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

Percentage Accurate: 84.7% → 95.9%

Time: 6.1s

Alternatives: 8

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: 95.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.0%

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

   1. associate-*l/ 82.9%

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

   2. distribute-rgt-out-- 76.6%

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

   3. associate-*r/ 78.6%

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

   4. associate-*l/ 94.4%

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

   5. *-inverses 94.4%

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

   6. *-lft-identity 94.4%

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

3. Simplified 94.4%

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

   1. associate-*r/ 94.0%

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

   2. clear-num 93.9%

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

5. Applied egg-rr 93.9%

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

   1. associate-/r* 97.1%

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

   2. div-inv 97.0%

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

7. Applied egg-rr 97.0%

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

8. Final simplification 97.0%

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

Alternative 2: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{+158} \lor \neg \left(y \leq -2.5 \cdot 10^{-149}\right) \land y \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+179)
   x
   (if (or (<= y -1.06e+158) (and (not (<= y -2.5e-149)) (<= y 3.1e-22)))
     (* x (/ (- z) y))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+179) {
		tmp = x;
	} else if ((y <= -1.06e+158) || (!(y <= -2.5e-149) && (y <= 3.1e-22))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	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 (y <= (-2.7d+179)) then
        tmp = x
    else if ((y <= (-1.06d+158)) .or. (.not. (y <= (-2.5d-149))) .and. (y <= 3.1d-22)) then
        tmp = x * (-z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+179) {
		tmp = x;
	} else if ((y <= -1.06e+158) || (!(y <= -2.5e-149) && (y <= 3.1e-22))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+179:
		tmp = x
	elif (y <= -1.06e+158) or (not (y <= -2.5e-149) and (y <= 3.1e-22)):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+179)
		tmp = x;
	elseif ((y <= -1.06e+158) || (!(y <= -2.5e-149) && (y <= 3.1e-22)))
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+179)
		tmp = x;
	elseif ((y <= -1.06e+158) || (~((y <= -2.5e-149)) && (y <= 3.1e-22)))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+179], x, If[Or[LessEqual[y, -1.06e+158], And[N[Not[LessEqual[y, -2.5e-149]], $MachinePrecision], LessEqual[y, 3.1e-22]]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999982e179 or -1.06e158 < y < -2.49999999999999984e-149 or 3.10000000000000013e-22 < y

   1. Initial program 76.9%

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

      1. associate-*l/ 78.4%

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

      2. distribute-rgt-out-- 77.1%

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

      3. associate-*r/ 73.4%

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

      4. associate-*l/ 96.5%

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

      5. *-inverses 96.5%

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

      6. *-lft-identity 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 78.5%

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

   if -2.69999999999999982e179 < y < -1.06e158 or -2.49999999999999984e-149 < y < 3.10000000000000013e-22

   1. Initial program 90.9%

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

      1. associate-*l/ 90.8%

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

      2. distribute-rgt-out-- 75.6%

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

      3. associate-*r/ 87.6%

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

      4. associate-*l/ 90.9%

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

      5. *-inverses 90.9%

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

      6. *-lft-identity 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in z around inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. associate-*l/ 79.0%

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

      3. distribute-rgt-neg-in 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{+158} \lor \neg \left(y \leq -2.5 \cdot 10^{-149}\right) \land y \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e+52) (* x (/ (- z) y)) (if (<= z 0.032) x (/ (- z) (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e+52) {
		tmp = x * (-z / y);
	} else if (z <= 0.032) {
		tmp = x;
	} else {
		tmp = -z / (y / x);
	}
	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 <= (-7.5d+52)) then
        tmp = x * (-z / y)
    else if (z <= 0.032d0) then
        tmp = x
    else
        tmp = -z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e+52) {
		tmp = x * (-z / y);
	} else if (z <= 0.032) {
		tmp = x;
	} else {
		tmp = -z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e+52:
		tmp = x * (-z / y)
	elif z <= 0.032:
		tmp = x
	else:
		tmp = -z / (y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e+52)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (z <= 0.032)
		tmp = x;
	else
		tmp = Float64(Float64(-z) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e+52)
		tmp = x * (-z / y);
	elseif (z <= 0.032)
		tmp = x;
	else
		tmp = -z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e+52], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.032], x, N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.49999999999999995e52

   1. Initial program 88.5%

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

      1. associate-*l/ 88.7%

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

      2. distribute-rgt-out-- 76.8%

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

      3. associate-*r/ 83.8%

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

      4. associate-*l/ 95.3%

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

      5. *-inverses 95.3%

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

      6. *-lft-identity 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. associate-*l/ 79.9%

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

      3. distribute-rgt-neg-in 79.9%

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

   6. Simplified 79.9%

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

   if -7.49999999999999995e52 < z < 0.032000000000000001

   1. Initial program 76.7%

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

      1. associate-*l/ 80.1%

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

      2. distribute-rgt-out-- 77.9%

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

      3. associate-*r/ 74.1%

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

      4. associate-*l/ 93.5%

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

      5. *-inverses 93.5%

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

      6. *-lft-identity 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 79.5%

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

   if 0.032000000000000001 < z

   1. Initial program 89.0%

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

      1. associate-*l/ 85.2%

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

      2. distribute-rgt-out-- 73.8%

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

      3. associate-*r/ 84.7%

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

      4. associate-*l/ 95.7%

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

      5. *-inverses 95.7%

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

      6. *-lft-identity 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around inf 72.4%

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

      1. mul-1-neg 72.4%

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

      2. associate-*l/ 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

   6. Simplified 64.2%

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

      1. distribute-rgt-neg-out 64.2%

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

      2. associate-/r/ 69.7%

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

      3. distribute-neg-frac 69.7%

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

   8. Applied egg-rr 69.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \end{array} \]

Alternative 4: 71.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 0.003:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e+52) (* x (/ (- z) y)) (if (<= z 0.003) x (/ (* x (- z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+52) {
		tmp = x * (-z / y);
	} else if (z <= 0.003) {
		tmp = x;
	} else {
		tmp = (x * -z) / 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 <= (-3.7d+52)) then
        tmp = x * (-z / y)
    else if (z <= 0.003d0) then
        tmp = x
    else
        tmp = (x * -z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+52) {
		tmp = x * (-z / y);
	} else if (z <= 0.003) {
		tmp = x;
	} else {
		tmp = (x * -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e+52:
		tmp = x * (-z / y)
	elif z <= 0.003:
		tmp = x
	else:
		tmp = (x * -z) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e+52)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (z <= 0.003)
		tmp = x;
	else
		tmp = Float64(Float64(x * Float64(-z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e+52)
		tmp = x * (-z / y);
	elseif (z <= 0.003)
		tmp = x;
	else
		tmp = (x * -z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e+52], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.003], x, N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7e52

   1. Initial program 88.5%

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

      1. associate-*l/ 88.7%

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

      2. distribute-rgt-out-- 76.8%

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

      3. associate-*r/ 83.8%

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

      4. associate-*l/ 95.3%

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

      5. *-inverses 95.3%

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

      6. *-lft-identity 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. associate-*l/ 79.9%

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

      3. distribute-rgt-neg-in 79.9%

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

   6. Simplified 79.9%

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

   if -3.7e52 < z < 0.0030000000000000001

   1. Initial program 76.7%

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

      1. associate-*l/ 80.1%

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

      2. distribute-rgt-out-- 77.9%

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

      3. associate-*r/ 74.1%

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

      4. associate-*l/ 93.5%

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

      5. *-inverses 93.5%

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

      6. *-lft-identity 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 79.5%

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

   if 0.0030000000000000001 < z

   1. Initial program 89.0%

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

      1. associate-*l/ 85.2%

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

      2. distribute-rgt-out-- 73.8%

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

      3. associate-*r/ 84.7%

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

      4. associate-*l/ 95.7%

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

      5. *-inverses 95.7%

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

      6. *-lft-identity 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

      3. distribute-rgt-neg-in 72.4%

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

   6. Simplified 72.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 0.003:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]

Alternative 5: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 3e+74) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3e+74) {
		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 <= 3d+74) 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 <= 3e+74) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 3e+74:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3e+74)
		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 <= 3e+74)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3e+74], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3e74

   1. Initial program 83.6%

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

      1. associate-*l/ 79.6%

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

      2. distribute-rgt-out-- 76.0%

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

      3. associate-*r/ 81.2%

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

      4. associate-*l/ 94.3%

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

      5. *-inverses 94.3%

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

      6. *-lft-identity 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 57.0%

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

   if 3e74 < x

   1. Initial program 76.3%

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

   2. Taylor expanded in y around inf 30.5%

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

      1. associate-/l* 57.7%

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

      2. div-inv 59.4%

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

      3. clear-num 59.5%

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

   4. Applied egg-rr 59.5%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.0%

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

   1. associate-*l/ 82.9%

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

   2. distribute-rgt-out-- 76.6%

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

   3. associate-*r/ 78.6%

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

   4. associate-*l/ 94.4%

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

   5. *-inverses 94.4%

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

   6. *-lft-identity 94.4%

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

3. Simplified 94.4%

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

4. Final simplification 94.4%

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

Alternative 7: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.0%

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

   1. associate-*l/ 82.9%

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

   2. distribute-rgt-out-- 76.6%

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

   3. associate-*r/ 78.6%

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

   4. associate-*l/ 94.4%

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

   5. *-inverses 94.4%

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

   6. *-lft-identity 94.4%

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

3. Simplified 94.4%

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

   1. clear-num 94.4%

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

   2. un-div-inv 95.1%

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

5. Applied egg-rr 95.1%

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

6. Final simplification 95.1%

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

Alternative 8: 50.3% 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 82.0%

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

   1. associate-*l/ 82.9%

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

   2. distribute-rgt-out-- 76.6%

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

   3. associate-*r/ 78.6%

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

   4. associate-*l/ 94.4%

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

   5. *-inverses 94.4%

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

   6. *-lft-identity 94.4%

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

3. Simplified 94.4%

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

4. Taylor expanded in z around 0 55.3%

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

5. Final simplification 55.3%

   \[\leadsto x \]

Developer target: 96.0% accurate, 0.6× 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 2023207 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (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))