Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.6% → 95.3%

Time: 23.4s

Alternatives: 15

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.6% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq \frac{-4825645764048353}{12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - t\right) \cdot \left(\frac{-1}{a - z} \cdot \left(y - z\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<=
       t_1
       -4825645764048353/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624)
    (+ x (* (- x t) (/ (- z y) (- a z))))
    (if (<= t_1 0)
      (+ t (/ (- a y) (/ z (- t x))))
      (+ x (* (- x t) (* (/ -1 (- a z)) (- y z))))))))

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 <= -4e-301) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else {
		tmp = x + ((x - t) * ((-1.0 / (a - z)) * (y - 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-4d-301)) then
        tmp = x + ((x - t) * ((z - y) / (a - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t + ((a - y) / (z / (t - x)))
    else
        tmp = x + ((x - t) * (((-1.0d0) / (a - z)) * (y - z)))
    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 + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -4e-301) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else {
		tmp = x + ((x - t) * ((-1.0 / (a - z)) * (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -4e-301:
		tmp = x + ((x - t) * ((z - y) / (a - z)))
	elif t_1 <= 0.0:
		tmp = t + ((a - y) / (z / (t - x)))
	else:
		tmp = x + ((x - t) * ((-1.0 / (a - z)) * (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -4e-301)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(-1.0 / Float64(a - z)) * Float64(y - z))));
	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 <= -4e-301)
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	elseif (t_1 <= 0.0)
		tmp = t + ((a - y) / (z / (t - x)));
	else
		tmp = x + ((x - t) * ((-1.0 / (a - z)) * (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4825645764048353/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0], N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(-1 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.0000000000000003e-301

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 83.6%

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

   3. Applied rewrites 83.6%

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

   if -4.0000000000000003e-301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

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

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

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

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. div-flip-rev N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

          \[\leadsto t + \frac{1}{\frac{\frac{z}{t - x}}{\color{blue}{a - y}}} \]

      19. div-flip-rev N/A

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

      20. lower-/.f64 N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 52.8%

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

   8. Applied rewrites 52.8%

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

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

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 83.5%

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

   3. Applied rewrites 83.5%

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

Alternative 2: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq \frac{-4825645764048353}{12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- x t) (/ (- z y) (- a z)))))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<=
       t_2
       -4825645764048353/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624)
    t_1
    (if (<= t_2 0) (+ t (/ (- a y) (/ z (- t x)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-301) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((a - y) / (z / (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) :: t_2
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / (a - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-4d-301)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + ((a - y) / (z / (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 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-301) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / (a - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -4e-301:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + ((a - y) / (z / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-301)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / (a - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -4e-301)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + ((a - y) / (z / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4825645764048353/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624], t$95$1, If[LessEqual[t$95$2, 0], N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.0000000000000003e-301 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 83.6%

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

   3. Applied rewrites 83.6%

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

   if -4.0000000000000003e-301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

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

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

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

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. div-flip-rev N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

          \[\leadsto t + \frac{1}{\frac{\frac{z}{t - x}}{\color{blue}{a - y}}} \]

      19. div-flip-rev N/A

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

      20. lower-/.f64 N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 52.8%

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

   8. Applied rewrites 52.8%

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

Alternative 3: 95.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq \frac{-4825645764048353}{12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- x t) (/ (- z y) (- a z)))))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<=
       t_2
       -4825645764048353/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624)
    t_1
    (if (<= t_2 0) (- t (* (/ (- t x) z) (- y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-301) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / (a - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-4d-301)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t - (((t - x) / z) * (y - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-301) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / (a - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -4e-301:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t - (((t - x) / z) * (y - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-301)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / (a - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -4e-301)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t - (((t - x) / z) * (y - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4825645764048353/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624], t$95$1, If[LessEqual[t$95$2, 0], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.0000000000000003e-301 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 83.6%

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

   3. Applied rewrites 83.6%

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

   if -4.0000000000000003e-301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. div-sub N/A

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

      9. sub-negate N/A

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

      10. sub-negate-rev N/A

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

      11. lift-*.f64 N/A

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

      12. associate-/l* N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

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

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

      16. lower-*.f64 N/A

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

   6. Applied rewrites 52.7%

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

Alternative 4: 78.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -138000000000000004093153144235505338658701474917114395344649268042739089770820652773162085813763379863345321602613064765749952472154112:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8999999999999999844710088704:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{6859310779502913}{762145642166990290864647761179972242614403843424065222377723867096038022172794340849684107193235344521442121855812163792833978437326241529856}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2050000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- y z) (/ t (- a z)))))
       (t_2 (+ t (* (- x t) (/ (- y a) z)))))
  (if (<=
       z
       -138000000000000004093153144235505338658701474917114395344649268042739089770820652773162085813763379863345321602613064765749952472154112)
    t_2
    (if (<= z -8999999999999999844710088704)
      t_1
      (if (<=
           z
           6859310779502913/762145642166990290864647761179972242614403843424065222377723867096038022172794340849684107193235344521442121855812163792833978437326241529856)
        (+ x (/ (* y (- t x)) (- a z)))
        (if (<= z 2050000000000) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double t_2 = t + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -1.38e+134) {
		tmp = t_2;
	} else if (z <= -9e+27) {
		tmp = t_1;
	} else if (z <= 9e-126) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 2050000000000.0) {
		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 = x + ((y - z) * (t / (a - z)))
    t_2 = t + ((x - t) * ((y - a) / z))
    if (z <= (-1.38d+134)) then
        tmp = t_2
    else if (z <= (-9d+27)) then
        tmp = t_1
    else if (z <= 9d-126) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 2050000000000.0d0) 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 = x + ((y - z) * (t / (a - z)));
	double t_2 = t + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -1.38e+134) {
		tmp = t_2;
	} else if (z <= -9e+27) {
		tmp = t_1;
	} else if (z <= 9e-126) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 2050000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	t_2 = t + ((x - t) * ((y - a) / z))
	tmp = 0
	if z <= -1.38e+134:
		tmp = t_2
	elif z <= -9e+27:
		tmp = t_1
	elif z <= 9e-126:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 2050000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	t_2 = Float64(t + Float64(Float64(x - t) * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -1.38e+134)
		tmp = t_2;
	elseif (z <= -9e+27)
		tmp = t_1;
	elseif (z <= 9e-126)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 2050000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	t_2 = t + ((x - t) * ((y - a) / z));
	tmp = 0.0;
	if (z <= -1.38e+134)
		tmp = t_2;
	elseif (z <= -9e+27)
		tmp = t_1;
	elseif (z <= 9e-126)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 2050000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -138000000000000004093153144235505338658701474917114395344649268042739089770820652773162085813763379863345321602613064765749952472154112], t$95$2, If[LessEqual[z, -8999999999999999844710088704], t$95$1, If[LessEqual[z, 6859310779502913/762145642166990290864647761179972242614403843424065222377723867096038022172794340849684107193235344521442121855812163792833978437326241529856], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2050000000000], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.38e134 or 2.05e12 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   if -1.38e134 < z < -8.9999999999999998e27 or 9.0000000000000005e-126 < z < 2.05e12

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.3%

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

   if -8.9999999999999998e27 < z < 9.0000000000000005e-126

   1. Initial program 79.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 54.7%

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

   4. Applied rewrites 54.7%

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

Alternative 5: 78.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -30000000000000000948382466048:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{520997997575091}{2977131414714805823690030317109266572712515013375254774912983855843898524112477893944078543723575564536883288499266264815757728270805630976}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2050000000000:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ t (* (- x t) (/ (- y a) z)))))
  (if (<= z -30000000000000000948382466048)
    t_1
    (if (<=
         z
         520997997575091/2977131414714805823690030317109266572712515013375254774912983855843898524112477893944078543723575564536883288499266264815757728270805630976)
      (+ x (/ (* y (- t x)) (- a z)))
      (if (<= z 2050000000000) (+ x (/ (* t (- y z)) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -3e+28) {
		tmp = t_1;
	} else if (z <= 1.75e-124) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 2050000000000.0) {
		tmp = x + ((t * (y - z)) / (a - z));
	} 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 + ((x - t) * ((y - a) / z))
    if (z <= (-3d+28)) then
        tmp = t_1
    else if (z <= 1.75d-124) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 2050000000000.0d0) then
        tmp = x + ((t * (y - z)) / (a - z))
    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 + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -3e+28) {
		tmp = t_1;
	} else if (z <= 1.75e-124) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 2050000000000.0) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) * ((y - a) / z))
	tmp = 0
	if z <= -3e+28:
		tmp = t_1
	elif z <= 1.75e-124:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 2050000000000.0:
		tmp = x + ((t * (y - z)) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -3e+28)
		tmp = t_1;
	elseif (z <= 1.75e-124)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 2050000000000.0)
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) * ((y - a) / z));
	tmp = 0.0;
	if (z <= -3e+28)
		tmp = t_1;
	elseif (z <= 1.75e-124)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 2050000000000.0)
		tmp = x + ((t * (y - z)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -30000000000000000948382466048], t$95$1, If[LessEqual[z, 520997997575091/2977131414714805823690030317109266572712515013375254774912983855843898524112477893944078543723575564536883288499266264815757728270805630976], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2050000000000], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000001e28 or 2.05e12 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   if -3.0000000000000001e28 < z < 1.7499999999999999e-124

   1. Initial program 79.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 54.7%

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

   4. Applied rewrites 54.7%

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

   if 1.7499999999999999e-124 < z < 2.05e12

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 55.5%

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

   4. Applied rewrites 55.5%

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

Alternative 6: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t \cdot \left(y - z\right)}{a - z}\\ t_2 := t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -85999999999999998896126747031913950778816040297344791989994017316795973699655221479323918150864890160471663734042053387896069831000064:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq \frac{-6902436815285787}{3255866422304616344765552632188114158762089024568314531443485259650408807528140659922574316831813618526821245406949824436469141432675471230646169947427163108444901161872077421124549944292877941762189949285100879873872435565174053364826112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{6787859625549757}{23817051317718446589520242536874132581700120107002038199303870846751188192899823151552628349788604516295066307994130118526061826166445047808}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2050000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (/ (* t (- y z)) (- a z))))
       (t_2 (+ t (* (- x t) (/ (- y a) z)))))
  (if (<=
       z
       -85999999999999998896126747031913950778816040297344791989994017316795973699655221479323918150864890160471663734042053387896069831000064)
    t_2
    (if (<=
         z
         -6902436815285787/3255866422304616344765552632188114158762089024568314531443485259650408807528140659922574316831813618526821245406949824436469141432675471230646169947427163108444901161872077421124549944292877941762189949285100879873872435565174053364826112)
      t_1
      (if (<=
           z
           6787859625549757/23817051317718446589520242536874132581700120107002038199303870846751188192899823151552628349788604516295066307994130118526061826166445047808)
        (+ x (* (- t x) (/ y a)))
        (if (<= z 2050000000000) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * (y - z)) / (a - z));
	double t_2 = t + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -8.6e+133) {
		tmp = t_2;
	} else if (z <= -2.12e-222) {
		tmp = t_1;
	} else if (z <= 2.85e-124) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2050000000000.0) {
		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 = x + ((t * (y - z)) / (a - z))
    t_2 = t + ((x - t) * ((y - a) / z))
    if (z <= (-8.6d+133)) then
        tmp = t_2
    else if (z <= (-2.12d-222)) then
        tmp = t_1
    else if (z <= 2.85d-124) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 2050000000000.0d0) 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 = x + ((t * (y - z)) / (a - z));
	double t_2 = t + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -8.6e+133) {
		tmp = t_2;
	} else if (z <= -2.12e-222) {
		tmp = t_1;
	} else if (z <= 2.85e-124) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2050000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * (y - z)) / (a - z))
	t_2 = t + ((x - t) * ((y - a) / z))
	tmp = 0
	if z <= -8.6e+133:
		tmp = t_2
	elif z <= -2.12e-222:
		tmp = t_1
	elif z <= 2.85e-124:
		tmp = x + ((t - x) * (y / a))
	elif z <= 2050000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)))
	t_2 = Float64(t + Float64(Float64(x - t) * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -8.6e+133)
		tmp = t_2;
	elseif (z <= -2.12e-222)
		tmp = t_1;
	elseif (z <= 2.85e-124)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 2050000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * (y - z)) / (a - z));
	t_2 = t + ((x - t) * ((y - a) / z));
	tmp = 0.0;
	if (z <= -8.6e+133)
		tmp = t_2;
	elseif (z <= -2.12e-222)
		tmp = t_1;
	elseif (z <= 2.85e-124)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 2050000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -85999999999999998896126747031913950778816040297344791989994017316795973699655221479323918150864890160471663734042053387896069831000064], t$95$2, If[LessEqual[z, -6902436815285787/3255866422304616344765552632188114158762089024568314531443485259650408807528140659922574316831813618526821245406949824436469141432675471230646169947427163108444901161872077421124549944292877941762189949285100879873872435565174053364826112], t$95$1, If[LessEqual[z, 6787859625549757/23817051317718446589520242536874132581700120107002038199303870846751188192899823151552628349788604516295066307994130118526061826166445047808], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2050000000000], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5999999999999999e133 or 2.05e12 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   if -8.5999999999999999e133 < z < -2.1200000000000001e-222 or 2.8499999999999999e-124 < z < 2.05e12

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 55.5%

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

   4. Applied rewrites 55.5%

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

   if -2.1200000000000001e-222 < z < 2.8499999999999999e-124

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 47.8%

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

   6. Applied rewrites 47.8%

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

Alternative 7: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq \frac{-5099505842092539}{121416805764108066932466369176469931665150427440758720078238275608681517825325531136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{3266710722441009}{340282366920938463463374607431768211456}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ t (* (- x t) (/ (- y a) z)))))
  (if (<=
       z
       -5099505842092539/121416805764108066932466369176469931665150427440758720078238275608681517825325531136)
    t_1
    (if (<=
         z
         3266710722441009/340282366920938463463374607431768211456)
      (+ x (* (- t x) (/ y a)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -4.2e-68) {
		tmp = t_1;
	} else if (z <= 9.6e-24) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) * ((y - a) / z))
    if (z <= (-4.2d-68)) then
        tmp = t_1
    else if (z <= 9.6d-24) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) * ((y - a) / z));
	double tmp;
	if (z <= -4.2e-68) {
		tmp = t_1;
	} else if (z <= 9.6e-24) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) * ((y - a) / z))
	tmp = 0
	if z <= -4.2e-68:
		tmp = t_1
	elif z <= 9.6e-24:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -4.2e-68)
		tmp = t_1;
	elseif (z <= 9.6e-24)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) * ((y - a) / z));
	tmp = 0.0;
	if (z <= -4.2e-68)
		tmp = t_1;
	elseif (z <= 9.6e-24)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5099505842092539/121416805764108066932466369176469931665150427440758720078238275608681517825325531136], t$95$1, If[LessEqual[z, 3266710722441009/340282366920938463463374607431768211456], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e-68 or 9.5999999999999993e-24 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   if -4.2000000000000002e-68 < z < 9.5999999999999993e-24

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 47.8%

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

   6. Applied rewrites 47.8%

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

Alternative 8: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -620000000000000003212457350491329463065743578269686069966198026144487760686059902922307079391982416738548459206260587836559484403366779647513569787150099426184693122343108608:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq \frac{-2676089423823675}{5575186299632655785383929568162090376495104}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3299999999999999905342712846524970004371795945284041350065477064438034921550654301697269184162914950315529134220983140352:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- y z) (/ t a)))))
  (if (<=
       a
       -620000000000000003212457350491329463065743578269686069966198026144487760686059902922307079391982416738548459206260587836559484403366779647513569787150099426184693122343108608)
    t_1
    (if (<=
         a
         -2676089423823675/5575186299632655785383929568162090376495104)
      (+ x (* (- t x) (/ y a)))
      (if (<=
           a
           3299999999999999905342712846524970004371795945284041350065477064438034921550654301697269184162914950315529134220983140352)
        (+ t (* (- x t) (/ y z)))
        t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -6.2e+173) {
		tmp = t_1;
	} else if (a <= -4.8e-28) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.3e+120) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / a))
    if (a <= (-6.2d+173)) then
        tmp = t_1
    else if (a <= (-4.8d-28)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 3.3d+120) then
        tmp = t + ((x - t) * (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -6.2e+173) {
		tmp = t_1;
	} else if (a <= -4.8e-28) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.3e+120) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -6.2e+173:
		tmp = t_1
	elif a <= -4.8e-28:
		tmp = x + ((t - x) * (y / a))
	elif a <= 3.3e+120:
		tmp = t + ((x - t) * (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -6.2e+173)
		tmp = t_1;
	elseif (a <= -4.8e-28)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 3.3e+120)
		tmp = Float64(t + Float64(Float64(x - t) * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -6.2e+173)
		tmp = t_1;
	elseif (a <= -4.8e-28)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 3.3e+120)
		tmp = t + ((x - t) * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -620000000000000003212457350491329463065743578269686069966198026144487760686059902922307079391982416738548459206260587836559484403366779647513569787150099426184693122343108608], t$95$1, If[LessEqual[a, -2676089423823675/5575186299632655785383929568162090376495104], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3299999999999999905342712846524970004371795945284041350065477064438034921550654301697269184162914950315529134220983140352], N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.2e173 or 3.2999999999999999e120 < a

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 43.5%

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

   if -6.2e173 < a < -4.8000000000000004e-28

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 47.8%

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

   6. Applied rewrites 47.8%

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

   if -4.8000000000000004e-28 < a < 3.2999999999999999e120

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 49.5%

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

   9. Applied rewrites 49.5%

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

Alternative 9: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq \frac{-5099505842092539}{121416805764108066932466369176469931665150427440758720078238275608681517825325531136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{3266710722441009}{340282366920938463463374607431768211456}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ t (* (- x t) (/ y z)))))
  (if (<=
       z
       -5099505842092539/121416805764108066932466369176469931665150427440758720078238275608681517825325531136)
    t_1
    (if (<=
         z
         3266710722441009/340282366920938463463374607431768211456)
      (+ x (* (- t x) (/ y a)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) * (y / z));
	double tmp;
	if (z <= -4.2e-68) {
		tmp = t_1;
	} else if (z <= 9.6e-24) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) * (y / z))
    if (z <= (-4.2d-68)) then
        tmp = t_1
    else if (z <= 9.6d-24) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) * (y / z));
	double tmp;
	if (z <= -4.2e-68) {
		tmp = t_1;
	} else if (z <= 9.6e-24) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) * (y / z))
	tmp = 0
	if z <= -4.2e-68:
		tmp = t_1
	elif z <= 9.6e-24:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) * Float64(y / z)))
	tmp = 0.0
	if (z <= -4.2e-68)
		tmp = t_1;
	elseif (z <= 9.6e-24)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) * (y / z));
	tmp = 0.0;
	if (z <= -4.2e-68)
		tmp = t_1;
	elseif (z <= 9.6e-24)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5099505842092539/121416805764108066932466369176469931665150427440758720078238275608681517825325531136], t$95$1, If[LessEqual[z, 3266710722441009/340282366920938463463374607431768211456], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e-68 or 9.5999999999999993e-24 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 49.5%

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

   9. Applied rewrites 49.5%

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

   if -4.2000000000000002e-68 < z < 9.5999999999999993e-24

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 47.8%

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

   6. Applied rewrites 47.8%

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

Alternative 10: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq \frac{-8742010015015781}{971334446112864535459730953411759453321203419526069760625906204869452142602604249088}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{1725436586697641}{53919893334301279589334030174039261347274288845081144962207220498432}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ t (* (- x t) (/ y z)))))
  (if (<=
       z
       -8742010015015781/971334446112864535459730953411759453321203419526069760625906204869452142602604249088)
    t_1
    (if (<=
         z
         1725436586697641/53919893334301279589334030174039261347274288845081144962207220498432)
      (+ x (/ (* t y) a))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) * (y / z));
	double tmp;
	if (z <= -9e-69) {
		tmp = t_1;
	} else if (z <= 3.2e-53) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) * (y / z))
    if (z <= (-9d-69)) then
        tmp = t_1
    else if (z <= 3.2d-53) then
        tmp = x + ((t * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) * (y / z));
	double tmp;
	if (z <= -9e-69) {
		tmp = t_1;
	} else if (z <= 3.2e-53) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) * (y / z))
	tmp = 0
	if z <= -9e-69:
		tmp = t_1
	elif z <= 3.2e-53:
		tmp = x + ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) * Float64(y / z)))
	tmp = 0.0
	if (z <= -9e-69)
		tmp = t_1;
	elseif (z <= 3.2e-53)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) * (y / z));
	tmp = 0.0;
	if (z <= -9e-69)
		tmp = t_1;
	elseif (z <= 3.2e-53)
		tmp = x + ((t * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8742010015015781/971334446112864535459730953411759453321203419526069760625906204869452142602604249088], t$95$1, If[LessEqual[z, 1725436586697641/53919893334301279589334030174039261347274288845081144962207220498432], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000002e-69 or 3.2000000000000001e-53 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 49.5%

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

   9. Applied rewrites 49.5%

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

   if -9.0000000000000002e-69 < z < 3.2000000000000001e-53

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + \frac{t \cdot y}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 37.8%

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

   7. Applied rewrites 37.8%

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

Alternative 11: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -1480000000000000000:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq \frac{6877123763982683}{237142198758023568227473377297792835283496928595231875152809132048206089502588928}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -1480000000000000000)
  (+ x (/ (* t y) a))
  (if (<=
       a
       6877123763982683/237142198758023568227473377297792835283496928595231875152809132048206089502588928)
    (+ t (/ (* y (- x t)) z))
    (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.48e+18) {
		tmp = x + ((t * y) / a);
	} else if (a <= 2.9e-65) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = x + t;
	}
	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 <= (-1.48d+18)) then
        tmp = x + ((t * y) / a)
    else if (a <= 2.9d-65) then
        tmp = t + ((y * (x - t)) / z)
    else
        tmp = x + t
    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 <= -1.48e+18) {
		tmp = x + ((t * y) / a);
	} else if (a <= 2.9e-65) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.48e+18:
		tmp = x + ((t * y) / a)
	elif a <= 2.9e-65:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.48e+18)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (a <= 2.9e-65)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.48e+18)
		tmp = x + ((t * y) / a);
	elseif (a <= 2.9e-65)
		tmp = t + ((y * (x - t)) / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1480000000000000000], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6877123763982683/237142198758023568227473377297792835283496928595231875152809132048206089502588928], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.48e18

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + \frac{t \cdot y}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 37.8%

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

   7. Applied rewrites 37.8%

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

   if -1.48e18 < a < 2.8999999999999998e-65

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

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

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. mult-flip-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.1%

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

   9. Applied rewrites 45.1%

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

   if 2.8999999999999998e-65 < a

   1. Initial program 79.6%

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

   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 x around 0

      \[\leadsto x + t \]
   9. Step-by-step derivation

   10. Applied rewrites 34.3%

       \[\leadsto x + t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{if}\;z \leq -28000000000000001471563169792:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2320000000000000000000:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ t (/ (* x (- y a)) z))))
  (if (<= z -28000000000000001471563169792)
    t_1
    (if (<= z 2320000000000000000000) (+ x (/ (* t y) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * (y - a)) / z);
	double tmp;
	if (z <= -2.8e+28) {
		tmp = t_1;
	} else if (z <= 2.32e+21) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x * (y - a)) / z)
    if (z <= (-2.8d+28)) then
        tmp = t_1
    else if (z <= 2.32d+21) then
        tmp = x + ((t * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * (y - a)) / z);
	double tmp;
	if (z <= -2.8e+28) {
		tmp = t_1;
	} else if (z <= 2.32e+21) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x * (y - a)) / z)
	tmp = 0
	if z <= -2.8e+28:
		tmp = t_1
	elif z <= 2.32e+21:
		tmp = x + ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x * Float64(y - a)) / z))
	tmp = 0.0
	if (z <= -2.8e+28)
		tmp = t_1;
	elseif (z <= 2.32e+21)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x * (y - a)) / z);
	tmp = 0.0;
	if (z <= -2.8e+28)
		tmp = t_1;
	elseif (z <= 2.32e+21)
		tmp = x + ((t * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -28000000000000001471563169792], t$95$1, If[LessEqual[z, 2320000000000000000000], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e28 or 2.32e21 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   if -2.8000000000000001e28 < z < 2.32e21

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + \frac{t \cdot y}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 37.8%

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

   7. Applied rewrites 37.8%

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

Alternative 13: 51.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -8600000000000000169248555008:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1499999999999999918362846480564224:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a \cdot \left(t - x\right)}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -8600000000000000169248555008)
  (+ x t)
  (if (<= z 1499999999999999918362846480564224)
    (+ x (/ (* t y) a))
    (+ t (/ (* a (- t x)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+27) {
		tmp = x + t;
	} else if (z <= 1.5e+33) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t + ((a * (t - x)) / 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 <= (-8.6d+27)) then
        tmp = x + t
    else if (z <= 1.5d+33) then
        tmp = x + ((t * y) / a)
    else
        tmp = t + ((a * (t - x)) / 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 <= -8.6e+27) {
		tmp = x + t;
	} else if (z <= 1.5e+33) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t + ((a * (t - x)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+27:
		tmp = x + t
	elif z <= 1.5e+33:
		tmp = x + ((t * y) / a)
	else:
		tmp = t + ((a * (t - x)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+27)
		tmp = Float64(x + t);
	elseif (z <= 1.5e+33)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(t + Float64(Float64(a * Float64(t - x)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e+27)
		tmp = x + t;
	elseif (z <= 1.5e+33)
		tmp = x + ((t * y) / a);
	else
		tmp = t + ((a * (t - x)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8600000000000000169248555008], N[(x + t), $MachinePrecision], If[LessEqual[z, 1499999999999999918362846480564224], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000002e27

   1. Initial program 79.6%

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

   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 x around 0

      \[\leadsto x + t \]
   9. Step-by-step derivation

   10. Applied rewrites 34.3%

       \[\leadsto x + t \]

   if -8.6000000000000002e27 < z < 1.4999999999999999e33

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + \frac{t \cdot y}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 37.8%

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

   7. Applied rewrites 37.8%

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

   if 1.4999999999999999e33 < z

   1. Initial program 79.6%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   3. 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%

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

   4. Applied rewrites 46.4%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 29.5%

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

   7. Applied rewrites 29.5%

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

Alternative 14: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -8600000000000000169248555008:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 77999999999999999862150877151232:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{x}{t}\right) \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -8600000000000000169248555008)
  (+ x t)
  (if (<= z 77999999999999999862150877151232)
    (+ x (/ (* t y) a))
    (* (+ 1 (/ x t)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+27) {
		tmp = x + t;
	} else if (z <= 7.8e+31) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = (1.0 + (x / t)) * t;
	}
	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 <= (-8.6d+27)) then
        tmp = x + t
    else if (z <= 7.8d+31) then
        tmp = x + ((t * y) / a)
    else
        tmp = (1.0d0 + (x / t)) * t
    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 <= -8.6e+27) {
		tmp = x + t;
	} else if (z <= 7.8e+31) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = (1.0 + (x / t)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+27:
		tmp = x + t
	elif z <= 7.8e+31:
		tmp = x + ((t * y) / a)
	else:
		tmp = (1.0 + (x / t)) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+27)
		tmp = Float64(x + t);
	elseif (z <= 7.8e+31)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(Float64(1.0 + Float64(x / t)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e+27)
		tmp = x + t;
	elseif (z <= 7.8e+31)
		tmp = x + ((t * y) / a);
	else
		tmp = (1.0 + (x / t)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8600000000000000169248555008], N[(x + t), $MachinePrecision], If[LessEqual[z, 77999999999999999862150877151232], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(1 + N[(x / t), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000002e27

   1. Initial program 79.6%

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

   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 x around 0

      \[\leadsto x + t \]
   9. Step-by-step derivation

   10. Applied rewrites 34.3%

       \[\leadsto x + t \]

   if -8.6000000000000002e27 < z < 7.8e31

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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%

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

   4. Applied rewrites 43.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + \frac{t \cdot y}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 37.8%

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

   7. Applied rewrites 37.8%

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

   if 7.8e31 < z

   1. Initial program 79.6%

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

   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 x around 0

      \[\leadsto x + t \]
   9. Step-by-step derivation

   10. Applied rewrites 34.3%

       \[\leadsto x + t \]
   11. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \color{blue}{x + t} \]

       2. +-commutative N/A

          \[\leadsto \color{blue}{t + x} \]

       3. sum-to-mult N/A

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

       4. lower-unsound-*.f64 N/A

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

       5. lower-unsound-+.f64 N/A

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

       6. lower-unsound-/.f64 31.5%

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

   12. Applied rewrites 31.5%

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

Alternative 15: 34.3% accurate, 7.3× speedup

Math

\[x + t \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

Derivation

1. Initial program 79.6%

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

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 x around 0

   \[\leadsto x + t \]
9. Step-by-step derivation

10. Applied rewrites 34.3%

    \[\leadsto x + t \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))