Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.7% → 95.8%

Time: 3.5s

Alternatives: 13

Speedup: 0.5×

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+171}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\mathsf{fma}\left(-t, z, \left(1 - z\right) \cdot y\right)}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 4e+171)
     (* x t_1)
     (* (/ x z) (/ (fma (- t) z (* (- 1.0 z) y)) (- 1.0 z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 4e+171) {
		tmp = x * t_1;
	} else {
		tmp = (x / z) * (fma(-t, z, ((1.0 - z) * y)) / (1.0 - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 4e+171)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(Float64(x / z) * Float64(fma(Float64(-t), z, Float64(Float64(1.0 - z) * y)) / Float64(1.0 - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+171], N[(x * t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(N[((-t) * z + N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 3.99999999999999982e171

   1. Initial program 96.1%

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

   if 3.99999999999999982e171 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 88.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 88.1

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

   3. Applied rewrites 88.1%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. frac-times N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. frac-2neg N/A

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

      12. lower-*.f64 N/A

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

      13. frac-sub N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. times-frac N/A

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

      17. lower-*.f64 N/A

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

      18. lower-/.f64 N/A

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

   5. Applied rewrites 94.4%

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

Alternative 2: 96.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 1e+305) (* x t_1) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+305) {
		tmp = x * t_1;
	} else {
		tmp = y * (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)
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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 1d+305) then
        tmp = x * t_1
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+305) {
		tmp = x * t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 1e+305:
		tmp = x * t_1
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 1e+305)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 1e+305)
		tmp = x * t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+305], N[(x * t$95$1), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 9.9999999999999994e304

   1. Initial program 96.5%

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

   if 9.9999999999999994e304 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 69.6%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 87.5

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 19.2%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 23.7

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

   9. Applied rewrites 23.7%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 98.4%

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

Alternative 3: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.7:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \left(1 + z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.7)
   (* (+ t y) (/ x z))
   (if (<= z 1.0) (* x (- (/ y z) (* (+ 1.0 z) t))) (/ (* (+ t y) x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.7) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - ((1.0 + z) * t));
	} else {
		tmp = ((t + y) * 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)
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) :: tmp
    if (z <= (-0.7d0)) then
        tmp = (t + y) * (x / z)
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - ((1.0d0 + z) * t))
    else
        tmp = ((t + y) * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.7) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - ((1.0 + z) * t));
	} else {
		tmp = ((t + y) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.7:
		tmp = (t + y) * (x / z)
	elif z <= 1.0:
		tmp = x * ((y / z) - ((1.0 + z) * t))
	else:
		tmp = ((t + y) * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.7)
		tmp = Float64(Float64(t + y) * Float64(x / z));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - Float64(Float64(1.0 + z) * t)));
	else
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.7)
		tmp = (t + y) * (x / z);
	elseif (z <= 1.0)
		tmp = x * ((y / z) - ((1.0 + z) * t));
	else
		tmp = ((t + y) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.7], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - N[(N[(1.0 + z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.69999999999999996

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.0

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

   4. Applied rewrites 86.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 86.0

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

   7. Applied rewrites 86.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 87.2

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

   9. Applied rewrites 87.2%

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

   if -0.69999999999999996 < z < 1

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.1

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

   4. Applied rewrites 92.1%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 92.1

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

   7. Applied rewrites 92.1%

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

   if 1 < z

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 86.8

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

   7. Applied rewrites 86.8%

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

Alternative 4: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.7:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \mathsf{fma}\left(t, z, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.7)
   (* (+ t y) (/ x z))
   (if (<= z 1.0) (* x (- (/ y z) (fma t z t))) (/ (* (+ t y) x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.7) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - fma(t, z, t));
	} else {
		tmp = ((t + y) * x) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.7)
		tmp = Float64(Float64(t + y) * Float64(x / z));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - fma(t, z, t)));
	else
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.7], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.69999999999999996

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.0

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

   4. Applied rewrites 86.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 86.0

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

   7. Applied rewrites 86.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 87.2

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

   9. Applied rewrites 87.2%

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

   if -0.69999999999999996 < z < 1

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.1

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

   4. Applied rewrites 92.1%

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

   if 1 < z

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 86.8

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

   7. Applied rewrites 86.8%

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

Alternative 5: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -3e+121)
     t_1
     (if (<= t -9.6e-281)
       (* x (/ y z))
       (if (<= t 5.8e+158) (* y (/ x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3e+121) {
		tmp = t_1;
	} else if (t <= -9.6e-281) {
		tmp = x * (y / z);
	} else if (t <= 5.8e+158) {
		tmp = y * (x / 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)
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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-3d+121)) then
        tmp = t_1
    else if (t <= (-9.6d-281)) then
        tmp = x * (y / z)
    else if (t <= 5.8d+158) then
        tmp = y * (x / 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 t_1 = x * (t / z);
	double tmp;
	if (t <= -3e+121) {
		tmp = t_1;
	} else if (t <= -9.6e-281) {
		tmp = x * (y / z);
	} else if (t <= 5.8e+158) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -3e+121:
		tmp = t_1
	elif t <= -9.6e-281:
		tmp = x * (y / z)
	elif t <= 5.8e+158:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -3e+121)
		tmp = t_1;
	elseif (t <= -9.6e-281)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 5.8e+158)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -3e+121)
		tmp = t_1;
	elseif (t <= -9.6e-281)
		tmp = x * (y / z);
	elseif (t <= 5.8e+158)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+121], t$95$1, If[LessEqual[t, -9.6e-281], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+158], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0000000000000002e121 or 5.80000000000000048e158 < t

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 96.4

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

   3. Applied rewrites 96.4%

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

   4. Taylor expanded in y around 0

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

      1. frac-times N/A

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

      2. *-commutative N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. frac-2neg N/A

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

      6. frac-sub N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r/ N/A

         \[\leadsto x \cdot \frac{-1 \cdot t}{\color{blue}{1 - z}} \]

      10. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{-1 \cdot t}{\color{blue}{1 - z}} \]

      11. mul-1-neg N/A

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

      12. lift-neg.f64 N/A

          \[\leadsto x \cdot \frac{-t}{\color{blue}{1} - z} \]

      13. lift--.f64 78.5

          \[\leadsto x \cdot \frac{-t}{1 - \color{blue}{z}} \]

   6. Applied rewrites 78.5%

      \[\leadsto x \cdot \color{blue}{\frac{-t}{1 - z}} \]

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 55.6

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

   9. Applied rewrites 55.6%

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

   if -3.0000000000000002e121 < t < -9.6000000000000002e-281

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf

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

      1. lift-/.f64 73.4

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

   4. Applied rewrites 73.4%

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

   if -9.6000000000000002e-281 < t < 5.80000000000000048e158

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 76.3

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

   4. Applied rewrites 76.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 28.5%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 30.0

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

   9. Applied rewrites 30.0%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 71.8%

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

Alternative 6: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+122}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9e+122)
   (/ (* t x) z)
   (if (<= t -9.6e-281)
     (* x (/ y z))
     (if (<= t 8.4e+158) (* y (/ x z)) (* t (/ x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e+122) {
		tmp = (t * x) / z;
	} else if (t <= -9.6e-281) {
		tmp = x * (y / z);
	} else if (t <= 8.4e+158) {
		tmp = y * (x / z);
	} else {
		tmp = 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)
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) :: tmp
    if (t <= (-9d+122)) then
        tmp = (t * x) / z
    else if (t <= (-9.6d-281)) then
        tmp = x * (y / z)
    else if (t <= 8.4d+158) then
        tmp = y * (x / z)
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e+122) {
		tmp = (t * x) / z;
	} else if (t <= -9.6e-281) {
		tmp = x * (y / z);
	} else if (t <= 8.4e+158) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9e+122:
		tmp = (t * x) / z
	elif t <= -9.6e-281:
		tmp = x * (y / z)
	elif t <= 8.4e+158:
		tmp = y * (x / z)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9e+122)
		tmp = Float64(Float64(t * x) / z);
	elseif (t <= -9.6e-281)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 8.4e+158)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9e+122)
		tmp = (t * x) / z;
	elseif (t <= -9.6e-281)
		tmp = x * (y / z);
	elseif (t <= 8.4e+158)
		tmp = y * (x / z);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9e+122], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -9.6e-281], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+158], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.99999999999999995e122

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 56.3

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

   4. Applied rewrites 56.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 46.7%

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

   if -8.99999999999999995e122 < t < -9.6000000000000002e-281

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf

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

      1. lift-/.f64 73.3

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

   4. Applied rewrites 73.3%

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

   if -9.6000000000000002e-281 < t < 8.3999999999999996e158

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 76.2

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

   4. Applied rewrites 76.2%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 28.5%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 30.0

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

   9. Applied rewrites 30.0%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 71.8%

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

   if 8.3999999999999996e158 < t

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 54.9

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

   4. Applied rewrites 54.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 46.1%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 47.6

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

   9. Applied rewrites 47.6%

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

Alternative 7: 89.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05)
   (* (+ t y) (/ x z))
   (if (<= z 1.0) (* x (- (/ y z) t)) (/ (* (+ t y) x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = ((t + y) * 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)
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) :: tmp
    if (z <= (-1.05d0)) then
        tmp = (t + y) * (x / z)
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = ((t + y) * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = ((t + y) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05:
		tmp = (t + y) * (x / z)
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = ((t + y) * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05)
		tmp = Float64(Float64(t + y) * Float64(x / z));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05)
		tmp = (t + y) * (x / z);
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = ((t + y) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.0

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

   4. Applied rewrites 86.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 86.0

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

   7. Applied rewrites 86.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 87.3

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

   9. Applied rewrites 87.3%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 91.8%

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

   if 1 < z

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 86.8

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

   7. Applied rewrites 86.8%

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

Alternative 8: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-55}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-55)
   (* (+ t y) (/ x z))
   (if (<= z 1.0) (* y (/ x z)) (/ (* (+ t y) x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-55) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.0) {
		tmp = y * (x / z);
	} else {
		tmp = ((t + y) * 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)
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) :: tmp
    if (z <= (-7.5d-55)) then
        tmp = (t + y) * (x / z)
    else if (z <= 1.0d0) then
        tmp = y * (x / z)
    else
        tmp = ((t + y) * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-55) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.0) {
		tmp = y * (x / z);
	} else {
		tmp = ((t + y) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-55:
		tmp = (t + y) * (x / z)
	elif z <= 1.0:
		tmp = y * (x / z)
	else:
		tmp = ((t + y) * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-55)
		tmp = Float64(Float64(t + y) * Float64(x / z));
	elseif (z <= 1.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-55)
		tmp = (t + y) * (x / z);
	elseif (z <= 1.0)
		tmp = y * (x / z);
	else
		tmp = ((t + y) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-55], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000023e-55

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 82.4

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

   4. Applied rewrites 82.4%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 82.4

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

   7. Applied rewrites 82.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 83.3

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

   9. Applied rewrites 83.3%

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

   if -7.50000000000000023e-55 < z < 1

   1. Initial program 91.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 55.2

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

   4. Applied rewrites 55.2%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 13.6%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 16.0

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

   9. Applied rewrites 16.0%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 70.1%

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

   if 1 < z

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 86.8

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

   7. Applied rewrites 86.8%

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

Alternative 9: 78.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ t y) (/ x z))))
   (if (<= z -7.5e-55) t_1 (if (<= z 1.0) (* y (/ x z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t + y) * (x / z);
	double tmp;
	if (z <= -7.5e-55) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = y * (x / 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (t + y) * (x / z)
    if (z <= (-7.5d-55)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = y * (x / 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 t_1 = (t + y) * (x / z);
	double tmp;
	if (z <= -7.5e-55) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t + y) * (x / z)
	tmp = 0
	if z <= -7.5e-55:
		tmp = t_1
	elif z <= 1.0:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t + y) * Float64(x / z))
	tmp = 0.0
	if (z <= -7.5e-55)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t + y) * (x / z);
	tmp = 0.0;
	if (z <= -7.5e-55)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-55], t$95$1, If[LessEqual[z, 1.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000023e-55 or 1 < z

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 84.5

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

   7. Applied rewrites 84.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 84.7

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

   9. Applied rewrites 84.7%

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

   if -7.50000000000000023e-55 < z < 1

   1. Initial program 91.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 55.2

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

   4. Applied rewrites 55.2%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 13.6%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 16.0

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

   9. Applied rewrites 16.0%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 70.1%

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

Alternative 10: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.65e+96)
   (/ (* t x) z)
   (if (<= t 8.4e+158) (* y (/ x z)) (* t (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e+96) {
		tmp = (t * x) / z;
	} else if (t <= 8.4e+158) {
		tmp = y * (x / z);
	} else {
		tmp = 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)
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) :: tmp
    if (t <= (-1.65d+96)) then
        tmp = (t * x) / z
    else if (t <= 8.4d+158) then
        tmp = y * (x / z)
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e+96) {
		tmp = (t * x) / z;
	} else if (t <= 8.4e+158) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.65e+96:
		tmp = (t * x) / z
	elif t <= 8.4e+158:
		tmp = y * (x / z)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.65e+96)
		tmp = Float64(Float64(t * x) / z);
	elseif (t <= 8.4e+158)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.65e+96)
		tmp = (t * x) / z;
	elseif (t <= 8.4e+158)
		tmp = y * (x / z);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.65e+96], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 8.4e+158], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.64999999999999992e96

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 57.7

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

   4. Applied rewrites 57.7%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 45.9%

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

   if -1.64999999999999992e96 < t < 8.3999999999999996e158

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 77.5

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 28.5%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 29.9

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

   9. Applied rewrites 29.9%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 72.4%

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

   if 8.3999999999999996e158 < t

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 54.9

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

   4. Applied rewrites 54.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 46.1%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 47.6

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

   9. Applied rewrites 47.6%

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

Alternative 11: 64.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= t -1.6e+96) t_1 (if (<= t 8.4e+158) (* y (/ x z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (t <= -1.6e+96) {
		tmp = t_1;
	} else if (t <= 8.4e+158) {
		tmp = y * (x / 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)
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) :: t_1
    real(8) :: tmp
    t_1 = t * (x / z)
    if (t <= (-1.6d+96)) then
        tmp = t_1
    else if (t <= 8.4d+158) then
        tmp = y * (x / 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 t_1 = t * (x / z);
	double tmp;
	if (t <= -1.6e+96) {
		tmp = t_1;
	} else if (t <= 8.4e+158) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if t <= -1.6e+96:
		tmp = t_1
	elif t <= 8.4e+158:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t <= -1.6e+96)
		tmp = t_1;
	elseif (t <= 8.4e+158)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (t <= -1.6e+96)
		tmp = t_1;
	elseif (t <= 8.4e+158)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+96], t$95$1, If[LessEqual[t, 8.4e+158], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000003e96 or 8.3999999999999996e158 < t

   1. Initial program 96.3%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 56.5

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

   4. Applied rewrites 56.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 46.0%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 46.2

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

   9. Applied rewrites 46.2%

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

   if -1.60000000000000003e96 < t < 8.3999999999999996e158

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 77.5

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 28.5%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 29.9

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

   9. Applied rewrites 29.9%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 72.4%

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

Alternative 12: 43.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-t, z, -t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= z -0.75) t_1 (if (<= z 1.0) (* x (fma (- t) z (- t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (z <= -0.75) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * fma(-t, z, -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (z <= -0.75)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x * fma(Float64(-t), z, Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.75], t$95$1, If[LessEqual[z, 1.0], N[(x * N[((-t) * z + (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.75 or 1 < z

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 86.4

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

   4. Applied rewrites 86.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 52.9%

      \[\leadsto \frac{t \cdot x}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 52.8

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

   9. Applied rewrites 52.8%

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

   if -0.75 < z < 1

   1. Initial program 92.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 92.3

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

   3. Applied rewrites 92.3%

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

   4. Taylor expanded in y around 0

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

      1. frac-times N/A

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

      2. *-commutative N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. frac-2neg N/A

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

      6. frac-sub N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r/ N/A

         \[\leadsto x \cdot \frac{-1 \cdot t}{\color{blue}{1 - z}} \]

      10. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{-1 \cdot t}{\color{blue}{1 - z}} \]

      11. mul-1-neg N/A

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

      12. lift-neg.f64 N/A

          \[\leadsto x \cdot \frac{-t}{\color{blue}{1} - z} \]

      13. lift--.f64 35.0

          \[\leadsto x \cdot \frac{-t}{1 - \color{blue}{z}} \]

   6. Applied rewrites 35.0%

      \[\leadsto x \cdot \color{blue}{\frac{-t}{1 - z}} \]

   7. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-1 \cdot t, z, -1 \cdot t\right) \]

      4. mul-1-neg N/A

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

      5. lift-neg.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-t, z, -1 \cdot t\right) \]

      6. mul-1-neg N/A

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

      7. lift-neg.f64 34.7

         \[\leadsto x \cdot \mathsf{fma}\left(-t, z, -t\right) \]

   9. Applied rewrites 34.7%

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

Alternative 13: 23.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(-t\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. frac-2neg N/A

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

   3. mul-1-neg N/A

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

   4. *-commutative N/A

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

   5. mul-1-neg N/A

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

   6. times-frac N/A

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

   7. lower-*.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower-/.f64 94.7

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

3. Applied rewrites 94.7%

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

4. Taylor expanded in y around 0

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

   1. frac-times N/A

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

   2. *-commutative N/A

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

   3. mul-1-neg N/A

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

   4. mul-1-neg N/A

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

   5. frac-2neg N/A

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

   6. frac-sub N/A

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

   7. *-commutative N/A

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

   8. *-commutative N/A

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

   9. associate-*r/ N/A

      \[\leadsto x \cdot \frac{-1 \cdot t}{\color{blue}{1 - z}} \]

   10. lower-/.f64 N/A

       \[\leadsto x \cdot \frac{-1 \cdot t}{\color{blue}{1 - z}} \]

   11. mul-1-neg N/A

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

   12. lift-neg.f64 N/A

       \[\leadsto x \cdot \frac{-t}{\color{blue}{1} - z} \]

   13. lift--.f64 46.7

       \[\leadsto x \cdot \frac{-t}{1 - \color{blue}{z}} \]

6. Applied rewrites 46.7%

   \[\leadsto x \cdot \color{blue}{\frac{-t}{1 - z}} \]

7. Taylor expanded in z around 0

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

   1. mul-1-neg N/A

      \[\leadsto x \cdot \left(\mathsf{neg}\left(t\right)\right) \]

   2. lift-neg.f64 23.4

      \[\leadsto x \cdot \left(-t\right) \]

9. Applied rewrites 23.4%

   \[\leadsto x \cdot \left(-t\right) \]
10. Add Preprocessing

Developer Target 1: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - 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)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - 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 t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2025095 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))