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

Percentage Accurate: 84.9% → 97.6%

Time: 7.2s

Alternatives: 6

Speedup: 1.0×

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: 84.9% 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: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2 \cdot 10^{-62}:\\ \;\;\;\;x\_m - \frac{z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\frac{y}{y - z}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= x_m 2e-62) (- x_m (/ z (/ y x_m))) (/ x_m (/ y (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 2e-62) {
		tmp = x_m - (z / (y / x_m));
	} else {
		tmp = x_m / (y / (y - z));
	}
	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 <= 2d-62) then
        tmp = x_m - (z / (y / x_m))
    else
        tmp = x_m / (y / (y - z))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 2e-62) {
		tmp = x_m - (z / (y / x_m));
	} else {
		tmp = x_m / (y / (y - z));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 2e-62:
		tmp = x_m - (z / (y / x_m))
	else:
		tmp = x_m / (y / (y - z))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 2e-62)
		tmp = Float64(x_m - Float64(z / Float64(y / x_m)));
	else
		tmp = Float64(x_m / Float64(y / Float64(y - z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 2e-62)
		tmp = x_m - (z / (y / x_m));
	else
		tmp = x_m / (y / (y - z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 2e-62], N[(x$95$m - N[(z / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.0000000000000001e-62

   1. Initial program 85.3%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 93.2%

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

      1. *-inverses N/A

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

      2. div-sub N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(y - z\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{y} - z\right)\right) \]

      9. --lowering--.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   6. Applied egg-rr 80.5%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. div-sub N/A

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

      5. un-div-inv N/A

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

      6. clear-num N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-inverses N/A

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

      11. *-rgt-identity N/A

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

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z}{\frac{y}{x}}\right)}\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      14. /-lowering-/.f64 93.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   8. Applied egg-rr 93.2%

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

   if 2.0000000000000001e-62 < x

   1. Initial program 80.6%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

      1. *-inverses N/A

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

      2. div-sub N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(y - z\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{y} - z\right)\right) \]

      9. --lowering--.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   6. Applied egg-rr 93.2%

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

      1. flip-- N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. *-rgt-identity N/A

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

      5. clear-num N/A

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

      6. flip-- N/A

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

      7. div-inv N/A

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

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{y}{y - z}\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(y - z\right)}\right)\right) \]

      10. --lowering--.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   8. Applied egg-rr 99.9%

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

Alternative 2: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.9 \cdot 10^{-63}:\\ \;\;\;\;x\_m - \frac{z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

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-63) (- x_m (/ z (/ y x_m))) (* 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-63) {
		tmp = x_m - (z / (y / x_m));
	} 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-63) then
        tmp = x_m - (z / (y / x_m))
    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-63) {
		tmp = x_m - (z / (y / x_m));
	} 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-63:
		tmp = x_m - (z / (y / x_m))
	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-63)
		tmp = Float64(x_m - Float64(z / Float64(y / x_m)));
	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-63)
		tmp = x_m - (z / (y / x_m));
	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-63], N[(x$95$m - N[(z / N[(y / x$95$m), $MachinePrecision]), $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 < 1.90000000000000009e-63

   1. Initial program 85.3%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 93.2%

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

      1. *-inverses N/A

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

      2. div-sub N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(y - z\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{y} - z\right)\right) \]

      9. --lowering--.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   6. Applied egg-rr 80.5%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. div-sub N/A

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

      5. un-div-inv N/A

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

      6. clear-num N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-inverses N/A

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

      11. *-rgt-identity N/A

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

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z}{\frac{y}{x}}\right)}\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      14. /-lowering-/.f64 93.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   8. Applied egg-rr 93.2%

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

   if 1.90000000000000009e-63 < x

   1. Initial program 80.6%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   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. Add Preprocessing

Alternative 3: 95.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 2.25 \cdot 10^{+94}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{y}\\ \end{array} \end{array} \]

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 2.25e+94) (* x_m (- 1.0 (/ z y))) (* (- y 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 <= 2.25e+94) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (y - 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 <= 2.25d+94) then
        tmp = x_m * (1.0d0 - (z / y))
    else
        tmp = (y - 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 <= 2.25e+94) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (y - 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 <= 2.25e+94:
		tmp = x_m * (1.0 - (z / y))
	else:
		tmp = (y - 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 <= 2.25e+94)
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(Float64(y - z) * 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 <= 2.25e+94)
		tmp = x_m * (1.0 - (z / y));
	else
		tmp = (y - 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, 2.25e+94], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 2.24999999999999986e94

   1. Initial program 82.9%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 97.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 97.6%

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

   if 2.24999999999999986e94 < z

   1. Initial program 88.5%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 84.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 84.4%

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

      1. *-inverses N/A

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

      2. div-sub N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(y - z\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{y} - z\right)\right) \]

      9. --lowering--.f64 92.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   6. Applied egg-rr 92.8%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.25 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2 \cdot 10^{+57}:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x\_m}{y}\\ \end{array} \end{array} \]

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 (<= x_m 2e+57) x_m (* y (/ 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 (x_m <= 2e+57) {
		tmp = x_m;
	} else {
		tmp = y * (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 (x_m <= 2d+57) then
        tmp = x_m
    else
        tmp = y * (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 (x_m <= 2e+57) {
		tmp = x_m;
	} else {
		tmp = y * (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 x_m <= 2e+57:
		tmp = x_m
	else:
		tmp = y * (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 (x_m <= 2e+57)
		tmp = x_m;
	else
		tmp = Float64(y * 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 (x_m <= 2e+57)
		tmp = x_m;
	else
		tmp = y * (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[x$95$m, 2e+57], x$95$m, N[(y * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.0000000000000001e57

   1. Initial program 86.9%

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 94.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   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

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

   7. Simplified 50.4%

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

   if 2.0000000000000001e57 < x

   1. Initial program 69.5%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 25.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), y\right) \]

   5. Simplified 25.0%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 60.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right) \]

   7. Applied egg-rr 60.8%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

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 - (z / y)))
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 - (z / y)));
}

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 - (z / y)))

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 * Float64(1.0 - Float64(z / y))))
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 - (z / y)));
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 * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.0%

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

   1. associate-/l* N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

   3. div-sub N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

   5. *-inverses N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

   6. /-lowering-/.f64 95.1%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

3. Simplified 95.1%

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

Alternative 6: 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 84.0%

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

   1. associate-/l* N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{y}\right)}\right) \]

   3. div-sub N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{y} - \color{blue}{\frac{z}{y}}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{y}\right), \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

   5. *-inverses N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

   6. /-lowering-/.f64 95.1%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

3. Simplified 95.1%

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

5. Taylor expanded in z around 0

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

7. Simplified 50.2%

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

Developer Target 1: 95.7% 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 2024150 
(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))