Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 85.1% → 95.9%

Time: 5.0s

Alternatives: 5

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: 85.1% 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, 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 83.6%

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

   1. associate-/l* 96.5%

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

   2. remove-double-neg 96.5%

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

   3. unsub-neg 96.5%

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

   4. div-sub 96.5%

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

   5. remove-double-neg 96.5%

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

   6. distribute-frac-neg2 96.5%

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

   7. *-inverses 96.5%

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

   8. metadata-eval 96.5%

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

3. Simplified 96.5%

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

Alternative 2: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+80} \lor \neg \left(y \leq 8200\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+80) (not (<= y 8200.0))) (* y (/ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+80) || !(y <= 8200.0)) {
		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 ((y <= (-4.2d+80)) .or. (.not. (y <= 8200.0d0))) 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 ((y <= -4.2e+80) || !(y <= 8200.0)) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+80) or not (y <= 8200.0):
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+80) || !(y <= 8200.0))
		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 ((y <= -4.2e+80) || ~((y <= 8200.0)))
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+80], N[Not[LessEqual[y, 8200.0]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000003e80 or 8200 < y

   1. Initial program 88.6%

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

      1. associate-/l* 91.9%

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

      2. remove-double-neg 91.9%

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

      3. unsub-neg 91.9%

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

      4. div-sub 91.9%

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

      5. remove-double-neg 91.9%

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

      6. distribute-frac-neg2 91.9%

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

      7. *-inverses 91.9%

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

      8. metadata-eval 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around inf 75.4%

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

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   if -4.20000000000000003e80 < y < 8200

   1. Initial program 80.0%

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

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   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 73.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+80} \lor \neg \left(y \leq 8200\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+80} \lor \neg \left(y \leq 6000\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+80) (not (<= y 6000.0))) (* x (/ y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+80) || !(y <= 6000.0)) {
		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 ((y <= (-5.8d+80)) .or. (.not. (y <= 6000.0d0))) 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 ((y <= -5.8e+80) || !(y <= 6000.0)) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+80) or not (y <= 6000.0):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+80) || !(y <= 6000.0))
		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 ((y <= -5.8e+80) || ~((y <= 6000.0)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e+80], N[Not[LessEqual[y, 6000.0]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999971e80 or 6e3 < y

   1. Initial program 88.6%

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

      1. associate-/l* 91.9%

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

      2. remove-double-neg 91.9%

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

      3. unsub-neg 91.9%

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

      4. div-sub 91.9%

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

      5. remove-double-neg 91.9%

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

      6. distribute-frac-neg2 91.9%

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

      7. *-inverses 91.9%

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

      8. metadata-eval 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around inf 73.5%

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

   if -5.79999999999999971e80 < y < 6e3

   1. Initial program 80.0%

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

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   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 73.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+80} \lor \neg \left(y \leq 6000\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.4e+80) (* y (/ x z)) (if (<= y 5000.0) x (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+80) {
		tmp = y * (x / z);
	} else if (y <= 5000.0) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.4d+80)) then
        tmp = y * (x / z)
    else if (y <= 5000.0d0) then
        tmp = x
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+80) {
		tmp = y * (x / z);
	} else if (y <= 5000.0) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.4e+80:
		tmp = y * (x / z)
	elif y <= 5000.0:
		tmp = x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.4e+80)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 5000.0)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.4e+80)
		tmp = y * (x / z);
	elseif (y <= 5000.0)
		tmp = x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.4e+80], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5000.0], x, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.40000000000000005e80

   1. Initial program 84.8%

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

      1. associate-/l* 91.1%

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

      2. remove-double-neg 91.1%

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

      3. unsub-neg 91.1%

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

      4. div-sub 91.1%

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

      5. remove-double-neg 91.1%

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

      6. distribute-frac-neg2 91.1%

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

      7. *-inverses 91.1%

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

      8. metadata-eval 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around inf 74.3%

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

      1. associate-*l/ 79.6%

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

      2. *-commutative 79.6%

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

   7. Simplified 79.6%

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

   if -4.40000000000000005e80 < y < 5e3

   1. Initial program 80.0%

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

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   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 73.9%

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

   if 5e3 < y

   1. Initial program 91.1%

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

      1. associate-/l* 92.4%

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

      2. remove-double-neg 92.4%

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

      3. unsub-neg 92.4%

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

      4. div-sub 92.5%

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

      5. remove-double-neg 92.5%

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

      6. distribute-frac-neg2 92.5%

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

      7. *-inverses 92.5%

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

      8. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around inf 73.1%

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

      1. associate-*r/ 76.1%

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

      2. associate-*l/ 78.9%

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

      3. *-commutative 78.9%

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

      4. clear-num 78.8%

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

      5. un-div-inv 79.0%

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

   7. Applied egg-rr 79.0%

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

Alternative 5: 50.5% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.6%

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

   1. associate-/l* 96.5%

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

   2. remove-double-neg 96.5%

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

   3. unsub-neg 96.5%

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

   4. div-sub 96.5%

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

   5. remove-double-neg 96.5%

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

   6. distribute-frac-neg2 96.5%

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

   7. *-inverses 96.5%

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

   8. metadata-eval 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in y around 0 51.3%

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

Developer Target 1: 96.2% 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 2024158 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ z (+ y z))))

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