Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.6% → 95.9%

Time: 5.4s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \frac{y}{z}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

   1. associate-*l/ 83.3%

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

   2. remove-double-neg 83.3%

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

   3. unsub-neg 83.3%

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

   4. distribute-rgt-out-- 77.8%

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

   5. *-commutative 77.8%

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

   6. remove-double-neg 77.8%

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

   7. distribute-frac-neg2 77.8%

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

   8. distribute-frac-neg 77.8%

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

   9. associate-*l/ 83.1%

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

   10. associate-/l* 94.8%

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

   11. *-inverses 94.8%

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

   12. *-rgt-identity 94.8%

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

   13. associate-*r/ 93.4%

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

   14. *-commutative 93.4%

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

   15. associate-*r/ 96.9%

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

   16. fma-neg 96.9%

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

   17. remove-double-neg 96.9%

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

3. Simplified 96.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y}{z}, x\right)} \]
4. Add Preprocessing

5. Final simplification 96.9%

   \[\leadsto \mathsf{fma}\left(x, \frac{y}{z}, x\right) \]
6. Add Preprocessing

Alternative 2: 70.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.75e+93) x (if (<= z 1.22e+60) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.75e+93) {
		tmp = x;
	} else if (z <= 1.22e+60) {
		tmp = x * (y / z);
	} 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 <= (-3.75d+93)) then
        tmp = x
    else if (z <= 1.22d+60) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.75e+93) {
		tmp = x;
	} else if (z <= 1.22e+60) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.75e+93:
		tmp = x
	elif z <= 1.22e+60:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.75e+93)
		tmp = x;
	elseif (z <= 1.22e+60)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.75e+93)
		tmp = x;
	elseif (z <= 1.22e+60)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.75e+93], x, If[LessEqual[z, 1.22e+60], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7500000000000001e93 or 1.21999999999999995e60 < z

   1. Initial program 66.9%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. distribute-frac-neg2 100.0%

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

      6. remove-double-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. div-sub 100.0%

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

      9. *-inverses 100.0%

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

      10. metadata-eval 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-lft-in 100.0%

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

      15. distribute-lft-neg-out 100.0%

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

      16. distribute-rgt-neg-out 100.0%

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

      17. distribute-frac-neg2 100.0%

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

      18. remove-double-neg 100.0%

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

      19. distribute-lft-neg-in 100.0%

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

      20. distribute-rgt-neg-in 100.0%

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

      21. distribute-lft-in 100.0%

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

      22. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.6%

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

   if -3.7500000000000001e93 < z < 1.21999999999999995e60

   1. Initial program 94.8%

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

      1. associate-/l* 95.2%

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

      2. remove-double-neg 95.2%

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

      3. distribute-lft-neg-in 95.2%

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

      4. distribute-rgt-neg-in 95.2%

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

      5. distribute-frac-neg2 95.2%

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

      6. remove-double-neg 95.2%

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

      7. unsub-neg 95.2%

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

      8. div-sub 95.2%

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

      9. *-inverses 95.2%

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

      10. metadata-eval 95.2%

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

      11. sub-neg 95.2%

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

      12. metadata-eval 95.2%

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

      13. metadata-eval 95.2%

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

      14. distribute-lft-in 95.2%

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

      15. distribute-lft-neg-out 95.2%

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

      16. distribute-rgt-neg-out 95.2%

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

      17. distribute-frac-neg2 95.2%

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

      18. remove-double-neg 95.2%

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

      19. distribute-lft-neg-in 95.2%

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

      20. distribute-rgt-neg-in 95.2%

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

      21. distribute-lft-in 95.2%

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

      22. sub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around inf 72.9%

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

      1. associate-*r/ 72.7%

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

   7. Simplified 72.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+94) x (if (<= z 2.9e+60) (* y (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+94) {
		tmp = x;
	} else if (z <= 2.9e+60) {
		tmp = y * (x / z);
	} 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 <= (-1.55d+94)) then
        tmp = x
    else if (z <= 2.9d+60) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+94) {
		tmp = x;
	} else if (z <= 2.9e+60) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+94:
		tmp = x
	elif z <= 2.9e+60:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+94)
		tmp = x;
	elseif (z <= 2.9e+60)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e+94)
		tmp = x;
	elseif (z <= 2.9e+60)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+94], x, If[LessEqual[z, 2.9e+60], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999996e94 or 2.9e60 < z

   1. Initial program 66.9%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. distribute-frac-neg2 100.0%

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

      6. remove-double-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. div-sub 100.0%

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

      9. *-inverses 100.0%

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

      10. metadata-eval 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-lft-in 100.0%

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

      15. distribute-lft-neg-out 100.0%

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

      16. distribute-rgt-neg-out 100.0%

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

      17. distribute-frac-neg2 100.0%

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

      18. remove-double-neg 100.0%

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

      19. distribute-lft-neg-in 100.0%

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

      20. distribute-rgt-neg-in 100.0%

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

      21. distribute-lft-in 100.0%

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

      22. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.6%

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

   if -1.54999999999999996e94 < z < 2.9e60

   1. Initial program 94.8%

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

      1. associate-/l* 95.2%

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

      2. remove-double-neg 95.2%

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

      3. distribute-lft-neg-in 95.2%

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

      4. distribute-rgt-neg-in 95.2%

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

      5. distribute-frac-neg2 95.2%

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

      6. remove-double-neg 95.2%

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

      7. unsub-neg 95.2%

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

      8. div-sub 95.2%

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

      9. *-inverses 95.2%

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

      10. metadata-eval 95.2%

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

      11. sub-neg 95.2%

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

      12. metadata-eval 95.2%

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

      13. metadata-eval 95.2%

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

      14. distribute-lft-in 95.2%

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

      15. distribute-lft-neg-out 95.2%

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

      16. distribute-rgt-neg-out 95.2%

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

      17. distribute-frac-neg2 95.2%

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

      18. remove-double-neg 95.2%

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

      19. distribute-lft-neg-in 95.2%

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

      20. distribute-rgt-neg-in 95.2%

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

      21. distribute-lft-in 95.2%

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

      22. sub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 74.9%

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

   7. Applied egg-rr 74.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+117) (* y (/ x z)) (if (<= y 6e-34) x (/ (* x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+117) {
		tmp = y * (x / z);
	} else if (y <= 6e-34) {
		tmp = x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.8d+117)) then
        tmp = y * (x / z)
    else if (y <= 6d-34) then
        tmp = x
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+117) {
		tmp = y * (x / z);
	} else if (y <= 6e-34) {
		tmp = x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+117:
		tmp = y * (x / z)
	elif y <= 6e-34:
		tmp = x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+117)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 6e-34)
		tmp = x;
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+117)
		tmp = y * (x / z);
	elseif (y <= 6e-34)
		tmp = x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+117], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-34], x, N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e117

   1. Initial program 89.0%

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

      1. associate-/l* 92.7%

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

      2. remove-double-neg 92.7%

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

      3. distribute-lft-neg-in 92.7%

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

      4. distribute-rgt-neg-in 92.7%

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

      5. distribute-frac-neg2 92.7%

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

      6. remove-double-neg 92.7%

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

      7. unsub-neg 92.7%

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

      8. div-sub 92.7%

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

      9. *-inverses 92.7%

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

      10. metadata-eval 92.7%

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

      11. sub-neg 92.7%

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

      12. metadata-eval 92.7%

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

      13. metadata-eval 92.7%

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

      14. distribute-lft-in 92.7%

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

      15. distribute-lft-neg-out 92.7%

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

      16. distribute-rgt-neg-out 92.7%

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

      17. distribute-frac-neg2 92.7%

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

      18. remove-double-neg 92.7%

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

      19. distribute-lft-neg-in 92.7%

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

      20. distribute-rgt-neg-in 92.7%

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

      21. distribute-lft-in 92.7%

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

      22. sub-neg 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-/l* 89.6%

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

   7. Applied egg-rr 89.6%

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

   if -3.8000000000000002e117 < y < 6e-34

   1. Initial program 80.7%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. distribute-frac-neg2 99.9%

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

      6. remove-double-neg 99.9%

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

      7. unsub-neg 99.9%

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

      8. div-sub 99.9%

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

      9. *-inverses 99.9%

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

      10. metadata-eval 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. distribute-lft-in 99.9%

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

      15. distribute-lft-neg-out 99.9%

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

      16. distribute-rgt-neg-out 99.9%

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

      17. distribute-frac-neg2 99.9%

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

      18. remove-double-neg 99.9%

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

      19. distribute-lft-neg-in 99.9%

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

      20. distribute-rgt-neg-in 99.9%

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

      21. distribute-lft-in 99.9%

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

      22. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 72.1%

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

   if 6e-34 < y

   1. Initial program 88.3%

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

      1. associate-/l* 94.8%

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

      2. remove-double-neg 94.8%

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

      3. distribute-lft-neg-in 94.8%

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

      4. distribute-rgt-neg-in 94.8%

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

      5. distribute-frac-neg2 94.8%

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

      6. remove-double-neg 94.8%

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

      7. unsub-neg 94.8%

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

      8. div-sub 94.8%

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

      9. *-inverses 94.8%

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

      10. metadata-eval 94.8%

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

      11. sub-neg 94.8%

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

      12. metadata-eval 94.8%

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

      13. metadata-eval 94.8%

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

      14. distribute-lft-in 94.8%

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

      15. distribute-lft-neg-out 94.8%

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

      16. distribute-rgt-neg-out 94.8%

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

      17. distribute-frac-neg2 94.8%

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

      18. remove-double-neg 94.8%

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

      19. distribute-lft-neg-in 94.8%

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

      20. distribute-rgt-neg-in 94.8%

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

      21. distribute-lft-in 94.8%

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

      22. sub-neg 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around inf 78.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) - (-1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

   1. associate-/l* 96.9%

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

   2. remove-double-neg 96.9%

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

   3. distribute-lft-neg-in 96.9%

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

   4. distribute-rgt-neg-in 96.9%

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

   5. distribute-frac-neg2 96.9%

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

   6. remove-double-neg 96.9%

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

   7. unsub-neg 96.9%

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

   8. div-sub 96.9%

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

   9. *-inverses 96.9%

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

   10. metadata-eval 96.9%

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

   11. sub-neg 96.9%

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

   12. metadata-eval 96.9%

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

   13. metadata-eval 96.9%

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

   14. distribute-lft-in 96.9%

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

   15. distribute-lft-neg-out 96.9%

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

   16. distribute-rgt-neg-out 96.9%

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

   17. distribute-frac-neg2 96.9%

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

   18. remove-double-neg 96.9%

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

   19. distribute-lft-neg-in 96.9%

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

   20. distribute-rgt-neg-in 96.9%

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

   21. distribute-lft-in 96.9%

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

   22. sub-neg 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 6: 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 84.6%

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

   1. associate-/l* 96.9%

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

   2. remove-double-neg 96.9%

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

   3. distribute-lft-neg-in 96.9%

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

   4. distribute-rgt-neg-in 96.9%

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

   5. distribute-frac-neg2 96.9%

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

   6. remove-double-neg 96.9%

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

   7. unsub-neg 96.9%

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

   8. div-sub 96.9%

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

   9. *-inverses 96.9%

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

   10. metadata-eval 96.9%

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

   11. sub-neg 96.9%

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

   12. metadata-eval 96.9%

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

   13. metadata-eval 96.9%

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

   14. distribute-lft-in 96.9%

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

   15. distribute-lft-neg-out 96.9%

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

   16. distribute-rgt-neg-out 96.9%

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

   17. distribute-frac-neg2 96.9%

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

   18. remove-double-neg 96.9%

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

   19. distribute-lft-neg-in 96.9%

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

   20. distribute-rgt-neg-in 96.9%

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

   21. distribute-lft-in 96.9%

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

   22. sub-neg 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in y around 0 45.2%

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

6. Final simplification 45.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))