqual[y, 920000000000000017773994917407618219622006784], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e147 or 9.2000000000000002e44 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto y \cdot \frac{t}{a - \color{blue}{z}} \]

      2. lower--.f64 23.4%

         \[\leadsto y \cdot \frac{t}{a - z} \]

   7. Applied rewrites 23.4%

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]

   if -1.2999999999999999e147 < y < 9.2000000000000002e44

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 41.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{if}\;y \leq -3150000000000000064284969159874311689514361096988281839886662509860462691717156695854977457588840479124276687248905910808558607317955988038119305882107904:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 11199999999999999266636761500785285580346219368070827845276274434151467108484710924288:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* y (- x t)) z)))
  (if (<=
       y
       -3150000000000000064284969159874311689514361096988281839886662509860462691717156695854977457588840479124276687248905910808558607317955988038119305882107904)
    t_1
    (if (<=
         y
         11199999999999999266636761500785285580346219368070827845276274434151467108484710924288)
      (+ t x)
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double tmp;
	if (y <= -3.15e+153) {
		tmp = t_1;
	} else if (y <= 1.12e+85) {
		tmp = t + 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 * (x - t)) / z
    if (y <= (-3.15d+153)) then
        tmp = t_1
    else if (y <= 1.12d+85) then
        tmp = t + 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 * (x - t)) / z;
	double tmp;
	if (y <= -3.15e+153) {
		tmp = t_1;
	} else if (y <= 1.12e+85) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (x - t)) / z
	tmp = 0
	if y <= -3.15e+153:
		tmp = t_1
	elif y <= 1.12e+85:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / z)
	tmp = 0.0
	if (y <= -3.15e+153)
		tmp = t_1;
	elseif (y <= 1.12e+85)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (x - t)) / z;
	tmp = 0.0;
	if (y <= -3.15e+153)
		tmp = t_1;
	elseif (y <= 1.12e+85)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -3150000000000000064284969159874311689514361096988281839886662509860462691717156695854977457588840479124276687248905910808558607317955988038119305882107904], t$95$1, If[LessEqual[y, 11199999999999999266636761500785285580346219368070827845276274434151467108484710924288], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1500000000000001e153 or 1.1199999999999999e85 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      3. lift-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      4. sub-div N/A

         \[\leadsto y \cdot \frac{t - x}{\color{blue}{a - z}} \]

      5. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\color{blue}{a} - z} \]

      6. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \]

      7. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - \color{blue}{z}} \]

      8. sub-negate-rev N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \]

      9. lift--.f64 N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \]

      10. frac-2neg-rev N/A

          \[\leadsto y \cdot \frac{x - t}{\color{blue}{z - a}} \]

      11. div-flip N/A

          \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z - a}{x - t}}} \]

      12. metadata-eval N/A

          \[\leadsto y \cdot \frac{\mathsf{neg}\left(-1\right)}{\frac{\color{blue}{z - a}}{x - t}} \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto y \cdot \frac{\mathsf{neg}\left(-1\right)}{\color{blue}{\frac{z - a}{x - t}}} \]

      14. metadata-eval N/A

          \[\leadsto y \cdot \frac{1}{\frac{\color{blue}{z - a}}{x - t}} \]

      15. lower-unsound-/.f64 41.7%

          \[\leadsto y \cdot \frac{1}{\frac{z - a}{\color{blue}{x - t}}} \]

   6. Applied rewrites 41.7%

      \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z - a}{x - t}}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      3. lower--.f64 23.4%

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

   9. Applied rewrites 23.4%

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]

   if -3.1500000000000001e153 < y < 1.1199999999999999e85

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 40.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \frac{t \cdot y}{a - z}\\ \mathbf{if}\;y \leq -50999999999999999913463833549768098307226747205863239969121231761549111670275507377143393897037216678997213998797862879886381730568557053240719466212871897088:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 180000000000000016537542150923784084643392395473784873467797301027047301048967180400844950344295254010622589839497394619678720:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* t y) (- a z))))
  (if (<=
       y
       -50999999999999999913463833549768098307226747205863239969121231761549111670275507377143393897037216678997213998797862879886381730568557053240719466212871897088)
    t_1
    (if (<=
         y
         180000000000000016537542150923784084643392395473784873467797301027047301048967180400844950344295254010622589839497394619678720)
      (+ t x)
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / (a - z);
	double tmp;
	if (y <= -5.1e+157) {
		tmp = t_1;
	} else if (y <= 1.8e+125) {
		tmp = t + 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 = (t * y) / (a - z)
    if (y <= (-5.1d+157)) then
        tmp = t_1
    else if (y <= 1.8d+125) then
        tmp = t + 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 = (t * y) / (a - z);
	double tmp;
	if (y <= -5.1e+157) {
		tmp = t_1;
	} else if (y <= 1.8e+125) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / (a - z)
	tmp = 0
	if y <= -5.1e+157:
		tmp = t_1
	elif y <= 1.8e+125:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / Float64(a - z))
	tmp = 0.0
	if (y <= -5.1e+157)
		tmp = t_1;
	elseif (y <= 1.8e+125)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / (a - z);
	tmp = 0.0;
	if (y <= -5.1e+157)
		tmp = t_1;
	elseif (y <= 1.8e+125)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -50999999999999999913463833549768098307226747205863239969121231761549111670275507377143393897037216678997213998797862879886381730568557053240719466212871897088], t$95$1, If[LessEqual[y, 180000000000000016537542150923784084643392395473784873467797301027047301048967180400844950344295254010622589839497394619678720], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1e157 or 1.8000000000000002e125 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.6%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - \color{blue}{z}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - z} \]

      3. lower--.f64 21.6%

         \[\leadsto \frac{t \cdot y}{a - z} \]

   7. Applied rewrites 21.6%

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]

   if -5.1e157 < y < 1.8000000000000002e125

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 39.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 295000000000000004344791912536394558108844251514140744190522484346814426623697136233468449779680802677124290236833767055363244594916579383928253056153621501775798717408760314312729365944671056842509684572160:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* t (/ y a))))
  (if (<=
       y
       -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528)
    t_1
    (if (<=
         y
         295000000000000004344791912536394558108844251514140744190522484346814426623697136233468449779680802677124290236833767055363244594916579383928253056153621501775798717408760314312729365944671056842509684572160)
      (+ t x)
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -1.3e+147) {
		tmp = t_1;
	} else if (y <= 2.95e+206) {
		tmp = t + 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 = t * (y / a)
    if (y <= (-1.3d+147)) then
        tmp = t_1
    else if (y <= 2.95d+206) then
        tmp = t + 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 = t * (y / a);
	double tmp;
	if (y <= -1.3e+147) {
		tmp = t_1;
	} else if (y <= 2.95e+206) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -1.3e+147:
		tmp = t_1
	elif y <= 2.95e+206:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -1.3e+147)
		tmp = t_1;
	elseif (y <= 2.95e+206)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -1.3e+147)
		tmp = t_1;
	elseif (y <= 2.95e+206)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1299999999999999935905125042608528024070569499276670001017534653649590958815701108287851124338230693249026350807211601062882461692784770903103766528], t$95$1, If[LessEqual[y, 295000000000000004344791912536394558108844251514140744190522484346814426623697136233468449779680802677124290236833767055363244594916579383928253056153621501775798717408760314312729365944671056842509684572160], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e147 or 2.95e206 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 55.5%

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot t}{a - z}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)} \]

      3. sub-flip N/A

         \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(a - z\right)\right)}}\right)\right) \]

      6. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}\right)\right) \]

      7. sub-negate-rev N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      8. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(z - a\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)} \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      12. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      13. lift-*.f64 N/A

          \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      14. associate-/l* N/A

          \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      15. *-commutative N/A

          \[\leadsto x + \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

      16. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{t}{a - z}\right)\right) \cdot \left(y - z\right)} \]

   6. Applied rewrites 64.3%

      \[\leadsto \color{blue}{x - \frac{t}{z - a} \cdot \left(y - z\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 52.4%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   9. Applied rewrites 52.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   10. Taylor expanded in z around 0

       \[\leadsto t \cdot \frac{y}{\color{blue}{a}} \]
   11. Step-by-step derivation

       1. lower-/.f64 18.9%

          \[\leadsto t \cdot \frac{y}{a} \]

   12. Applied rewrites 18.9%

       \[\leadsto t \cdot \frac{y}{\color{blue}{a}} \]

   if -1.2999999999999999e147 < y < 2.95e206

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 35.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 295000000000000004344791912536394558108844251514140744190522484346814426623697136233468449779680802677124290236833767055363244594916579383928253056153621501775798717408760314312729365944671056842509684572160:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     y
     295000000000000004344791912536394558108844251514140744190522484346814426623697136233468449779680802677124290236833767055363244594916579383928253056153621501775798717408760314312729365944671056842509684572160)
  (+ t x)
  (/ (* t y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.95e+206) {
		tmp = t + x;
	} else {
		tmp = (t * y) / a;
	}
	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 (y <= 2.95d+206) then
        tmp = t + x
    else
        tmp = (t * y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.95e+206) {
		tmp = t + x;
	} else {
		tmp = (t * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.95e+206:
		tmp = t + x
	else:
		tmp = (t * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.95e+206)
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(t * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.95e+206)
		tmp = t + x;
	else
		tmp = (t * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 295000000000000004344791912536394558108844251514140744190522484346814426623697136233468449779680802677124290236833767055363244594916579383928253056153621501775798717408760314312729365944671056842509684572160], N[(t + x), $MachinePrecision], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.95e206

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 20.0%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 20.0%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

         \[\leadsto \left(-x\right) + x \]

   9. Applied rewrites 2.8%

      \[\leadsto \color{blue}{\left(-x\right) + x} \]

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 34.3%

       \[\leadsto t + x \]

   if 2.95e206 < y

   1. Initial program 67.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 55.5%

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot t}{a - z}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)} \]

      3. sub-flip N/A

         \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{a - z}\right)\right)\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}}\right)\right)\right)\right) \]

      5. distribute-neg-frac2 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(a - z\right)\right)}}\right)\right) \]

      6. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}\right)\right) \]

      7. sub-negate-rev N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      8. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(y - z\right) \cdot t}{\color{blue}{z - a}}\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\left(z - a\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)} \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      12. lift--.f64 N/A

          \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{a - z}} \]

      13. lift-*.f64 N/A

          \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      14. associate-/l* N/A

          \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      15. *-commutative N/A

          \[\leadsto x + \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

      16. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{t}{a - z}\right)\right) \cdot \left(y - z\right)} \]

   6. Applied rewrites 64.3%

      \[\leadsto \color{blue}{x - \frac{t}{z - a} \cdot \left(y - z\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 52.4%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   9. Applied rewrites 52.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{t \cdot y}{\color{blue}{a}} \]
   11. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{t \cdot y}{a} \]

       2. lower-*.f64 16.6%

          \[\leadsto \frac{t \cdot y}{a} \]

   12. Applied rewrites 16.6%

       \[\leadsto \frac{t \cdot y}{\color{blue}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 34.3% accurate, 7.3× speedup

Math

\[t + x \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ t x))

C

double code(double x, double y, double z, double t, double a) {
	return t + x;
}

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 = t + x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t + x;
}

Python

def code(x, y, z, t, a):
	return t + x

Julia

function code(x, y, z, t, a)
	return Float64(t + x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t + x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(t + x), $MachinePrecision]

Derivation

1. Initial program 67.6%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 20.0%

      \[\leadsto x + \left(t - \color{blue}{x}\right) \]

4. Applied rewrites 20.0%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
6. Step-by-step derivation

   1. lower-*.f64 2.8%

      \[\leadsto x + -1 \cdot x \]

7. Applied rewrites 2.8%

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
8. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + -1 \cdot x} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   3. lower-+.f64 2.8%

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   4. lift-*.f64 N/A

      \[\leadsto -1 \cdot x + x \]

   5. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

   6. lower-neg.f64 2.8%

      \[\leadsto \left(-x\right) + x \]

9. Applied rewrites 2.8%

   \[\leadsto \color{blue}{\left(-x\right) + x} \]

10. Taylor expanded in x around 0

    \[\leadsto t + x \]
11. Step-by-step derivation

12. Applied rewrites 34.3%

    \[\leadsto t + x \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y z) (- t x)) (- a z))))