Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 84.6% → 96.5%

Time: 7.4s

Alternatives: 8

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y - z)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y - z)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x\_m}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x\_m, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* (- y z) x_m) y) -5e+107)
    (/ (- y z) (/ y x_m))
    (fma (/ (- z) y) x_m 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 tmp;
	if ((((y - z) * x_m) / y) <= -5e+107) {
		tmp = (y - z) / (y / x_m);
	} else {
		tmp = fma((-z / y), x_m, 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)
	tmp = 0.0
	if (Float64(Float64(Float64(y - z) * x_m) / y) <= -5e+107)
		tmp = Float64(Float64(y - z) / Float64(y / x_m));
	else
		tmp = fma(Float64(Float64(-z) / y), x_m, 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_] := N[(x$95$s * If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision], -5e+107], N[(N[(y - z), $MachinePrecision] / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision], N[(N[((-z) / y), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -5.0000000000000002e107

   1. Initial program 83.0%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 93.0

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

   4. Applied rewrites 93.0%

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

   if -5.0000000000000002e107 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 88.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.6

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

   4. Applied rewrites 95.6%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. *-inverses N/A

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

      12. metadata-eval N/A

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

      13. associate-/r/ N/A

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

      14. clear-num N/A

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

      15. /-rgt-identity N/A

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

      16. lift-neg.f64 N/A

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

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

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

      18. clear-num N/A

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

      19. lift-/.f64 N/A

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

      20. div-inv N/A

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

      21. lift-/.f64 N/A

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

      22. associate-/r/ N/A

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

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

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

      24. distribute-frac-neg2 N/A

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

      25. lower-fma.f64 N/A

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

   6. Applied rewrites 95.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\left(y - z\right) \cdot x\_m}{y}\\ t_1 := \frac{-x\_m}{y} \cdot z\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{-z}{y} \cdot x\_m\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\frac{x\_m}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* (- y z) x_m) y)) (t_1 (* (/ (- x_m) y) z)))
   (*
    x_s
    (if (<= t_0 -5e+107)
      t_1
      (if (<= t_0 0.0)
        (* (/ (- z) y) x_m)
        (if (<= t_0 2e+177) (/ x_m 1.0) 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_0 = ((y - z) * x_m) / y;
	double t_1 = (-x_m / y) * z;
	double tmp;
	if (t_0 <= -5e+107) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = (-z / y) * x_m;
	} else if (t_0 <= 2e+177) {
		tmp = x_m / 1.0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((y - z) * x_m) / y
    t_1 = (-x_m / y) * z
    if (t_0 <= (-5d+107)) then
        tmp = t_1
    else if (t_0 <= 0.0d0) then
        tmp = (-z / y) * x_m
    else if (t_0 <= 2d+177) then
        tmp = x_m / 1.0d0
    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_0 = ((y - z) * x_m) / y;
	double t_1 = (-x_m / y) * z;
	double tmp;
	if (t_0 <= -5e+107) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = (-z / y) * x_m;
	} else if (t_0 <= 2e+177) {
		tmp = x_m / 1.0;
	} 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_0 = ((y - z) * x_m) / y
	t_1 = (-x_m / y) * z
	tmp = 0
	if t_0 <= -5e+107:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = (-z / y) * x_m
	elif t_0 <= 2e+177:
		tmp = x_m / 1.0
	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_0 = Float64(Float64(Float64(y - z) * x_m) / y)
	t_1 = Float64(Float64(Float64(-x_m) / y) * z)
	tmp = 0.0
	if (t_0 <= -5e+107)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(Float64(-z) / y) * x_m);
	elseif (t_0 <= 2e+177)
		tmp = Float64(x_m / 1.0);
	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_0 = ((y - z) * x_m) / y;
	t_1 = (-x_m / y) * z;
	tmp = 0.0;
	if (t_0 <= -5e+107)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = (-z / y) * x_m;
	elseif (t_0 <= 2e+177)
		tmp = x_m / 1.0;
	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_] := Block[{t$95$0 = N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -5e+107], t$95$1, If[LessEqual[t$95$0, 0.0], N[(N[((-z) / y), $MachinePrecision] * x$95$m), $MachinePrecision], If[LessEqual[t$95$0, 2e+177], N[(x$95$m / 1.0), $MachinePrecision], t$95$1]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -5.0000000000000002e107 or 2e177 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 72.4

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

   5. Applied rewrites 72.4%

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

   if -5.0000000000000002e107 < (/.f64 (*.f64 x (-.f64 y z)) y) < 0.0

   1. Initial program 82.9%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 28.4

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

   5. Applied rewrites 28.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 33.3

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

   7. Applied rewrites 33.3%

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

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 2e177

   1. Initial program 99.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 96.7

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

   4. Applied rewrites 96.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 72.8%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{-z}{y} \cdot x\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\left(y - z\right) \cdot x\_m}{y}\\ t_1 := \frac{\left(-z\right) \cdot x\_m}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\frac{x\_m}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* (- y z) x_m) y)) (t_1 (/ (* (- z) x_m) y)))
   (* x_s (if (<= t_0 -4e-294) t_1 (if (<= t_0 2e+177) (/ x_m 1.0) 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_0 = ((y - z) * x_m) / y;
	double t_1 = (-z * x_m) / y;
	double tmp;
	if (t_0 <= -4e-294) {
		tmp = t_1;
	} else if (t_0 <= 2e+177) {
		tmp = x_m / 1.0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((y - z) * x_m) / y
    t_1 = (-z * x_m) / y
    if (t_0 <= (-4d-294)) then
        tmp = t_1
    else if (t_0 <= 2d+177) then
        tmp = x_m / 1.0d0
    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_0 = ((y - z) * x_m) / y;
	double t_1 = (-z * x_m) / y;
	double tmp;
	if (t_0 <= -4e-294) {
		tmp = t_1;
	} else if (t_0 <= 2e+177) {
		tmp = x_m / 1.0;
	} 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_0 = ((y - z) * x_m) / y
	t_1 = (-z * x_m) / y
	tmp = 0
	if t_0 <= -4e-294:
		tmp = t_1
	elif t_0 <= 2e+177:
		tmp = x_m / 1.0
	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_0 = Float64(Float64(Float64(y - z) * x_m) / y)
	t_1 = Float64(Float64(Float64(-z) * x_m) / y)
	tmp = 0.0
	if (t_0 <= -4e-294)
		tmp = t_1;
	elseif (t_0 <= 2e+177)
		tmp = Float64(x_m / 1.0);
	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_0 = ((y - z) * x_m) / y;
	t_1 = (-z * x_m) / y;
	tmp = 0.0;
	if (t_0 <= -4e-294)
		tmp = t_1;
	elseif (t_0 <= 2e+177)
		tmp = x_m / 1.0;
	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_] := Block[{t$95$0 = N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[((-z) * x$95$m), $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -4e-294], t$95$1, If[LessEqual[t$95$0, 2e+177], N[(x$95$m / 1.0), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -4.00000000000000007e-294 or 2e177 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.7

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

   5. Applied rewrites 60.7%

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

   if -4.00000000000000007e-294 < (/.f64 (*.f64 x (-.f64 y z)) y) < 2e177

   1. Initial program 83.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.2

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

   4. Applied rewrites 97.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 68.3%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -4 \cdot 10^{-294}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\left(y - z\right) \cdot x\_m}{y}\\ t_1 := \frac{-x\_m}{y} \cdot z\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\frac{x\_m}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* (- y z) x_m) y)) (t_1 (* (/ (- x_m) y) z)))
   (* x_s (if (<= t_0 0.0) t_1 (if (<= t_0 2e+177) (/ x_m 1.0) 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_0 = ((y - z) * x_m) / y;
	double t_1 = (-x_m / y) * z;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+177) {
		tmp = x_m / 1.0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((y - z) * x_m) / y
    t_1 = (-x_m / y) * z
    if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 2d+177) then
        tmp = x_m / 1.0d0
    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_0 = ((y - z) * x_m) / y;
	double t_1 = (-x_m / y) * z;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+177) {
		tmp = x_m / 1.0;
	} 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_0 = ((y - z) * x_m) / y
	t_1 = (-x_m / y) * z
	tmp = 0
	if t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 2e+177:
		tmp = x_m / 1.0
	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_0 = Float64(Float64(Float64(y - z) * x_m) / y)
	t_1 = Float64(Float64(Float64(-x_m) / y) * z)
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+177)
		tmp = Float64(x_m / 1.0);
	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_0 = ((y - z) * x_m) / y;
	t_1 = (-x_m / y) * z;
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+177)
		tmp = x_m / 1.0;
	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_] := Block[{t$95$0 = N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 2e+177], N[(x$95$m / 1.0), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 0.0 or 2e177 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 83.1%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 58.4

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

   5. Applied rewrites 58.4%

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

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 2e177

   1. Initial program 99.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 96.7

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

   4. Applied rewrites 96.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 72.8%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x\_m}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{-z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x\_m, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* (- y z) x_m) y) -5e+107)
    (/ (- z) (/ y x_m))
    (fma (/ (- z) y) x_m 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 tmp;
	if ((((y - z) * x_m) / y) <= -5e+107) {
		tmp = -z / (y / x_m);
	} else {
		tmp = fma((-z / y), x_m, 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)
	tmp = 0.0
	if (Float64(Float64(Float64(y - z) * x_m) / y) <= -5e+107)
		tmp = Float64(Float64(-z) / Float64(y / x_m));
	else
		tmp = fma(Float64(Float64(-z) / y), x_m, 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_] := N[(x$95$s * If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision], -5e+107], N[((-z) / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision], N[(N[((-z) / y), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -5.0000000000000002e107

   1. Initial program 83.0%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 93.0

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

   4. Applied rewrites 93.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 72.5

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

   7. Applied rewrites 72.5%

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

   if -5.0000000000000002e107 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 88.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.6

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

   4. Applied rewrites 95.6%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. *-inverses N/A

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

      12. metadata-eval N/A

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

      13. associate-/r/ N/A

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

      14. clear-num N/A

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

      15. /-rgt-identity N/A

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

      16. lift-neg.f64 N/A

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

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

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

      18. clear-num N/A

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

      19. lift-/.f64 N/A

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

      20. div-inv N/A

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

      21. lift-/.f64 N/A

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

      22. associate-/r/ N/A

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

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

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

      24. distribute-frac-neg2 N/A

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

      25. lower-fma.f64 N/A

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

   6. Applied rewrites 95.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x\_m}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x\_m, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* (- y z) x_m) y) -5e+107)
    (* (/ (- x_m) y) z)
    (fma (/ (- z) y) x_m 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 tmp;
	if ((((y - z) * x_m) / y) <= -5e+107) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = fma((-z / y), x_m, 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)
	tmp = 0.0
	if (Float64(Float64(Float64(y - z) * x_m) / y) <= -5e+107)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	else
		tmp = fma(Float64(Float64(-z) / y), x_m, 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_] := N[(x$95$s * If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision], -5e+107], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], N[(N[((-z) / y), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -5.0000000000000002e107

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -5.0000000000000002e107 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 88.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.6

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

   4. Applied rewrites 95.6%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. *-inverses N/A

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

      12. metadata-eval N/A

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

      13. associate-/r/ N/A

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

      14. clear-num N/A

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

      15. /-rgt-identity N/A

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

      16. lift-neg.f64 N/A

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

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

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

      18. clear-num N/A

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

      19. lift-/.f64 N/A

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

      20. div-inv N/A

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

      21. lift-/.f64 N/A

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

      22. associate-/r/ N/A

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

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

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

      24. distribute-frac-neg2 N/A

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

      25. lower-fma.f64 N/A

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

   6. Applied rewrites 95.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x\_m}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* (- y z) x_m) y) -5e+107)
    (* (/ (- x_m) y) z)
    (* (/ (- y z) y) 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 tmp;
	if ((((y - z) * x_m) / y) <= -5e+107) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = ((y - z) / y) * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((((y - z) * x_m) / y) <= (-5d+107)) then
        tmp = (-x_m / y) * z
    else
        tmp = ((y - z) / y) * 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 tmp;
	if ((((y - z) * x_m) / y) <= -5e+107) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = ((y - z) / y) * 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):
	tmp = 0
	if (((y - z) * x_m) / y) <= -5e+107:
		tmp = (-x_m / y) * z
	else:
		tmp = ((y - z) / y) * 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)
	tmp = 0.0
	if (Float64(Float64(Float64(y - z) * x_m) / y) <= -5e+107)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	else
		tmp = Float64(Float64(Float64(y - z) / y) * 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)
	tmp = 0.0;
	if ((((y - z) * x_m) / y) <= -5e+107)
		tmp = (-x_m / y) * z;
	else
		tmp = ((y - z) / y) * 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_] := N[(x$95$s * If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision], -5e+107], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -5.0000000000000002e107

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -5.0000000000000002e107 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 88.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 95.7

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

   4. Applied rewrites 95.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.4% accurate, 1.7× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (/ x_m 1.0)))

C

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

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * (x_m / 1.0d0)
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) {
	return x_s * (x_m / 1.0);
}

Python

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

Julia

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

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * (x_m / 1.0);
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_] := N[(x$95$s * N[(x$95$m / 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 94.3

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

4. Applied rewrites 94.3%

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

5. Taylor expanded in y around inf

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

7. Applied rewrites 48.2%

   \[\leadsto \frac{x}{\color{blue}{1}} \]
8. Add Preprocessing

Developer Target 1: 95.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024332 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

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