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

Percentage Accurate: 85.4% → 97.7%

Time: 5.8s

Alternatives: 9

Speedup: 0.6×

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: 85.4% 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: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;x\_m - \frac{x\_m \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

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 (<= x_m 1.9e-45) (- x_m (/ (* x_m z) y)) (* x_m (- 1.0 (/ z y))))))

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 (x_m <= 1.9e-45) {
		tmp = x_m - ((x_m * z) / y);
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	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 (x_m <= 1.9d-45) then
        tmp = x_m - ((x_m * z) / y)
    else
        tmp = x_m * (1.0d0 - (z / y))
    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 (x_m <= 1.9e-45) {
		tmp = x_m - ((x_m * z) / y);
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	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 x_m <= 1.9e-45:
		tmp = x_m - ((x_m * z) / y)
	else:
		tmp = x_m * (1.0 - (z / y))
	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 (x_m <= 1.9e-45)
		tmp = Float64(x_m - Float64(Float64(x_m * z) / y));
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	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 (x_m <= 1.9e-45)
		tmp = x_m - ((x_m * z) / y);
	else
		tmp = x_m * (1.0 - (z / y));
	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[x$95$m, 1.9e-45], N[(x$95$m - N[(N[(x$95$m * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.89999999999999999e-45

   1. Initial program 87.6%

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

      1. remove-double-neg 87.6%

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

      2. distribute-frac-neg2 87.6%

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

      3. distribute-frac-neg 87.6%

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

      4. distribute-rgt-neg-in 87.6%

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

      5. associate-/l* 94.1%

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

      6. distribute-frac-neg 94.1%

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

      7. distribute-frac-neg2 94.1%

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

      8. remove-double-neg 94.1%

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

      9. div-sub 94.1%

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

      10. *-inverses 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 93.4%

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

      1. associate-*r/ 93.4%

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

      2. mul-1-neg 93.4%

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

      3. distribute-rgt-neg-out 93.4%

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

   7. Simplified 93.4%

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

   if 1.89999999999999999e-45 < x

   1. Initial program 74.9%

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

      1. remove-double-neg 74.9%

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

      2. distribute-frac-neg2 74.9%

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

      3. distribute-frac-neg 74.9%

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

      4. distribute-rgt-neg-in 74.9%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+101} \lor \neg \left(z \leq 6.2 \cdot 10^{+123}\right):\\ \;\;\;\;x\_m \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2.4e+101) (not (<= z 6.2e+123))) (* x_m (/ (- 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 ((z <= -2.4e+101) || !(z <= 6.2e+123)) {
		tmp = x_m * (-z / y);
	} else {
		tmp = 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 ((z <= (-2.4d+101)) .or. (.not. (z <= 6.2d+123))) then
        tmp = x_m * (-z / y)
    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 tmp;
	if ((z <= -2.4e+101) || !(z <= 6.2e+123)) {
		tmp = x_m * (-z / y);
	} 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):
	tmp = 0
	if (z <= -2.4e+101) or not (z <= 6.2e+123):
		tmp = x_m * (-z / y)
	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)
	tmp = 0.0
	if ((z <= -2.4e+101) || !(z <= 6.2e+123))
		tmp = Float64(x_m * Float64(Float64(-z) / y));
	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)
	tmp = 0.0;
	if ((z <= -2.4e+101) || ~((z <= 6.2e+123)))
		tmp = x_m * (-z / y);
	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_] := N[(x$95$s * If[Or[LessEqual[z, -2.4e+101], N[Not[LessEqual[z, 6.2e+123]], $MachinePrecision]], N[(x$95$m * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999988e101 or 6.20000000000000013e123 < z

   1. Initial program 87.7%

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

      1. remove-double-neg 87.7%

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

      2. distribute-frac-neg2 87.7%

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

      3. distribute-frac-neg 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. associate-/l* 89.9%

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

      6. distribute-frac-neg 89.9%

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

      7. distribute-frac-neg2 89.9%

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

      8. remove-double-neg 89.9%

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

      9. div-sub 89.9%

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

      10. *-inverses 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. associate-*l/ 79.8%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

      4. associate-*r/ 79.8%

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

      5. mul-1-neg 79.8%

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

   7. Simplified 79.8%

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

      1. distribute-frac-neg 79.8%

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

      2. distribute-rgt-neg-out 79.8%

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

      3. div-inv 79.7%

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

      4. add-sqr-sqrt 29.4%

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

      5. sqrt-unprod 20.1%

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

      6. sqr-neg 20.1%

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

      7. sqrt-unprod 0.6%

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

      8. add-sqr-sqrt 1.3%

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

      9. associate-*r* 1.1%

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

      10. *-commutative 1.1%

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

      11. associate-*l* 1.2%

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

      12. add-sqr-sqrt 0.5%

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

      13. sqrt-unprod 19.9%

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

      14. sqr-neg 19.9%

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

      15. sqrt-unprod 30.4%

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

      16. add-sqr-sqrt 76.5%

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

      17. div-inv 76.6%

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

   9. Applied egg-rr 76.6%

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

   if -2.39999999999999988e101 < z < 6.20000000000000013e123

   1. Initial program 83.0%

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

      1. remove-double-neg 83.0%

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

      2. distribute-frac-neg2 83.0%

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

      3. distribute-frac-neg 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. associate-/l* 98.3%

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

      6. distribute-frac-neg 98.3%

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

      7. distribute-frac-neg2 98.3%

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

      8. remove-double-neg 98.3%

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

      9. div-sub 98.3%

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

      10. *-inverses 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 75.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+101} \lor \neg \left(z \leq 6.2 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+101} \lor \neg \left(z \leq 3.5 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{x\_m}{\frac{y}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -5.6e+101) (not (<= z 3.5e+123))) (/ x_m (/ y (- 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 tmp;
	if ((z <= -5.6e+101) || !(z <= 3.5e+123)) {
		tmp = x_m / (y / -z);
	} else {
		tmp = 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 ((z <= (-5.6d+101)) .or. (.not. (z <= 3.5d+123))) then
        tmp = x_m / (y / -z)
    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 tmp;
	if ((z <= -5.6e+101) || !(z <= 3.5e+123)) {
		tmp = x_m / (y / -z);
	} 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):
	tmp = 0
	if (z <= -5.6e+101) or not (z <= 3.5e+123):
		tmp = x_m / (y / -z)
	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)
	tmp = 0.0
	if ((z <= -5.6e+101) || !(z <= 3.5e+123))
		tmp = Float64(x_m / Float64(y / Float64(-z)));
	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)
	tmp = 0.0;
	if ((z <= -5.6e+101) || ~((z <= 3.5e+123)))
		tmp = x_m / (y / -z);
	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_] := N[(x$95$s * If[Or[LessEqual[z, -5.6e+101], N[Not[LessEqual[z, 3.5e+123]], $MachinePrecision]], N[(x$95$m / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999962e101 or 3.5e123 < z

   1. Initial program 87.7%

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

      1. remove-double-neg 87.7%

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

      2. distribute-frac-neg2 87.7%

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

      3. distribute-frac-neg 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. associate-/l* 89.9%

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

      6. distribute-frac-neg 89.9%

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

      7. distribute-frac-neg2 89.9%

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

      8. remove-double-neg 89.9%

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

      9. div-sub 89.9%

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

      10. *-inverses 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. associate-*l/ 79.8%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

      4. associate-*r/ 79.8%

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

      5. mul-1-neg 79.8%

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

   7. Simplified 79.8%

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

      1. distribute-frac-neg 79.8%

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

      2. distribute-rgt-neg-out 79.8%

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

      3. div-inv 79.7%

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

      4. add-sqr-sqrt 29.4%

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

      5. sqrt-unprod 20.1%

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

      6. sqr-neg 20.1%

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

      7. sqrt-unprod 0.6%

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

      8. add-sqr-sqrt 1.3%

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

      9. associate-*r* 1.1%

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

      10. *-commutative 1.1%

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

      11. associate-*l* 1.2%

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

      12. add-sqr-sqrt 0.5%

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

      13. sqrt-unprod 19.9%

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

      14. sqr-neg 19.9%

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

      15. sqrt-unprod 30.4%

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

      16. add-sqr-sqrt 76.5%

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

      17. div-inv 76.6%

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

   9. Applied egg-rr 76.6%

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

       1. clear-num 76.6%

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

       2. un-div-inv 78.6%

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

   11. Applied egg-rr 78.6%

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

   if -5.59999999999999962e101 < z < 3.5e123

   1. Initial program 83.0%

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

      1. remove-double-neg 83.0%

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

      2. distribute-frac-neg2 83.0%

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

      3. distribute-frac-neg 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. associate-/l* 98.3%

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

      6. distribute-frac-neg 98.3%

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

      7. distribute-frac-neg2 98.3%

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

      8. remove-double-neg 98.3%

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

      9. div-sub 98.3%

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

      10. *-inverses 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 75.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+101} \lor \neg \left(z \leq 3.5 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+103}:\\ \;\;\;\;\frac{x\_m}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+123}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-x\_m}}\\ \end{array} \end{array} \]

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 (<= z -2.95e+103)
    (/ x_m (/ y (- z)))
    (if (<= z 3.5e+123) x_m (/ 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 (z <= -2.95e+103) {
		tmp = x_m / (y / -z);
	} else if (z <= 3.5e+123) {
		tmp = x_m;
	} else {
		tmp = 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 (z <= (-2.95d+103)) then
        tmp = x_m / (y / -z)
    else if (z <= 3.5d+123) then
        tmp = x_m
    else
        tmp = 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 (z <= -2.95e+103) {
		tmp = x_m / (y / -z);
	} else if (z <= 3.5e+123) {
		tmp = x_m;
	} else {
		tmp = 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 z <= -2.95e+103:
		tmp = x_m / (y / -z)
	elif z <= 3.5e+123:
		tmp = x_m
	else:
		tmp = 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 (z <= -2.95e+103)
		tmp = Float64(x_m / Float64(y / Float64(-z)));
	elseif (z <= 3.5e+123)
		tmp = x_m;
	else
		tmp = Float64(z / Float64(y / Float64(-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 (z <= -2.95e+103)
		tmp = x_m / (y / -z);
	elseif (z <= 3.5e+123)
		tmp = x_m;
	else
		tmp = 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[z, -2.95e+103], N[(x$95$m / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+123], x$95$m, N[(z / N[(y / (-x$95$m)), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.9499999999999999e103

   1. Initial program 85.3%

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

      1. remove-double-neg 85.3%

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

      2. distribute-frac-neg2 85.3%

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

      3. distribute-frac-neg 85.3%

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

      4. distribute-rgt-neg-in 85.3%

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

      5. associate-/l* 97.8%

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

      6. distribute-frac-neg 97.8%

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

      7. distribute-frac-neg2 97.8%

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

      8. remove-double-neg 97.8%

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

      9. div-sub 97.8%

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

      10. *-inverses 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around inf 75.1%

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

      1. associate-*l/ 75.1%

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

      2. associate-*l* 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-*r/ 75.1%

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

      5. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

      1. distribute-frac-neg 75.1%

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

      2. distribute-rgt-neg-out 75.1%

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

      3. div-inv 75.1%

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

      4. add-sqr-sqrt 31.0%

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

      5. sqrt-unprod 23.4%

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

      6. sqr-neg 23.4%

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

      7. sqrt-unprod 0.8%

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

      8. add-sqr-sqrt 1.5%

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

      9. associate-*r* 1.4%

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

      10. *-commutative 1.4%

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

      11. associate-*l* 1.5%

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

      12. add-sqr-sqrt 0.7%

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

      13. sqrt-unprod 23.2%

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

      14. sqr-neg 23.2%

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

      15. sqrt-unprod 32.9%

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

      16. add-sqr-sqrt 79.1%

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

      17. div-inv 79.3%

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

   9. Applied egg-rr 79.3%

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

       1. clear-num 79.2%

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

       2. un-div-inv 79.3%

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

   11. Applied egg-rr 79.3%

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

   if -2.9499999999999999e103 < z < 3.5e123

   1. Initial program 83.0%

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

      1. remove-double-neg 83.0%

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

      2. distribute-frac-neg2 83.0%

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

      3. distribute-frac-neg 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. associate-/l* 98.3%

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

      6. distribute-frac-neg 98.3%

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

      7. distribute-frac-neg2 98.3%

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

      8. remove-double-neg 98.3%

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

      9. div-sub 98.3%

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

      10. *-inverses 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 75.1%

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

   if 3.5e123 < z

   1. Initial program 90.5%

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

      1. remove-double-neg 90.5%

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

      2. distribute-frac-neg2 90.5%

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

      3. distribute-frac-neg 90.5%

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

      4. distribute-rgt-neg-in 90.5%

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

      5. associate-/l* 80.9%

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

      6. distribute-frac-neg 80.9%

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

      7. distribute-frac-neg2 80.9%

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

      8. remove-double-neg 80.9%

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

      9. div-sub 80.9%

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

      10. *-inverses 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. associate-*l/ 85.3%

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

      2. associate-*l* 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-*r/ 85.3%

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

      5. mul-1-neg 85.3%

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

   7. Simplified 85.3%

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

      1. distribute-frac-neg 85.3%

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

      2. distribute-rgt-neg-out 85.3%

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

      3. div-inv 85.1%

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

      4. add-sqr-sqrt 27.6%

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

      5. sqrt-unprod 16.4%

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

      6. sqr-neg 16.4%

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

      7. sqrt-unprod 0.5%

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

      8. add-sqr-sqrt 1.0%

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

      9. associate-*r* 0.9%

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

      10. *-commutative 0.9%

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

      11. associate-*l* 0.8%

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

      12. add-sqr-sqrt 0.4%

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

      13. sqrt-unprod 16.1%

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

      14. sqr-neg 16.1%

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

      15. sqrt-unprod 27.5%

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

      16. add-sqr-sqrt 73.6%

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

      17. div-inv 73.6%

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

   9. Applied egg-rr 73.6%

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

       1. *-commutative 73.6%

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

       2. associate-/r/ 83.0%

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

   11. Applied egg-rr 83.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+101}:\\ \;\;\;\;\frac{x\_m}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+123}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x\_m}{y}\\ \end{array} \end{array} \]

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 (<= z -3.7e+101)
    (/ x_m (/ y (- z)))
    (if (<= z 3.7e+123) x_m (* z (/ (- x_m) y))))))

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 (z <= -3.7e+101) {
		tmp = x_m / (y / -z);
	} else if (z <= 3.7e+123) {
		tmp = x_m;
	} else {
		tmp = z * (-x_m / y);
	}
	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 (z <= (-3.7d+101)) then
        tmp = x_m / (y / -z)
    else if (z <= 3.7d+123) then
        tmp = x_m
    else
        tmp = z * (-x_m / y)
    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 (z <= -3.7e+101) {
		tmp = x_m / (y / -z);
	} else if (z <= 3.7e+123) {
		tmp = x_m;
	} else {
		tmp = z * (-x_m / y);
	}
	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 z <= -3.7e+101:
		tmp = x_m / (y / -z)
	elif z <= 3.7e+123:
		tmp = x_m
	else:
		tmp = z * (-x_m / y)
	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 (z <= -3.7e+101)
		tmp = Float64(x_m / Float64(y / Float64(-z)));
	elseif (z <= 3.7e+123)
		tmp = x_m;
	else
		tmp = Float64(z * Float64(Float64(-x_m) / y));
	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 (z <= -3.7e+101)
		tmp = x_m / (y / -z);
	elseif (z <= 3.7e+123)
		tmp = x_m;
	else
		tmp = z * (-x_m / y);
	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[z, -3.7e+101], N[(x$95$m / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+123], x$95$m, N[(z * N[((-x$95$m) / y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3.6999999999999997e101

   1. Initial program 85.3%

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

      1. remove-double-neg 85.3%

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

      2. distribute-frac-neg2 85.3%

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

      3. distribute-frac-neg 85.3%

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

      4. distribute-rgt-neg-in 85.3%

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

      5. associate-/l* 97.8%

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

      6. distribute-frac-neg 97.8%

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

      7. distribute-frac-neg2 97.8%

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

      8. remove-double-neg 97.8%

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

      9. div-sub 97.8%

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

      10. *-inverses 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around inf 75.1%

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

      1. associate-*l/ 75.1%

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

      2. associate-*l* 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-*r/ 75.1%

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

      5. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

      1. distribute-frac-neg 75.1%

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

      2. distribute-rgt-neg-out 75.1%

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

      3. div-inv 75.1%

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

      4. add-sqr-sqrt 31.0%

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

      5. sqrt-unprod 23.4%

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

      6. sqr-neg 23.4%

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

      7. sqrt-unprod 0.8%

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

      8. add-sqr-sqrt 1.5%

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

      9. associate-*r* 1.4%

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

      10. *-commutative 1.4%

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

      11. associate-*l* 1.5%

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

      12. add-sqr-sqrt 0.7%

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

      13. sqrt-unprod 23.2%

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

      14. sqr-neg 23.2%

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

      15. sqrt-unprod 32.9%

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

      16. add-sqr-sqrt 79.1%

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

      17. div-inv 79.3%

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

   9. Applied egg-rr 79.3%

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

       1. clear-num 79.2%

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

       2. un-div-inv 79.3%

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

   11. Applied egg-rr 79.3%

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

   if -3.6999999999999997e101 < z < 3.69999999999999996e123

   1. Initial program 83.0%

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

      1. remove-double-neg 83.0%

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

      2. distribute-frac-neg2 83.0%

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

      3. distribute-frac-neg 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. associate-/l* 98.3%

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

      6. distribute-frac-neg 98.3%

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

      7. distribute-frac-neg2 98.3%

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

      8. remove-double-neg 98.3%

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

      9. div-sub 98.3%

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

      10. *-inverses 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 75.1%

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

   if 3.69999999999999996e123 < z

   1. Initial program 90.5%

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

      1. remove-double-neg 90.5%

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

      2. distribute-frac-neg2 90.5%

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

      3. distribute-frac-neg 90.5%

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

      4. distribute-rgt-neg-in 90.5%

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

      5. associate-/l* 80.9%

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

      6. distribute-frac-neg 80.9%

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

      7. distribute-frac-neg2 80.9%

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

      8. remove-double-neg 80.9%

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

      9. div-sub 80.9%

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

      10. *-inverses 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. associate-*l/ 85.3%

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

      2. associate-*l* 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-*r/ 85.3%

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

      5. mul-1-neg 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+101}:\\ \;\;\;\;\frac{x\_m}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+123}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

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 (<= z -2.6e+101)
    (/ x_m (/ y (- z)))
    (if (<= z 3.5e+123) x_m (/ (* x_m (- z)) y)))))

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 (z <= -2.6e+101) {
		tmp = x_m / (y / -z);
	} else if (z <= 3.5e+123) {
		tmp = x_m;
	} else {
		tmp = (x_m * -z) / y;
	}
	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 (z <= (-2.6d+101)) then
        tmp = x_m / (y / -z)
    else if (z <= 3.5d+123) then
        tmp = x_m
    else
        tmp = (x_m * -z) / y
    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 (z <= -2.6e+101) {
		tmp = x_m / (y / -z);
	} else if (z <= 3.5e+123) {
		tmp = x_m;
	} else {
		tmp = (x_m * -z) / y;
	}
	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 z <= -2.6e+101:
		tmp = x_m / (y / -z)
	elif z <= 3.5e+123:
		tmp = x_m
	else:
		tmp = (x_m * -z) / y
	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 (z <= -2.6e+101)
		tmp = Float64(x_m / Float64(y / Float64(-z)));
	elseif (z <= 3.5e+123)
		tmp = x_m;
	else
		tmp = Float64(Float64(x_m * Float64(-z)) / y);
	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 (z <= -2.6e+101)
		tmp = x_m / (y / -z);
	elseif (z <= 3.5e+123)
		tmp = x_m;
	else
		tmp = (x_m * -z) / y;
	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[z, -2.6e+101], N[(x$95$m / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+123], x$95$m, N[(N[(x$95$m * (-z)), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e101

   1. Initial program 85.3%

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

      1. remove-double-neg 85.3%

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

      2. distribute-frac-neg2 85.3%

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

      3. distribute-frac-neg 85.3%

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

      4. distribute-rgt-neg-in 85.3%

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

      5. associate-/l* 97.8%

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

      6. distribute-frac-neg 97.8%

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

      7. distribute-frac-neg2 97.8%

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

      8. remove-double-neg 97.8%

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

      9. div-sub 97.8%

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

      10. *-inverses 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around inf 75.1%

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

      1. associate-*l/ 75.1%

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

      2. associate-*l* 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-*r/ 75.1%

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

      5. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

      1. distribute-frac-neg 75.1%

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

      2. distribute-rgt-neg-out 75.1%

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

      3. div-inv 75.1%

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

      4. add-sqr-sqrt 31.0%

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

      5. sqrt-unprod 23.4%

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

      6. sqr-neg 23.4%

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

      7. sqrt-unprod 0.8%

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

      8. add-sqr-sqrt 1.5%

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

      9. associate-*r* 1.4%

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

      10. *-commutative 1.4%

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

      11. associate-*l* 1.5%

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

      12. add-sqr-sqrt 0.7%

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

      13. sqrt-unprod 23.2%

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

      14. sqr-neg 23.2%

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

      15. sqrt-unprod 32.9%

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

      16. add-sqr-sqrt 79.1%

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

      17. div-inv 79.3%

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

   9. Applied egg-rr 79.3%

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

       1. clear-num 79.2%

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

       2. un-div-inv 79.3%

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

   11. Applied egg-rr 79.3%

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

   if -2.6e101 < z < 3.5e123

   1. Initial program 83.0%

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

      1. remove-double-neg 83.0%

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

      2. distribute-frac-neg2 83.0%

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

      3. distribute-frac-neg 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. associate-/l* 98.3%

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

      6. distribute-frac-neg 98.3%

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

      7. distribute-frac-neg2 98.3%

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

      8. remove-double-neg 98.3%

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

      9. div-sub 98.3%

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

      10. *-inverses 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 75.1%

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

   if 3.5e123 < z

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0 90.3%

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

      1. associate-*r* 90.3%

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

      2. *-commutative 90.3%

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

      3. mul-1-neg 90.3%

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

   5. Simplified 90.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{+180}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

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 (<= z 1.6e+180) (* x_m (- 1.0 (/ z y))) (/ (* x_m (- z)) y))))

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 (z <= 1.6e+180) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (x_m * -z) / y;
	}
	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 (z <= 1.6d+180) then
        tmp = x_m * (1.0d0 - (z / y))
    else
        tmp = (x_m * -z) / y
    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 (z <= 1.6e+180) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (x_m * -z) / y;
	}
	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 z <= 1.6e+180:
		tmp = x_m * (1.0 - (z / y))
	else:
		tmp = (x_m * -z) / y
	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 (z <= 1.6e+180)
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(Float64(x_m * Float64(-z)) / y);
	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 (z <= 1.6e+180)
		tmp = x_m * (1.0 - (z / y));
	else
		tmp = (x_m * -z) / y;
	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[z, 1.6e+180], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * (-z)), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 1.59999999999999997e180

   1. Initial program 83.2%

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

      1. remove-double-neg 83.2%

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

      2. distribute-frac-neg2 83.2%

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

      3. distribute-frac-neg 83.2%

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

      4. distribute-rgt-neg-in 83.2%

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

      5. associate-/l* 97.8%

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

      6. distribute-frac-neg 97.8%

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

      7. distribute-frac-neg2 97.8%

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

      8. remove-double-neg 97.8%

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

      9. div-sub 97.9%

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

      10. *-inverses 97.9%

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

   3. Simplified 97.9%

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

   if 1.59999999999999997e180 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 96.3%

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

      1. associate-*r* 96.3%

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

      2. *-commutative 96.3%

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

      3. mul-1-neg 96.3%

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

   5. Simplified 96.3%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{+180}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 9.6 \cdot 10^{+179}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{y}\\ \end{array} \end{array} \]

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 (<= z 9.6e+179) (* x_m (- 1.0 (/ z y))) (/ (* x_m (- y z)) y))))

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 (z <= 9.6e+179) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (x_m * (y - z)) / y;
	}
	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 (z <= 9.6d+179) then
        tmp = x_m * (1.0d0 - (z / y))
    else
        tmp = (x_m * (y - z)) / y
    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 (z <= 9.6e+179) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (x_m * (y - z)) / y;
	}
	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 z <= 9.6e+179:
		tmp = x_m * (1.0 - (z / y))
	else:
		tmp = (x_m * (y - z)) / y
	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 (z <= 9.6e+179)
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(Float64(x_m * Float64(y - z)) / y);
	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 (z <= 9.6e+179)
		tmp = x_m * (1.0 - (z / y));
	else
		tmp = (x_m * (y - z)) / y;
	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[z, 9.6e+179], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 9.6000000000000005e179

   1. Initial program 83.2%

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

      1. remove-double-neg 83.2%

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

      2. distribute-frac-neg2 83.2%

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

      3. distribute-frac-neg 83.2%

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

      4. distribute-rgt-neg-in 83.2%

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

      5. associate-/l* 97.8%

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

      6. distribute-frac-neg 97.8%

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

      7. distribute-frac-neg2 97.8%

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

      8. remove-double-neg 97.8%

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

      9. div-sub 97.9%

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

      10. *-inverses 97.9%

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

   3. Simplified 97.9%

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

   if 9.6000000000000005e179 < z

   1. Initial program 96.5%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.6 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.2% accurate, 7.0× 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) :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) {
	return x_s * x_m;
}

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
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;
}

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

Julia

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

Derivation

1. Initial program 84.6%

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

   1. remove-double-neg 84.6%

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

   2. distribute-frac-neg2 84.6%

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

   3. distribute-frac-neg 84.6%

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

   4. distribute-rgt-neg-in 84.6%

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

   5. associate-/l* 95.5%

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

   6. distribute-frac-neg 95.5%

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

   7. distribute-frac-neg2 95.5%

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

   8. remove-double-neg 95.5%

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

   9. div-sub 95.5%

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

   10. *-inverses 95.5%

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

3. Simplified 95.5%

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

5. Taylor expanded in z around 0 55.4%

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

6. Final simplification 55.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.4% accurate, 0.4× 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 2024076 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

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

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