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

Percentage Accurate: 84.9% → 95.9%

Time: 6.0s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% 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 84.3%

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

   1. remove-double-neg 84.3%

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

   2. distribute-frac-neg2 84.3%

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

   3. distribute-frac-neg 84.3%

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

   4. distribute-rgt-neg-in 84.3%

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

   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 54.6%

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

   4. sqr-neg 54.6%

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

   5. sqrt-unprod 27.0%

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

   6. add-sqr-sqrt 50.5%

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

   7. cancel-sign-sub-inv 50.5%

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

   8. associate-*r/ 48.2%

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

   9. add-sqr-sqrt 21.5%

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

   10. sqrt-unprod 62.9%

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

   11. sqr-neg 62.9%

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

   12. sqrt-unprod 47.8%

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

   13. add-sqr-sqrt 94.2%

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

   14. *-commutative 94.2%

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

8. Applied egg-rr 94.2%

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

9. Taylor expanded in z around 0 94.2%

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

    1. associate-*l/ 91.6%

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

    2. associate-/r/ 97.9%

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

11. Simplified 97.9%

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

12. Final simplification 97.9%

    \[\leadsto x - \frac{x}{\frac{y}{z}} \]
13. Add Preprocessing

Alternative 2: 68.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+138} \lor \neg \left(z \leq 7.5 \cdot 10^{-6} \lor \neg \left(z \leq 6.9 \cdot 10^{+55}\right) \land z \leq 2.35 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e+138)
         (not (or (<= z 7.5e-6) (and (not (<= z 6.9e+55)) (<= z 2.35e+91)))))
   (* (/ z y) (- x))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+138) || !((z <= 7.5e-6) || (!(z <= 6.9e+55) && (z <= 2.35e+91)))) {
		tmp = (z / y) * -x;
	} 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 ((z <= (-3d+138)) .or. (.not. (z <= 7.5d-6) .or. (.not. (z <= 6.9d+55)) .and. (z <= 2.35d+91))) then
        tmp = (z / y) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+138) || !((z <= 7.5e-6) || (!(z <= 6.9e+55) && (z <= 2.35e+91)))) {
		tmp = (z / y) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e+138) or not ((z <= 7.5e-6) or (not (z <= 6.9e+55) and (z <= 2.35e+91))):
		tmp = (z / y) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e+138) || !((z <= 7.5e-6) || (!(z <= 6.9e+55) && (z <= 2.35e+91))))
		tmp = Float64(Float64(z / y) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e+138) || ~(((z <= 7.5e-6) || (~((z <= 6.9e+55)) && (z <= 2.35e+91)))))
		tmp = (z / y) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e+138], N[Not[Or[LessEqual[z, 7.5e-6], And[N[Not[LessEqual[z, 6.9e+55]], $MachinePrecision], LessEqual[z, 2.35e+91]]]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e138 or 7.50000000000000019e-6 < z < 6.9000000000000004e55 or 2.3499999999999999e91 < z

   1. Initial program 87.0%

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

      1. remove-double-neg 87.0%

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

      2. distribute-frac-neg2 87.0%

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

      3. distribute-frac-neg 87.0%

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

      4. distribute-rgt-neg-in 87.0%

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

      5. associate-/l* 94.3%

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

      6. distribute-frac-neg 94.3%

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

      7. distribute-frac-neg2 94.3%

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

      8. remove-double-neg 94.3%

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

      9. div-sub 94.3%

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

      10. *-inverses 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-frac-neg2 80.0%

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

   7. Simplified 80.0%

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

   if -3.0000000000000001e138 < z < 7.50000000000000019e-6 or 6.9000000000000004e55 < z < 2.3499999999999999e91

   1. Initial program 82.4%

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

      1. remove-double-neg 82.4%

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

      2. distribute-frac-neg2 82.4%

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

      3. distribute-frac-neg 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      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 75.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+138} \lor \neg \left(z \leq 7.5 \cdot 10^{-6} \lor \neg \left(z \leq 6.9 \cdot 10^{+55}\right) \land z \leq 2.35 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) (- x))))
   (if (<= z -3.5e+140)
     t_0
     (if (<= z 1.1e-5)
       x
       (if (<= z 6.8e+59) (* (- z) (/ x y)) (if (<= z 4.9e+91) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -x;
	double tmp;
	if (z <= -3.5e+140) {
		tmp = t_0;
	} else if (z <= 1.1e-5) {
		tmp = x;
	} else if (z <= 6.8e+59) {
		tmp = -z * (x / y);
	} else if (z <= 4.9e+91) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (z / y) * -x
    if (z <= (-3.5d+140)) then
        tmp = t_0
    else if (z <= 1.1d-5) then
        tmp = x
    else if (z <= 6.8d+59) then
        tmp = -z * (x / y)
    else if (z <= 4.9d+91) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z / y) * -x;
	double tmp;
	if (z <= -3.5e+140) {
		tmp = t_0;
	} else if (z <= 1.1e-5) {
		tmp = x;
	} else if (z <= 6.8e+59) {
		tmp = -z * (x / y);
	} else if (z <= 4.9e+91) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -x
	tmp = 0
	if z <= -3.5e+140:
		tmp = t_0
	elif z <= 1.1e-5:
		tmp = x
	elif z <= 6.8e+59:
		tmp = -z * (x / y)
	elif z <= 4.9e+91:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * Float64(-x))
	tmp = 0.0
	if (z <= -3.5e+140)
		tmp = t_0;
	elseif (z <= 1.1e-5)
		tmp = x;
	elseif (z <= 6.8e+59)
		tmp = Float64(Float64(-z) * Float64(x / y));
	elseif (z <= 4.9e+91)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -x;
	tmp = 0.0;
	if (z <= -3.5e+140)
		tmp = t_0;
	elseif (z <= 1.1e-5)
		tmp = x;
	elseif (z <= 6.8e+59)
		tmp = -z * (x / y);
	elseif (z <= 4.9e+91)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[z, -3.5e+140], t$95$0, If[LessEqual[z, 1.1e-5], x, If[LessEqual[z, 6.8e+59], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+91], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999989e140 or 4.9000000000000003e91 < z

   1. Initial program 86.8%

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

      1. remove-double-neg 86.8%

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

      2. distribute-frac-neg2 86.8%

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

      3. distribute-frac-neg 86.8%

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

      4. distribute-rgt-neg-in 86.8%

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

      5. associate-/l* 93.8%

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

      6. distribute-frac-neg 93.8%

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

      7. distribute-frac-neg2 93.8%

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

      8. remove-double-neg 93.8%

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

      9. div-sub 93.9%

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

      10. *-inverses 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-frac-neg2 80.1%

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

   7. Simplified 80.1%

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

   if -3.49999999999999989e140 < z < 1.1e-5 or 6.80000000000000012e59 < z < 4.9000000000000003e91

   1. Initial program 82.4%

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

      1. remove-double-neg 82.4%

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

      2. distribute-frac-neg2 82.4%

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

      3. distribute-frac-neg 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      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 75.9%

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

   if 1.1e-5 < z < 6.80000000000000012e59

   1. Initial program 89.9%

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

      1. remove-double-neg 89.9%

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

      2. distribute-frac-neg2 89.9%

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

      3. distribute-frac-neg 89.9%

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

      4. distribute-rgt-neg-in 89.9%

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

      5. associate-/l* 99.5%

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

      6. distribute-frac-neg 99.5%

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

      7. distribute-frac-neg2 99.5%

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

      8. remove-double-neg 99.5%

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

      9. div-sub 99.5%

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

      10. *-inverses 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around inf 79.3%

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

      1. associate-*l/ 78.7%

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

      2. associate-*l* 78.7%

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

      3. *-commutative 78.7%

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

      4. associate-*r/ 78.7%

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

      5. mul-1-neg 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+60}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.4e+138)
   (/ x (/ y (- z)))
   (if (<= z 8.5e-6)
     x
     (if (<= z 5.2e+60)
       (* (- z) (/ x y))
       (if (<= z 3e+91) x (* (/ z y) (- x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e+138) {
		tmp = x / (y / -z);
	} else if (z <= 8.5e-6) {
		tmp = x;
	} else if (z <= 5.2e+60) {
		tmp = -z * (x / y);
	} else if (z <= 3e+91) {
		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 <= (-3.4d+138)) then
        tmp = x / (y / -z)
    else if (z <= 8.5d-6) then
        tmp = x
    else if (z <= 5.2d+60) then
        tmp = -z * (x / y)
    else if (z <= 3d+91) 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 <= -3.4e+138) {
		tmp = x / (y / -z);
	} else if (z <= 8.5e-6) {
		tmp = x;
	} else if (z <= 5.2e+60) {
		tmp = -z * (x / y);
	} else if (z <= 3e+91) {
		tmp = x;
	} else {
		tmp = (z / y) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.4e+138:
		tmp = x / (y / -z)
	elif z <= 8.5e-6:
		tmp = x
	elif z <= 5.2e+60:
		tmp = -z * (x / y)
	elif z <= 3e+91:
		tmp = x
	else:
		tmp = (z / y) * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.4e+138)
		tmp = Float64(x / Float64(y / Float64(-z)));
	elseif (z <= 8.5e-6)
		tmp = x;
	elseif (z <= 5.2e+60)
		tmp = Float64(Float64(-z) * Float64(x / y));
	elseif (z <= 3e+91)
		tmp = x;
	else
		tmp = Float64(Float64(z / y) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.4e+138)
		tmp = x / (y / -z);
	elseif (z <= 8.5e-6)
		tmp = x;
	elseif (z <= 5.2e+60)
		tmp = -z * (x / y);
	elseif (z <= 3e+91)
		tmp = x;
	else
		tmp = (z / y) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.4e+138], N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-6], x, If[LessEqual[z, 5.2e+60], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+91], x, N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000011e138

   1. Initial program 88.6%

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

      1. remove-double-neg 88.6%

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

      2. distribute-frac-neg2 88.6%

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

      3. distribute-frac-neg 88.6%

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

      4. distribute-rgt-neg-in 88.6%

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

      5. associate-/l* 93.2%

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

      6. distribute-frac-neg 93.2%

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

      7. distribute-frac-neg2 93.2%

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

      8. remove-double-neg 93.2%

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

      9. div-sub 93.2%

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

      10. *-inverses 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 81.7%

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

      1. associate-*l/ 80.0%

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

      2. associate-*l* 80.0%

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

      3. *-commutative 80.0%

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

      4. associate-*r/ 80.0%

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

      5. mul-1-neg 80.0%

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

   7. Simplified 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/r/ 83.9%

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

      3. frac-2neg 83.9%

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

      4. remove-double-neg 83.9%

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

      5. distribute-neg-frac2 83.9%

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

   9. Applied egg-rr 83.9%

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

   if -3.40000000000000011e138 < z < 8.4999999999999999e-6 or 5.20000000000000016e60 < z < 3.00000000000000006e91

   1. Initial program 82.4%

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

      1. remove-double-neg 82.4%

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

      2. distribute-frac-neg2 82.4%

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

      3. distribute-frac-neg 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      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 75.9%

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

   if 8.4999999999999999e-6 < z < 5.20000000000000016e60

   1. Initial program 89.9%

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

      1. remove-double-neg 89.9%

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

      2. distribute-frac-neg2 89.9%

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

      3. distribute-frac-neg 89.9%

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

      4. distribute-rgt-neg-in 89.9%

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

      5. associate-/l* 99.5%

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

      6. distribute-frac-neg 99.5%

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

      7. distribute-frac-neg2 99.5%

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

      8. remove-double-neg 99.5%

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

      9. div-sub 99.5%

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

      10. *-inverses 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around inf 79.3%

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

      1. associate-*l/ 78.7%

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

      2. associate-*l* 78.7%

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

      3. *-commutative 78.7%

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

      4. associate-*r/ 78.7%

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

      5. mul-1-neg 78.7%

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

   7. Simplified 78.7%

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

   if 3.00000000000000006e91 < z

   1. Initial program 85.3%

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

      1. remove-double-neg 85.3%

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

      2. distribute-frac-neg2 85.3%

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

      3. distribute-frac-neg 85.3%

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

      4. distribute-rgt-neg-in 85.3%

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

      5. associate-/l* 94.4%

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

      6. distribute-frac-neg 94.4%

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

      7. distribute-frac-neg2 94.4%

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

      8. remove-double-neg 94.4%

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

      9. div-sub 94.4%

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

      10. *-inverses 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. distribute-frac-neg2 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+60}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+138)
   (/ x (/ y (- z)))
   (if (<= z 1.02e-5)
     x
     (if (<= z 3.9e+55)
       (/ (* x (- z)) y)
       (if (<= z 2.2e+91) x (* (/ z y) (- x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+138) {
		tmp = x / (y / -z);
	} else if (z <= 1.02e-5) {
		tmp = x;
	} else if (z <= 3.9e+55) {
		tmp = (x * -z) / y;
	} else if (z <= 2.2e+91) {
		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 <= (-3d+138)) then
        tmp = x / (y / -z)
    else if (z <= 1.02d-5) then
        tmp = x
    else if (z <= 3.9d+55) then
        tmp = (x * -z) / y
    else if (z <= 2.2d+91) 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 <= -3e+138) {
		tmp = x / (y / -z);
	} else if (z <= 1.02e-5) {
		tmp = x;
	} else if (z <= 3.9e+55) {
		tmp = (x * -z) / y;
	} else if (z <= 2.2e+91) {
		tmp = x;
	} else {
		tmp = (z / y) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+138:
		tmp = x / (y / -z)
	elif z <= 1.02e-5:
		tmp = x
	elif z <= 3.9e+55:
		tmp = (x * -z) / y
	elif z <= 2.2e+91:
		tmp = x
	else:
		tmp = (z / y) * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+138)
		tmp = Float64(x / Float64(y / Float64(-z)));
	elseif (z <= 1.02e-5)
		tmp = x;
	elseif (z <= 3.9e+55)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (z <= 2.2e+91)
		tmp = x;
	else
		tmp = Float64(Float64(z / y) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+138)
		tmp = x / (y / -z);
	elseif (z <= 1.02e-5)
		tmp = x;
	elseif (z <= 3.9e+55)
		tmp = (x * -z) / y;
	elseif (z <= 2.2e+91)
		tmp = x;
	else
		tmp = (z / y) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+138], N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-5], x, If[LessEqual[z, 3.9e+55], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.2e+91], x, N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0000000000000001e138

   1. Initial program 88.6%

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

      1. remove-double-neg 88.6%

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

      2. distribute-frac-neg2 88.6%

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

      3. distribute-frac-neg 88.6%

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

      4. distribute-rgt-neg-in 88.6%

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

      5. associate-/l* 93.2%

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

      6. distribute-frac-neg 93.2%

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

      7. distribute-frac-neg2 93.2%

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

      8. remove-double-neg 93.2%

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

      9. div-sub 93.2%

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

      10. *-inverses 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 81.7%

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

      1. associate-*l/ 80.0%

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

      2. associate-*l* 80.0%

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

      3. *-commutative 80.0%

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

      4. associate-*r/ 80.0%

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

      5. mul-1-neg 80.0%

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

   7. Simplified 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/r/ 83.9%

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

      3. frac-2neg 83.9%

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

      4. remove-double-neg 83.9%

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

      5. distribute-neg-frac2 83.9%

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

   9. Applied egg-rr 83.9%

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

   if -3.0000000000000001e138 < z < 1.0200000000000001e-5 or 3.90000000000000027e55 < z < 2.19999999999999999e91

   1. Initial program 82.4%

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

      1. remove-double-neg 82.4%

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

      2. distribute-frac-neg2 82.4%

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

      3. distribute-frac-neg 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      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 75.9%

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

   if 1.0200000000000001e-5 < z < 3.90000000000000027e55

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0 79.3%

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

      1. associate-*r* 79.3%

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

      2. mul-1-neg 79.3%

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

   5. Simplified 79.3%

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

   if 2.19999999999999999e91 < z

   1. Initial program 85.3%

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

      1. remove-double-neg 85.3%

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

      2. distribute-frac-neg2 85.3%

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

      3. distribute-frac-neg 85.3%

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

      4. distribute-rgt-neg-in 85.3%

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

      5. associate-/l* 94.4%

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

      6. distribute-frac-neg 94.4%

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

      7. distribute-frac-neg2 94.4%

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

      8. remove-double-neg 94.4%

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

      9. div-sub 94.4%

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

      10. *-inverses 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. distribute-frac-neg2 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 4e+84) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e+84) {
		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+84) 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+84) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4e+84:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4e+84)
		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+84)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4e+84], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.00000000000000023e84

   1. Initial program 86.1%

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

      1. remove-double-neg 86.1%

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

      2. distribute-frac-neg2 86.1%

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

      3. distribute-frac-neg 86.1%

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

      4. distribute-rgt-neg-in 86.1%

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

      5. associate-/l* 97.3%

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

      6. distribute-frac-neg 97.3%

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

      7. distribute-frac-neg2 97.3%

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

      8. remove-double-neg 97.3%

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

      9. div-sub 97.3%

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

      10. *-inverses 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around 0 50.4%

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

   if 4.00000000000000023e84 < x

   1. Initial program 74.4%

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

   3. Taylor expanded in y around inf 38.0%

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

      1. *-commutative 38.0%

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

      2. associate-/l* 66.1%

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

   5. Applied egg-rr 66.1%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 3.9e+90) x (/ (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.9e+90) {
		tmp = x;
	} else {
		tmp = (x * z) / 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 (x <= 3.9d+90) then
        tmp = x
    else
        tmp = (x * z) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.9e+90) {
		tmp = x;
	} else {
		tmp = (x * z) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 3.9e+90:
		tmp = x
	else:
		tmp = (x * z) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.9e+90)
		tmp = x;
	else
		tmp = Float64(Float64(x * z) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.9e+90)
		tmp = x;
	else
		tmp = (x * z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.9e+90], x, N[(N[(x * z), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.9000000000000002e90

   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* 97.3%

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

      6. distribute-frac-neg 97.3%

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

      7. distribute-frac-neg2 97.3%

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

      8. remove-double-neg 97.3%

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

      9. div-sub 97.3%

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

      10. *-inverses 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around 0 50.8%

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

   if 3.9000000000000002e90 < x

   1. Initial program 75.6%

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

      1. remove-double-neg 75.6%

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

      2. distribute-frac-neg2 75.6%

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

      3. distribute-frac-neg 75.6%

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

      4. distribute-rgt-neg-in 75.6%

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

      5. associate-/l* 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. remove-double-neg 100.0%

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

      9. div-sub 100.0%

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

      10. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 73.2%

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

      1. +-commutative 73.2%

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

      2. mul-1-neg 73.2%

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

      3. unsub-neg 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in z around 0 32.6%

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

      1. associate-*r/ 61.7%

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

      2. *-commutative 61.7%

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

   10. Applied egg-rr 61.7%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.7% 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 84.3%

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

   1. remove-double-neg 84.3%

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

   2. distribute-frac-neg2 84.3%

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

   3. distribute-frac-neg 84.3%

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

   4. distribute-rgt-neg-in 84.3%

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

   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. Final simplification 97.7%

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

Alternative 9: 50.8% 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 84.3%

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

   1. remove-double-neg 84.3%

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

   2. distribute-frac-neg2 84.3%

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

   3. distribute-frac-neg 84.3%

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

   4. distribute-rgt-neg-in 84.3%

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

   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 51.7%

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

6. Final simplification 51.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 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 2024080 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

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

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