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

Percentage Accurate: 84.3% → 95.9%

Time: 7.4s

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: 84.3% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.2%

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

   1. remove-double-neg 83.2%

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

   2. distribute-frac-neg2 83.2%

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

   3. distribute-frac-neg 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

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 97.7%

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

   2. distribute-rgt-in 97.7%

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

   3. *-un-lft-identity 97.7%

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

   4. distribute-neg-frac2 97.7%

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

6. Applied egg-rr 97.7%

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

   1. *-commutative 97.7%

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

   2. add-sqr-sqrt 45.6%

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

   3. sqrt-unprod 59.8%

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

   4. sqr-neg 59.8%

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

   5. sqrt-unprod 29.1%

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

   6. add-sqr-sqrt 51.7%

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

   7. cancel-sign-sub-inv 51.7%

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

   8. distribute-frac-neg2 51.7%

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

   9. distribute-rgt-neg-out 51.7%

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

   10. distribute-lft-neg-out 51.7%

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

   11. add-sqr-sqrt 29.1%

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

   12. sqrt-unprod 59.8%

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

   13. sqr-neg 59.8%

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

   14. sqrt-unprod 45.6%

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

   15. add-sqr-sqrt 97.7%

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

8. Applied egg-rr 97.7%

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

Alternative 2: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00082:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.00082) x (if (<= y 2.2e+55) (* z (/ x (- y))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.00082) {
		tmp = x;
	} else if (y <= 2.2e+55) {
		tmp = z * (x / -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 <= (-0.00082d0)) then
        tmp = x
    else if (y <= 2.2d+55) then
        tmp = z * (x / -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 <= -0.00082) {
		tmp = x;
	} else if (y <= 2.2e+55) {
		tmp = z * (x / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.00082:
		tmp = x
	elif y <= 2.2e+55:
		tmp = z * (x / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.00082)
		tmp = x;
	elseif (y <= 2.2e+55)
		tmp = Float64(z * Float64(x / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.00082)
		tmp = x;
	elseif (y <= 2.2e+55)
		tmp = z * (x / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.00082], x, If[LessEqual[y, 2.2e+55], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999998e-4 or 2.2000000000000001e55 < y

   1. Initial program 75.3%

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

      1. remove-double-neg 75.3%

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

      2. distribute-frac-neg2 75.3%

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

      3. distribute-frac-neg 75.3%

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

      4. distribute-rgt-neg-in 75.3%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.5%

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

   if -8.1999999999999998e-4 < y < 2.2000000000000001e55

   1. Initial program 90.9%

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

      1. remove-double-neg 90.9%

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

      2. distribute-frac-neg2 90.9%

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

      3. distribute-frac-neg 90.9%

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

      4. distribute-rgt-neg-in 90.9%

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

      5. associate-/l* 95.5%

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

      6. distribute-frac-neg 95.5%

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

      7. distribute-frac-neg2 95.5%

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

      8. remove-double-neg 95.5%

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

      9. div-sub 95.5%

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

      10. *-inverses 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. distribute-frac-neg2 73.5%

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

      3. *-commutative 73.5%

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

      4. associate-/l* 74.6%

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

   7. Simplified 74.6%

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

Alternative 3: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.65e-5) x (if (<= y 2.15e+55) (* x (/ z (- y))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.65e-5) {
		tmp = x;
	} else if (y <= 2.15e+55) {
		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 <= (-2.65d-5)) then
        tmp = x
    else if (y <= 2.15d+55) 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 <= -2.65e-5) {
		tmp = x;
	} else if (y <= 2.15e+55) {
		tmp = x * (z / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.65e-5:
		tmp = x
	elif y <= 2.15e+55:
		tmp = x * (z / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.65e-5)
		tmp = x;
	elseif (y <= 2.15e+55)
		tmp = Float64(x * Float64(z / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.65e-5)
		tmp = x;
	elseif (y <= 2.15e+55)
		tmp = x * (z / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.65e-5], x, If[LessEqual[y, 2.15e+55], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65e-5 or 2.1499999999999999e55 < y

   1. Initial program 75.3%

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

      1. remove-double-neg 75.3%

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

      2. distribute-frac-neg2 75.3%

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

      3. distribute-frac-neg 75.3%

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

      4. distribute-rgt-neg-in 75.3%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.5%

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

   if -2.65e-5 < y < 2.1499999999999999e55

   1. Initial program 90.9%

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

      1. remove-double-neg 90.9%

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

      2. distribute-frac-neg2 90.9%

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

      3. distribute-frac-neg 90.9%

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

      4. distribute-rgt-neg-in 90.9%

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

      5. associate-/l* 95.5%

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

      6. distribute-frac-neg 95.5%

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

      7. distribute-frac-neg2 95.5%

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

      8. remove-double-neg 95.5%

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

      9. div-sub 95.5%

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

      10. *-inverses 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. distribute-frac-neg2 73.5%

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

      3. associate-*r/ 73.2%

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

   7. Simplified 73.2%

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

Alternative 4: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 5e+23) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e+23) {
		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 <= 5d+23) 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 <= 5e+23) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5e+23:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5e+23)
		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 <= 5e+23)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5e+23], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.9999999999999999e23

   1. Initial program 85.8%

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

      1. remove-double-neg 85.8%

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

      2. distribute-frac-neg2 85.8%

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

      3. distribute-frac-neg 85.8%

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

      4. distribute-rgt-neg-in 85.8%

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

      5. associate-/l* 97.1%

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

      6. distribute-frac-neg 97.1%

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

      7. distribute-frac-neg2 97.1%

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

      8. remove-double-neg 97.1%

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

      9. div-sub 97.1%

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

      10. *-inverses 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 55.9%

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

   if 4.9999999999999999e23 < x

   1. Initial program 73.5%

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

   3. Taylor expanded in y around inf 16.5%

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

      1. *-commutative 16.5%

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

      2. associate-/l* 50.1%

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

   5. Applied egg-rr 50.1%

      \[\leadsto \color{blue}{y \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. 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 83.2%

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

   1. remove-double-neg 83.2%

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

   2. distribute-frac-neg2 83.2%

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

   3. distribute-frac-neg 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

Alternative 6: 49.8% 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 83.2%

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

   1. remove-double-neg 83.2%

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

   2. distribute-frac-neg2 83.2%

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

   3. distribute-frac-neg 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around 0 52.9%

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

Developer Target 1: 95.9% 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 2024146 
(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))