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

Percentage Accurate: 94.7% → 98.0%

Time: 6.0s

Alternatives: 13

Speedup: 0.9×

• 20.2% 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: 98.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+222}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, \left(-z\right) \cdot t\right) \cdot \frac{x}{\left(1 - z\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 (- INFINITY))
     (* (/ x z) y)
     (if (<= t_1 1e+222)
       (* x t_1)
       (* (fma (- 1.0 z) y (* (- z) t)) (/ x (* (- 1.0 z) 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 <= -((double) INFINITY)) {
		tmp = (x / z) * y;
	} else if (t_1 <= 1e+222) {
		tmp = x * t_1;
	} else {
		tmp = fma((1.0 - z), y, (-z * t)) * (x / ((1.0 - z) * 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 <= Float64(-Inf))
		tmp = Float64(Float64(x / z) * y);
	elseif (t_1 <= 1e+222)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(fma(Float64(1.0 - z), y, Float64(Float64(-z) * t)) * Float64(x / Float64(Float64(1.0 - z) * 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, (-Infinity)], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+222], N[(x * t$95$1), $MachinePrecision], N[(N[(N[(1.0 - z), $MachinePrecision] * y + N[((-z) * t), $MachinePrecision]), $MachinePrecision] * N[(x / N[(N[(1.0 - z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 61.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 99.8%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1e222

   1. Initial program 98.9%

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

   if 1e222 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 82.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 100.0

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

   6. Applied rewrites 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+222}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, \left(-z\right) \cdot t\right) \cdot \frac{x}{\left(1 - z\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+246)))
     (* (/ x z) y)
     (* x t_1))))

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 <= -((double) INFINITY)) || !(t_1 <= 2e+246)) {
		tmp = (x / z) * y;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+246)) {
		tmp = (x / z) * y;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+246):
		tmp = (x / z) * y
	else:
		tmp = x * t_1
	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 <= Float64(-Inf)) || !(t_1 <= 2e+246))
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(x * t_1);
	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 <= -Inf) || ~((t_1 <= 2e+246)))
		tmp = (x / z) * y;
	else
		tmp = x * t_1;
	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[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+246]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(x * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0 or 2.00000000000000014e246 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 71.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 2.00000000000000014e246

   1. Initial program 98.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.1% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (* x (/ (+ t y) z))
   (/ (* x (- y (* t z))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (x * (y - (t * z))) / 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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((t + y) / z)
    else
        tmp = (x * (y - (t * z))) / z
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = x * ((t + y) / z)
	else:
		tmp = (x * (y - (t * z))) / z
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 98.3%

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

   if -1 < z < 1

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= t -1.1e+96)
     t_1
     (if (<= t 3.3e+151) (* (/ x z) y) (if (<= t 1.4e+203) (* x (- t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (t <= -1.1e+96) {
		tmp = t_1;
	} else if (t <= 3.3e+151) {
		tmp = (x / z) * y;
	} else if (t <= 1.4e+203) {
		tmp = x * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 <= (-1.1d+96)) then
        tmp = t_1
    else if (t <= 3.3d+151) then
        tmp = (x / z) * y
    else if (t <= 1.4d+203) then
        tmp = x * -t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (t <= -1.1e+96) {
		tmp = t_1;
	} else if (t <= 3.3e+151) {
		tmp = (x / z) * y;
	} else if (t <= 1.4e+203) {
		tmp = x * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if t <= -1.1e+96:
		tmp = t_1
	elif t <= 3.3e+151:
		tmp = (x / z) * y
	elif t <= 1.4e+203:
		tmp = x * -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 (t <= -1.1e+96)
		tmp = t_1;
	elseif (t <= 3.3e+151)
		tmp = Float64(Float64(x / z) * y);
	elseif (t <= 1.4e+203)
		tmp = Float64(x * Float64(-t));
	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 <= -1.1e+96)
		tmp = t_1;
	elseif (t <= 3.3e+151)
		tmp = (x / z) * y;
	elseif (t <= 1.4e+203)
		tmp = x * -t;
	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, -1.1e+96], t$95$1, If[LessEqual[t, 3.3e+151], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.4e+203], N[(x * (-t)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0999999999999999e96 or 1.39999999999999995e203 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in z around -inf

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

   5. Applied rewrites 55.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.7%

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

   if -1.0999999999999999e96 < t < 3.30000000000000025e151

   1. Initial program 91.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 78.9

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 79.5%

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

   if 3.30000000000000025e151 < t < 1.39999999999999995e203

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.2%

      \[\leadsto x \cdot \left(-t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.9 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.9e-11)))
   (* x (/ (+ t y) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.9e-11)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 <= (-1.0d0)) .or. (.not. (z <= 1.9d-11))) then
        tmp = x * ((t + y) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.9e-11)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.9e-11):
		tmp = x * ((t + y) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.9e-11))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.9e-11)))
		tmp = x * ((t + y) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.9e-11]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.8999999999999999e-11 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 98.3%

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

   if -1 < z < 1.8999999999999999e-11

   1. Initial program 87.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.9 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-72} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e-72) (not (<= z 1.0))) (* x (/ (+ t y) z)) (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e-72) || !(z <= 1.0)) {
		tmp = x * ((t + y) / z);
	} 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) :: tmp
    if ((z <= (-4.8d-72)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((t + y) / z)
    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 tmp;
	if ((z <= -4.8e-72) || !(z <= 1.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e-72) or not (z <= 1.0):
		tmp = x * ((t + y) / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e-72) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e-72) || ~((z <= 1.0)))
		tmp = x * ((t + y) / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e-72], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-72 or 1 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 95.4%

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

   if -4.8e-72 < z < 1

   1. Initial program 86.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 98.2

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.4%

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

   9. Applied rewrites 77.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-72} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-72} \lor \neg \left(z \leq 5 \cdot 10^{-12}\right):\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e-72) (not (<= z 5e-12)))
   (* (+ t y) (/ x z))
   (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e-72) || !(z <= 5e-12)) {
		tmp = (t + y) * (x / z);
	} 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) :: tmp
    if ((z <= (-4.8d-72)) .or. (.not. (z <= 5d-12))) then
        tmp = (t + y) * (x / z)
    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 tmp;
	if ((z <= -4.8e-72) || !(z <= 5e-12)) {
		tmp = (t + y) * (x / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e-72) or not (z <= 5e-12):
		tmp = (t + y) * (x / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e-72) || !(z <= 5e-12))
		tmp = Float64(Float64(t + y) * Float64(x / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e-72) || ~((z <= 5e-12)))
		tmp = (t + y) * (x / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e-72], N[Not[LessEqual[z, 5e-12]], $MachinePrecision]], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-72 or 4.9999999999999997e-12 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in z around -inf

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.1%

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

   if -4.8e-72 < z < 4.9999999999999997e-12

   1. Initial program 85.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 98.2

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.2%

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

   9. Applied rewrites 77.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-72} \lor \neg \left(z \leq 5 \cdot 10^{-12}\right):\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-72}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-72)
   (* (+ t y) (/ x z))
   (if (<= z 1.9e-11) (/ (* y x) z) (/ (* (+ t y) x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-72) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.9e-11) {
		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 <= (-4.8d-72)) then
        tmp = (t + y) * (x / z)
    else if (z <= 1.9d-11) 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 <= -4.8e-72) {
		tmp = (t + y) * (x / z);
	} else if (z <= 1.9e-11) {
		tmp = (y * x) / z;
	} else {
		tmp = ((t + y) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-72:
		tmp = (t + y) * (x / z)
	elif z <= 1.9e-11:
		tmp = (y * x) / z
	else:
		tmp = ((t + y) * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-72)
		tmp = Float64(Float64(t + y) * Float64(x / z));
	elseif (z <= 1.9e-11)
		tmp = Float64(Float64(y * 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 <= -4.8e-72)
		tmp = (t + y) * (x / z);
	elseif (z <= 1.9e-11)
		tmp = (y * x) / z;
	else
		tmp = ((t + y) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-72], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-11], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e-72

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf

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

   5. Applied rewrites 83.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.5%

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

   if -4.8e-72 < z < 1.8999999999999999e-11

   1. Initial program 85.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 98.2

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.2%

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

   9. Applied rewrites 77.7%

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

   if 1.8999999999999999e-11 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 90.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-72}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+20} \lor \neg \left(z \leq 5.2 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.6e+20) (not (<= z 5.2e+120))) (* x (/ t z)) (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e+20) || !(z <= 5.2e+120)) {
		tmp = x * (t / z);
	} 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) :: tmp
    if ((z <= (-6.6d+20)) .or. (.not. (z <= 5.2d+120))) then
        tmp = x * (t / z)
    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 tmp;
	if ((z <= -6.6e+20) || !(z <= 5.2e+120)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.6e+20) or not (z <= 5.2e+120):
		tmp = x * (t / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.6e+20) || !(z <= 5.2e+120))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.6e+20) || ~((z <= 5.2e+120)))
		tmp = x * (t / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.6e+20], N[Not[LessEqual[z, 5.2e+120]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e20 or 5.1999999999999998e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 70.0%

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

   if -6.6e20 < z < 5.1999999999999998e120

   1. Initial program 89.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 72.6%

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

   9. Applied rewrites 75.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+20} \lor \neg \left(z \leq 5.2 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+20} \lor \neg \left(z \leq 5.2 \cdot 10^{+120}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.6e+20) (not (<= z 5.2e+120))) (* t (/ x z)) (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e+20) || !(z <= 5.2e+120)) {
		tmp = t * (x / z);
	} 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) :: tmp
    if ((z <= (-6.6d+20)) .or. (.not. (z <= 5.2d+120))) then
        tmp = t * (x / z)
    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 tmp;
	if ((z <= -6.6e+20) || !(z <= 5.2e+120)) {
		tmp = t * (x / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.6e+20) or not (z <= 5.2e+120):
		tmp = t * (x / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.6e+20) || !(z <= 5.2e+120))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.6e+20) || ~((z <= 5.2e+120)))
		tmp = t * (x / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.6e+20], N[Not[LessEqual[z, 5.2e+120]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e20 or 5.1999999999999998e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.3%

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

   if -6.6e20 < z < 5.1999999999999998e120

   1. Initial program 89.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 72.6%

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

   9. Applied rewrites 75.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+20} \lor \neg \left(z \leq 5.2 \cdot 10^{+120}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11} \lor \neg \left(z \leq 1.9 \cdot 10^{-11}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\mathsf{fma}\left(t, z, t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-11) (not (<= z 1.9e-11)))
   (* t (/ x z))
   (* x (- (fma t z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-11) || !(z <= 1.9e-11)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -fma(t, z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-11) || !(z <= 1.9e-11))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-fma(t, z, t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-11], N[Not[LessEqual[z, 1.9e-11]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-N[(t * z + t), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999992e-11 or 1.8999999999999999e-11 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around -inf

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

   5. Applied rewrites 88.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 55.0%

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

   if -1.79999999999999992e-11 < z < 1.8999999999999999e-11

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 30.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 30.5%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11} \lor \neg \left(z \leq 1.9 \cdot 10^{-11}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\mathsf{fma}\left(t, z, t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-\mathsf{fma}\left(t, z, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-11)
   (* t (/ x z))
   (if (<= z 1.9e-11) (* x (- (fma t z t))) (/ (* t x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-11) {
		tmp = t * (x / z);
	} else if (z <= 1.9e-11) {
		tmp = x * -fma(t, z, t);
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-11)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 1.9e-11)
		tmp = Float64(x * Float64(-fma(t, z, t)));
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-11], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-11], N[(x * (-N[(t * z + t), $MachinePrecision])), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999992e-11

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.5%

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

   if -1.79999999999999992e-11 < z < 1.8999999999999999e-11

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 30.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 30.5%

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

   if 1.8999999999999999e-11 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 53.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.7%

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

Alternative 13: 23.1% 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 93.6%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 47.1%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 23.5%

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

Developer Target 1: 95.2% 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 2025019 
(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)))))