Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.0% → 97.3%

Time: 3.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - 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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - 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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{+246}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-x\_m, z, y \cdot x\_m\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z - y}{z - t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* x_m (- y z)) (- t z)) 5e+246)
    (/ (fma (- x_m) z (* y x_m)) (- t z))
    (* x_m (/ (- z y) (- z t))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (((x_m * (y - z)) / (t - z)) <= 5e+246) {
		tmp = fma(-x_m, z, (y * x_m)) / (t - z);
	} else {
		tmp = x_m * ((z - y) / (z - t));
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x_m * Float64(y - z)) / Float64(t - z)) <= 5e+246)
		tmp = Float64(fma(Float64(-x_m), z, Float64(y * x_m)) / Float64(t - z));
	else
		tmp = Float64(x_m * Float64(Float64(z - y) / Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], 5e+246], N[(N[((-x$95$m) * z + N[(y * x$95$m), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(N[(z - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 4.99999999999999976e246

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 94.6

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

   4. Applied rewrites 94.6%

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

   if 4.99999999999999976e246 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 35.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 98.9

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

   3. Applied rewrites 98.9%

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

Alternative 2: 95.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot \left(y - z\right)}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+246}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z - y}{z - t}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m (- y z)) (- t z))))
   (* x_s (if (<= t_1 5e+246) t_1 (* x_m (/ (- z y) (- z t)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= 5e+246) {
		tmp = t_1;
	} else {
		tmp = x_m * ((z - y) / (z - t));
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m * (y - z)) / (t - z)
    if (t_1 <= 5d+246) then
        tmp = t_1
    else
        tmp = x_m * ((z - y) / (z - t))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= 5e+246) {
		tmp = t_1;
	} else {
		tmp = x_m * ((z - y) / (z - t));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= 5e+246:
		tmp = t_1
	else:
		tmp = x_m * ((z - y) / (z - t))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= 5e+246)
		tmp = t_1;
	else
		tmp = Float64(x_m * Float64(Float64(z - y) / Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= 5e+246)
		tmp = t_1;
	else
		tmp = x_m * ((z - y) / (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, 5e+246], t$95$1, N[(x$95$m * N[(N[(z - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 4.99999999999999976e246

   1. Initial program 94.6%

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

   if 4.99999999999999976e246 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 35.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 98.9

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

   3. Applied rewrites 98.9%

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

Alternative 3: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(x\_m \cdot \frac{z - y}{z - t}\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (* x_m (/ (- z y) (- z t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m * ((z - y) / (z - t)));
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * (x_m * ((z - y) / (z - t)))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m * ((z - y) / (z - t)));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * (x_m * ((z - y) / (z - t)))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(x_m * Float64(Float64(z - y) / Float64(z - t))))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (x_m * ((z - y) / (z - t)));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(x$95$m * N[(N[(z - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.0%

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

   1. lift--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-/l* N/A

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

   6. lower-*.f64 N/A

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

   7. negate-sub2 N/A

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

   8. negate-sub2 N/A

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

   9. frac-2neg-rev N/A

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

   10. lower-/.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lower--.f64 97.3

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

3. Applied rewrites 97.3%

   \[\leadsto \color{blue}{x \cdot \frac{z - y}{z - t}} \]
4. Add Preprocessing

Alternative 4: 74.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(y - z\right)\\ t_2 := \frac{t\_1}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+36}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-283}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+48}:\\ \;\;\;\;\frac{z \cdot x\_m}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \frac{y}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- y z))) (t_2 (/ t_1 (- t z))))
   (*
    x_s
    (if (<= t_2 -5e+36)
      (* x_m (/ y (- t z)))
      (if (<= t_2 2e-283)
        (/ t_1 t)
        (if (<= t_2 1e+48) (/ (* z x_m) (- z t)) (- x_m (* x_m (/ y z)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y - z);
	double t_2 = t_1 / (t - z);
	double tmp;
	if (t_2 <= -5e+36) {
		tmp = x_m * (y / (t - z));
	} else if (t_2 <= 2e-283) {
		tmp = t_1 / t;
	} else if (t_2 <= 1e+48) {
		tmp = (z * x_m) / (z - t);
	} else {
		tmp = x_m - (x_m * (y / z));
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m * (y - z)
    t_2 = t_1 / (t - z)
    if (t_2 <= (-5d+36)) then
        tmp = x_m * (y / (t - z))
    else if (t_2 <= 2d-283) then
        tmp = t_1 / t
    else if (t_2 <= 1d+48) then
        tmp = (z * x_m) / (z - t)
    else
        tmp = x_m - (x_m * (y / z))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y - z);
	double t_2 = t_1 / (t - z);
	double tmp;
	if (t_2 <= -5e+36) {
		tmp = x_m * (y / (t - z));
	} else if (t_2 <= 2e-283) {
		tmp = t_1 / t;
	} else if (t_2 <= 1e+48) {
		tmp = (z * x_m) / (z - t);
	} else {
		tmp = x_m - (x_m * (y / z));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (y - z)
	t_2 = t_1 / (t - z)
	tmp = 0
	if t_2 <= -5e+36:
		tmp = x_m * (y / (t - z))
	elif t_2 <= 2e-283:
		tmp = t_1 / t
	elif t_2 <= 1e+48:
		tmp = (z * x_m) / (z - t)
	else:
		tmp = x_m - (x_m * (y / z))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(y - z))
	t_2 = Float64(t_1 / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -5e+36)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	elseif (t_2 <= 2e-283)
		tmp = Float64(t_1 / t);
	elseif (t_2 <= 1e+48)
		tmp = Float64(Float64(z * x_m) / Float64(z - t));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y / z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (y - z);
	t_2 = t_1 / (t - z);
	tmp = 0.0;
	if (t_2 <= -5e+36)
		tmp = x_m * (y / (t - z));
	elseif (t_2 <= 2e-283)
		tmp = t_1 / t;
	elseif (t_2 <= 1e+48)
		tmp = (z * x_m) / (z - t);
	else
		tmp = x_m - (x_m * (y / z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$2, -5e+36], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-283], N[(t$95$1 / t), $MachinePrecision], If[LessEqual[t$95$2, 1e+48], N[(N[(z * x$95$m), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -4.99999999999999977e36

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 79.7

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

   4. Applied rewrites 79.7%

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

   if -4.99999999999999977e36 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.99999999999999989e-283

   1. Initial program 94.9%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 80.6%

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

   if 1.99999999999999989e-283 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.00000000000000004e48

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. negate-sub2 N/A

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

      4. frac-2neg-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 70.7

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

   4. Applied rewrites 70.7%

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

   if 1.00000000000000004e48 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 59.9%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 97.7

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in t around 0

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

      1. frac-2neg N/A

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

      2. negate-sub2 N/A

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

      3. negate-sub2 N/A

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

      4. associate-/l* N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 40.0

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

   6. Applied rewrites 40.0%

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

   7. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

         \[\leadsto x - 1 \cdot \frac{x \cdot y}{z} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-1}{-1} \cdot \frac{x \cdot y}{z} \]

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift-/.f64 70.4

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

   9. Applied rewrites 70.4%

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

Alternative 5: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y - z}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{-12}:\\ \;\;\;\;x\_m - x\_m \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ (- y z) t))))
   (*
    x_s
    (if (<= t -4.7e+17) t_1 (if (<= t 6.9e-12) (- x_m (* x_m (/ y z))) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * ((y - z) / t);
	double tmp;
	if (t <= -4.7e+17) {
		tmp = t_1;
	} else if (t <= 6.9e-12) {
		tmp = x_m - (x_m * (y / z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * ((y - z) / t)
    if (t <= (-4.7d+17)) then
        tmp = t_1
    else if (t <= 6.9d-12) then
        tmp = x_m - (x_m * (y / z))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * ((y - z) / t);
	double tmp;
	if (t <= -4.7e+17) {
		tmp = t_1;
	} else if (t <= 6.9e-12) {
		tmp = x_m - (x_m * (y / z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * ((y - z) / t)
	tmp = 0
	if t <= -4.7e+17:
		tmp = t_1
	elif t <= 6.9e-12:
		tmp = x_m - (x_m * (y / z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -4.7e+17)
		tmp = t_1;
	elseif (t <= 6.9e-12)
		tmp = Float64(x_m - Float64(x_m * Float64(y / z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * ((y - z) / t);
	tmp = 0.0;
	if (t <= -4.7e+17)
		tmp = t_1;
	elseif (t <= 6.9e-12)
		tmp = x_m - (x_m * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -4.7e+17], t$95$1, If[LessEqual[t, 6.9e-12], N[(x$95$m - N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.7e17 or 6.9000000000000001e-12 < t

   1. Initial program 83.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 97.4

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

   3. Applied rewrites 97.4%

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

   4. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. negate-sub2 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 72.6

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

   6. Applied rewrites 72.6%

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

   if -4.7e17 < t < 6.9000000000000001e-12

   1. Initial program 84.7%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 97.3

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

   3. Applied rewrites 97.3%

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

   4. Taylor expanded in t around 0

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

      1. frac-2neg N/A

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

      2. negate-sub2 N/A

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

      3. negate-sub2 N/A

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

      4. associate-/l* N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 64.4

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

   6. Applied rewrites 64.4%

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

   7. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

         \[\leadsto x - 1 \cdot \frac{x \cdot y}{z} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-1}{-1} \cdot \frac{x \cdot y}{z} \]

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift-/.f64 75.9

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

   9. Applied rewrites 75.9%

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

Alternative 6: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot \left(y - z\right)}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-283}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t\_1 \leq 10^{+48}:\\ \;\;\;\;\frac{z \cdot x\_m}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \frac{y}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m (- y z)) (- t z))))
   (*
    x_s
    (if (<= t_1 2e-283)
      (* x_m (/ y (- t z)))
      (if (<= t_1 1e+48) (/ (* z x_m) (- z t)) (- x_m (* x_m (/ y z))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= 2e-283) {
		tmp = x_m * (y / (t - z));
	} else if (t_1 <= 1e+48) {
		tmp = (z * x_m) / (z - t);
	} else {
		tmp = x_m - (x_m * (y / z));
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m * (y - z)) / (t - z)
    if (t_1 <= 2d-283) then
        tmp = x_m * (y / (t - z))
    else if (t_1 <= 1d+48) then
        tmp = (z * x_m) / (z - t)
    else
        tmp = x_m - (x_m * (y / z))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= 2e-283) {
		tmp = x_m * (y / (t - z));
	} else if (t_1 <= 1e+48) {
		tmp = (z * x_m) / (z - t);
	} else {
		tmp = x_m - (x_m * (y / z));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= 2e-283:
		tmp = x_m * (y / (t - z))
	elif t_1 <= 1e+48:
		tmp = (z * x_m) / (z - t)
	else:
		tmp = x_m - (x_m * (y / z))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= 2e-283)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	elseif (t_1 <= 1e+48)
		tmp = Float64(Float64(z * x_m) / Float64(z - t));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y / z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= 2e-283)
		tmp = x_m * (y / (t - z));
	elseif (t_1 <= 1e+48)
		tmp = (z * x_m) / (z - t);
	else
		tmp = x_m - (x_m * (y / z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, 2e-283], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+48], N[(N[(z * x$95$m), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.99999999999999989e-283

   1. Initial program 89.4%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 75.9

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

   4. Applied rewrites 75.9%

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

   if 1.99999999999999989e-283 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.00000000000000004e48

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. negate-sub2 N/A

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

      4. frac-2neg-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 70.7

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

   4. Applied rewrites 70.7%

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

   if 1.00000000000000004e48 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 59.9%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 97.7

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in t around 0

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

      1. frac-2neg N/A

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

      2. negate-sub2 N/A

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

      3. negate-sub2 N/A

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

      4. associate-/l* N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 40.0

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

   6. Applied rewrites 40.0%

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

   7. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

         \[\leadsto x - 1 \cdot \frac{x \cdot y}{z} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-1}{-1} \cdot \frac{x \cdot y}{z} \]

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift-/.f64 70.4

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

   9. Applied rewrites 70.4%

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

Alternative 7: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{-283}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* x_m (- y z)) (- t z)) 2e-283)
    (* x_m (/ y (- t z)))
    (- x_m (* x_m (/ y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (((x_m * (y - z)) / (t - z)) <= 2e-283) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = x_m - (x_m * (y / z));
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x_m * (y - z)) / (t - z)) <= 2d-283) then
        tmp = x_m * (y / (t - z))
    else
        tmp = x_m - (x_m * (y / z))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (((x_m * (y - z)) / (t - z)) <= 2e-283) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = x_m - (x_m * (y / z));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if ((x_m * (y - z)) / (t - z)) <= 2e-283:
		tmp = x_m * (y / (t - z))
	else:
		tmp = x_m - (x_m * (y / z))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x_m * Float64(y - z)) / Float64(t - z)) <= 2e-283)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y / z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (((x_m * (y - z)) / (t - z)) <= 2e-283)
		tmp = x_m * (y / (t - z));
	else
		tmp = x_m - (x_m * (y / z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], 2e-283], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.99999999999999989e-283

   1. Initial program 89.4%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 75.9

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

   4. Applied rewrites 75.9%

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

   if 1.99999999999999989e-283 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 80.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 97.9

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

   3. Applied rewrites 97.9%

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

   4. Taylor expanded in t around 0

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

      1. frac-2neg N/A

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

      2. negate-sub2 N/A

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

      3. negate-sub2 N/A

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

      4. associate-/l* N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 53.5

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

         \[\leadsto x - 1 \cdot \frac{x \cdot y}{z} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-1}{-1} \cdot \frac{x \cdot y}{z} \]

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift-/.f64 68.2

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

   9. Applied rewrites 68.2%

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

Alternative 8: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m - x\_m \cdot \frac{y}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-7}:\\ \;\;\;\;\frac{y \cdot x\_m}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (- x_m (* x_m (/ y z)))))
   (* x_s (if (<= z -2.7e-86) t_1 (if (<= z 1.05e-7) (/ (* y x_m) t) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m - (x_m * (y / z));
	double tmp;
	if (z <= -2.7e-86) {
		tmp = t_1;
	} else if (z <= 1.05e-7) {
		tmp = (y * x_m) / t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m - (x_m * (y / z))
    if (z <= (-2.7d-86)) then
        tmp = t_1
    else if (z <= 1.05d-7) then
        tmp = (y * x_m) / t
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m - (x_m * (y / z));
	double tmp;
	if (z <= -2.7e-86) {
		tmp = t_1;
	} else if (z <= 1.05e-7) {
		tmp = (y * x_m) / t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m - (x_m * (y / z))
	tmp = 0
	if z <= -2.7e-86:
		tmp = t_1
	elif z <= 1.05e-7:
		tmp = (y * x_m) / t
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m - Float64(x_m * Float64(y / z)))
	tmp = 0.0
	if (z <= -2.7e-86)
		tmp = t_1;
	elseif (z <= 1.05e-7)
		tmp = Float64(Float64(y * x_m) / t);
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m - (x_m * (y / z));
	tmp = 0.0;
	if (z <= -2.7e-86)
		tmp = t_1;
	elseif (z <= 1.05e-7)
		tmp = (y * x_m) / t;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m - N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -2.7e-86], t$95$1, If[LessEqual[z, 1.05e-7], N[(N[(y * x$95$m), $MachinePrecision] / t), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999992e-86 or 1.05e-7 < z

   1. Initial program 77.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. negate-sub2 N/A

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

      8. negate-sub2 N/A

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

      9. frac-2neg-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in t around 0

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

      1. frac-2neg N/A

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

      2. negate-sub2 N/A

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

      3. negate-sub2 N/A

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

      4. associate-/l* N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 53.9

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

   6. Applied rewrites 53.9%

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

   7. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

         \[\leadsto x - 1 \cdot \frac{x \cdot y}{z} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-1}{-1} \cdot \frac{x \cdot y}{z} \]

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lift-/.f64 70.7

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

   9. Applied rewrites 70.7%

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

   if -2.69999999999999992e-86 < z < 1.05e-7

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.1

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

   4. Applied rewrites 66.1%

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

Alternative 9: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{y \cdot x\_m}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x\_m}{z}, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -1.25e-13)
    x_m
    (if (<= z 1.1e-5) (/ (* y x_m) t) (fma t (/ x_m z) x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-13) {
		tmp = x_m;
	} else if (z <= 1.1e-5) {
		tmp = (y * x_m) / t;
	} else {
		tmp = fma(t, (x_m / z), x_m);
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -1.25e-13)
		tmp = x_m;
	elseif (z <= 1.1e-5)
		tmp = Float64(Float64(y * x_m) / t);
	else
		tmp = fma(t, Float64(x_m / z), x_m);
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -1.25e-13], x$95$m, If[LessEqual[z, 1.1e-5], N[(N[(y * x$95$m), $MachinePrecision] / t), $MachinePrecision], N[(t * N[(x$95$m / z), $MachinePrecision] + x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999997e-13

   1. Initial program 75.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 57.9%

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

   if -1.24999999999999997e-13 < z < 1.1e-5

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 62.8

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

   4. Applied rewrites 62.8%

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

   if 1.1e-5 < z

   1. Initial program 75.3%

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

   2. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. negate-sub2 N/A

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

      4. frac-2neg-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 56.5

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

   4. Applied rewrites 56.5%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 57.4

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

   7. Applied rewrites 57.4%

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

Alternative 10: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot x\_m}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -1.25e-13) x_m (if (<= z 8.5e-6) (/ (* y x_m) t) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-13) {
		tmp = x_m;
	} else if (z <= 8.5e-6) {
		tmp = (y * x_m) / t;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.25d-13)) then
        tmp = x_m
    else if (z <= 8.5d-6) then
        tmp = (y * x_m) / t
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-13) {
		tmp = x_m;
	} else if (z <= 8.5e-6) {
		tmp = (y * x_m) / t;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -1.25e-13:
		tmp = x_m
	elif z <= 8.5e-6:
		tmp = (y * x_m) / t
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -1.25e-13)
		tmp = x_m;
	elseif (z <= 8.5e-6)
		tmp = Float64(Float64(y * x_m) / t);
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -1.25e-13)
		tmp = x_m;
	elseif (z <= 8.5e-6)
		tmp = (y * x_m) / t;
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -1.25e-13], x$95$m, If[LessEqual[z, 8.5e-6], N[(N[(y * x$95$m), $MachinePrecision] / t), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999997e-13 or 8.4999999999999999e-6 < z

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 57.7%

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

   if -1.24999999999999997e-13 < z < 8.4999999999999999e-6

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 62.8

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

   4. Applied rewrites 62.8%

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

Alternative 11: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-13}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{x\_m}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -1.2e-13) x_m (if (<= z 2.9e-5) (* y (/ x_m t)) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-13) {
		tmp = x_m;
	} else if (z <= 2.9e-5) {
		tmp = y * (x_m / t);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d-13)) then
        tmp = x_m
    else if (z <= 2.9d-5) then
        tmp = y * (x_m / t)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-13) {
		tmp = x_m;
	} else if (z <= 2.9e-5) {
		tmp = y * (x_m / t);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -1.2e-13:
		tmp = x_m
	elif z <= 2.9e-5:
		tmp = y * (x_m / t)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -1.2e-13)
		tmp = x_m;
	elseif (z <= 2.9e-5)
		tmp = Float64(y * Float64(x_m / t));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e-13)
		tmp = x_m;
	elseif (z <= 2.9e-5)
		tmp = y * (x_m / t);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -1.2e-13], x$95$m, If[LessEqual[z, 2.9e-5], N[(y * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.1999999999999999e-13 or 2.9e-5 < z

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 57.7%

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

   if -1.1999999999999999e-13 < z < 2.9e-5

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 62.7

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

   4. Applied rewrites 62.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 62.9

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

   6. Applied rewrites 62.9%

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

Alternative 12: 35.7% accurate, 12.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s x_m))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * x_m;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * x_m
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * x_m;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * x_m)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * x_m;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 84.0%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 35.7%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025110 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64
  (/ (* x (- y z)) (- t z)))