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

Percentage Accurate: 84.7% → 96.0%

Time: 7.5s

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: 84.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{1}{x \cdot \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.8e+144) (/ (/ 1.0 y) (/ 1.0 (* x (- y z)))) (- x (/ x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.8e+144) {
		tmp = (1.0 / y) / (1.0 / (x * (y - z)));
	} else {
		tmp = x - (x / (y / z));
	}
	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 <= (-8.8d+144)) then
        tmp = (1.0d0 / y) / (1.0d0 / (x * (y - z)))
    else
        tmp = x - (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.8e+144) {
		tmp = (1.0 / y) / (1.0 / (x * (y - z)));
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.8e+144:
		tmp = (1.0 / y) / (1.0 / (x * (y - z)))
	else:
		tmp = x - (x / (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.8e+144)
		tmp = Float64(Float64(1.0 / y) / Float64(1.0 / Float64(x * Float64(y - z))));
	else
		tmp = Float64(x - Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.8e+144)
		tmp = (1.0 / y) / (1.0 / (x * (y - z)));
	else
		tmp = x - (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.8e+144], N[(N[(1.0 / y), $MachinePrecision] / N[(1.0 / N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999952e144

   1. Initial program 97.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 83.4%

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

   3. Simplified 83.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
   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. clear-num N/A

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

      5. div-inv N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 97.0%

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

   6. Applied egg-rr 97.0%

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

   if -8.79999999999999952e144 < z

   1. Initial program 82.1%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 97.7%

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

   3. Simplified 97.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. +-lowering-+.f64 N/A

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

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{y}{z}}\right)\right)\right), x\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

      8. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(0 - \frac{y}{z}\right)\right), x\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \left(\frac{y}{z}\right)\right)\right), x\right) \]

      12. /-lowering-/.f64 95.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, z\right)\right)\right), x\right) \]

   6. Applied egg-rr 95.2%

      \[\leadsto \color{blue}{\frac{x}{0 - \frac{y}{z}} + x} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{\frac{x}{0 - \frac{y}{z}}} \]

      2. sub0-neg N/A

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

      3. distribute-frac-neg2 N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. /-lowering-/.f64 98.0%

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

   8. Applied egg-rr 98.0%

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

Alternative 2: 96.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+154}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+154) (/ (* x (- y z)) y) (- x (/ x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+154) {
		tmp = (x * (y - z)) / y;
	} else {
		tmp = x - (x / (y / z));
	}
	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 <= (-1.1d+154)) then
        tmp = (x * (y - z)) / y
    else
        tmp = x - (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+154) {
		tmp = (x * (y - z)) / y;
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+154:
		tmp = (x * (y - z)) / y
	else:
		tmp = x - (x / (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+154)
		tmp = Float64(Float64(x * Float64(y - z)) / y);
	else
		tmp = Float64(x - Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+154)
		tmp = (x * (y - z)) / y;
	else
		tmp = x - (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+154], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001e154

   1. Initial program 99.8%

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

   if -1.1000000000000001e154 < z

   1. Initial program 82.1%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 97.4%

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

   3. Simplified 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. +-lowering-+.f64 N/A

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

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{y}{z}}\right)\right)\right), x\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

      8. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(0 - \frac{y}{z}\right)\right), x\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \left(\frac{y}{z}\right)\right)\right), x\right) \]

      12. /-lowering-/.f64 94.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, z\right)\right)\right), x\right) \]

   6. Applied egg-rr 94.5%

      \[\leadsto \color{blue}{\frac{x}{0 - \frac{y}{z}} + x} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{\frac{x}{0 - \frac{y}{z}}} \]

      2. sub0-neg N/A

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

      3. distribute-frac-neg2 N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. /-lowering-/.f64 97.6%

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

   8. Applied egg-rr 97.6%

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

Alternative 3: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 4e+33) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e+33) {
		tmp = x;
	} else {
		tmp = y * (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 (x <= 4d+33) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e+33) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4e+33:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4e+33)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4e+33)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4e+33], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.9999999999999998e33

   1. Initial program 86.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 49.4%

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

   if 3.9999999999999998e33 < x

   1. Initial program 75.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 29.1%

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

   5. Simplified 29.1%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-/r/ N/A

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

      5. clear-num N/A

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

      6. *-lft-identity N/A

         \[\leadsto \left(1 \cdot \frac{x}{y}\right) \cdot y \]

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

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

      8. *-lft-identity N/A

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

      9. /-lowering-/.f64 57.9%

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

   7. Applied egg-rr 57.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{x}{\frac{y}{z}} \end{array} \]

FPCore

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

C

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

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 - (x / (y / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x - N[(x / N[(y / z), $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 95.8%

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

3. Simplified 95.8%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. distribute-lft-in N/A

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

   4. *-rgt-identity N/A

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

   5. +-lowering-+.f64 N/A

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

   6. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{y}{z}}\right)\right)\right), x\right) \]

   7. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

   8. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\frac{y}{z}\right)}\right), x\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

   10. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(0 - \frac{y}{z}\right)\right), x\right) \]

   11. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \left(\frac{y}{z}\right)\right)\right), x\right) \]

   12. /-lowering-/.f64 92.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, z\right)\right)\right), x\right) \]

6. Applied egg-rr 92.8%

   \[\leadsto \color{blue}{\frac{x}{0 - \frac{y}{z}} + x} \]
7. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto x + \color{blue}{\frac{x}{0 - \frac{y}{z}}} \]

   2. sub0-neg N/A

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

   3. distribute-frac-neg2 N/A

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

   4. unsub-neg N/A

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

   5. --lowering--.f64 N/A

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

   6. /-lowering-/.f64 N/A

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

   7. /-lowering-/.f64 96.0%

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

8. Applied egg-rr 96.0%

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

Alternative 5: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{y}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (/ z y))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 * (1.0d0 - (z / y))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (z / y));
}

Python

def code(x, y, z):
	return x * (1.0 - (z / y))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(z / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (z / y));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(z / y), $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 95.8%

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

3. Simplified 95.8%

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

Alternative 6: 50.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

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 95.8%

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

3. Simplified 95.8%

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

5. Taylor expanded in z around 0

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

7. Simplified 49.7%

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

Developer Target 1: 96.3% 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 2024160 
(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))