Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.7% → 96.6%

Time: 4.8s

Alternatives: 7

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: 84.7% 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: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-*l/ 83.1%

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

3. Simplified 83.1%

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

   1. associate-/r/ 97.2%

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

   2. +-commutative 97.2%

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

5. Applied egg-rr 97.2%

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

6. Final simplification 97.2%

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

Alternative 2: 70.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2200000 \lor \neg \left(y \leq 7.8 \cdot 10^{+50} \lor \neg \left(y \leq 1.9 \cdot 10^{+142}\right) \land y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2200000.0)
         (not (or (<= y 7.8e+50) (and (not (<= y 1.9e+142)) (<= y 3.6e+176)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2200000.0) || !((y <= 7.8e+50) || (!(y <= 1.9e+142) && (y <= 3.6e+176)))) {
		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 <= (-2200000.0d0)) .or. (.not. (y <= 7.8d+50) .or. (.not. (y <= 1.9d+142)) .and. (y <= 3.6d+176))) 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 <= -2200000.0) || !((y <= 7.8e+50) || (!(y <= 1.9e+142) && (y <= 3.6e+176)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2200000.0) or not ((y <= 7.8e+50) or (not (y <= 1.9e+142) and (y <= 3.6e+176))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2200000.0) || !((y <= 7.8e+50) || (!(y <= 1.9e+142) && (y <= 3.6e+176))))
		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 <= -2200000.0) || ~(((y <= 7.8e+50) || (~((y <= 1.9e+142)) && (y <= 3.6e+176)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2200000.0], N[Not[Or[LessEqual[y, 7.8e+50], And[N[Not[LessEqual[y, 1.9e+142]], $MachinePrecision], LessEqual[y, 3.6e+176]]]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e6 or 7.79999999999999935e50 < y < 1.89999999999999995e142 or 3.59999999999999991e176 < y

   1. Initial program 92.7%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around 0 78.9%

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

      1. associate-*r/ 72.6%

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

   6. Simplified 72.6%

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

   if -2.2e6 < y < 7.79999999999999935e50 or 1.89999999999999995e142 < y < 3.59999999999999991e176

   1. Initial program 78.8%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 79.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2200000 \lor \neg \left(y \leq 7.8 \cdot 10^{+50} \lor \neg \left(y \leq 1.9 \cdot 10^{+142}\right) \land y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -620000 \lor \neg \left(y \leq 8.8 \cdot 10^{+50} \lor \neg \left(y \leq 6 \cdot 10^{+149}\right) \land y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -620000.0)
         (not (or (<= y 8.8e+50) (and (not (<= y 6e+149)) (<= y 3.6e+176)))))
   (/ (* x y) z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -620000.0) || !((y <= 8.8e+50) || (!(y <= 6e+149) && (y <= 3.6e+176)))) {
		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 <= (-620000.0d0)) .or. (.not. (y <= 8.8d+50) .or. (.not. (y <= 6d+149)) .and. (y <= 3.6d+176))) 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 <= -620000.0) || !((y <= 8.8e+50) || (!(y <= 6e+149) && (y <= 3.6e+176)))) {
		tmp = (x * y) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -620000.0) or not ((y <= 8.8e+50) or (not (y <= 6e+149) and (y <= 3.6e+176))):
		tmp = (x * y) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -620000.0) || !((y <= 8.8e+50) || (!(y <= 6e+149) && (y <= 3.6e+176))))
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -620000.0) || ~(((y <= 8.8e+50) || (~((y <= 6e+149)) && (y <= 3.6e+176)))))
		tmp = (x * y) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -620000.0], N[Not[Or[LessEqual[y, 8.8e+50], And[N[Not[LessEqual[y, 6e+149]], $MachinePrecision], LessEqual[y, 3.6e+176]]]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.2e5 or 8.80000000000000067e50 < y < 6.00000000000000007e149 or 3.59999999999999991e176 < y

   1. Initial program 92.7%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around 0 78.9%

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

   if -6.2e5 < y < 8.80000000000000067e50 or 6.00000000000000007e149 < y < 3.59999999999999991e176

   1. Initial program 78.8%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 79.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -620000 \lor \neg \left(y \leq 8.8 \cdot 10^{+50} \lor \neg \left(y \leq 6 \cdot 10^{+149}\right) \land y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-105} \lor \neg \left(z \leq 1.15 \cdot 10^{-82}\right) \land z \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-53)
   x
   (if (or (<= z 8e-105) (and (not (<= z 1.15e-82)) (<= z 1.25e-17)))
     (/ y (/ z x))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-53) {
		tmp = x;
	} else if ((z <= 8e-105) || (!(z <= 1.15e-82) && (z <= 1.25e-17))) {
		tmp = y / (z / 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 <= (-7.5d-53)) then
        tmp = x
    else if ((z <= 8d-105) .or. (.not. (z <= 1.15d-82)) .and. (z <= 1.25d-17)) then
        tmp = y / (z / 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 <= -7.5e-53) {
		tmp = x;
	} else if ((z <= 8e-105) || (!(z <= 1.15e-82) && (z <= 1.25e-17))) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-53:
		tmp = x
	elif (z <= 8e-105) or (not (z <= 1.15e-82) and (z <= 1.25e-17)):
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-53)
		tmp = x;
	elseif ((z <= 8e-105) || (!(z <= 1.15e-82) && (z <= 1.25e-17)))
		tmp = Float64(y / Float64(z / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-53)
		tmp = x;
	elseif ((z <= 8e-105) || (~((z <= 1.15e-82)) && (z <= 1.25e-17)))
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-53], x, If[Or[LessEqual[z, 8e-105], And[N[Not[LessEqual[z, 1.15e-82]], $MachinePrecision], LessEqual[z, 1.25e-17]]], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000001e-53 or 7.99999999999999972e-105 < z < 1.14999999999999998e-82 or 1.25e-17 < z

   1. Initial program 78.4%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in z around inf 80.0%

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

   if -7.5000000000000001e-53 < z < 7.99999999999999972e-105 or 1.14999999999999998e-82 < z < 1.25e-17

   1. Initial program 92.7%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 74.3%

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

      1. associate-*r/ 71.9%

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

   6. Simplified 71.9%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-/l* 76.7%

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

   8. Applied egg-rr 76.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-105} \lor \neg \left(z \leq 1.15 \cdot 10^{-82}\right) \land z \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -8000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (/ z y))))
   (if (<= y -8000000.0)
     t_0
     (if (<= y 3.7e+50)
       x
       (if (<= y 5.8e+149) (* x (/ y z)) (if (<= y 4.1e+176) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z / y);
	double tmp;
	if (y <= -8000000.0) {
		tmp = t_0;
	} else if (y <= 3.7e+50) {
		tmp = x;
	} else if (y <= 5.8e+149) {
		tmp = x * (y / z);
	} else if (y <= 4.1e+176) {
		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 = x / (z / y)
    if (y <= (-8000000.0d0)) then
        tmp = t_0
    else if (y <= 3.7d+50) then
        tmp = x
    else if (y <= 5.8d+149) then
        tmp = x * (y / z)
    else if (y <= 4.1d+176) 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 = x / (z / y);
	double tmp;
	if (y <= -8000000.0) {
		tmp = t_0;
	} else if (y <= 3.7e+50) {
		tmp = x;
	} else if (y <= 5.8e+149) {
		tmp = x * (y / z);
	} else if (y <= 4.1e+176) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z / y)
	tmp = 0
	if y <= -8000000.0:
		tmp = t_0
	elif y <= 3.7e+50:
		tmp = x
	elif y <= 5.8e+149:
		tmp = x * (y / z)
	elif y <= 4.1e+176:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (y <= -8000000.0)
		tmp = t_0;
	elseif (y <= 3.7e+50)
		tmp = x;
	elseif (y <= 5.8e+149)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 4.1e+176)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z / y);
	tmp = 0.0;
	if (y <= -8000000.0)
		tmp = t_0;
	elseif (y <= 3.7e+50)
		tmp = x;
	elseif (y <= 5.8e+149)
		tmp = x * (y / z);
	elseif (y <= 4.1e+176)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8000000.0], t$95$0, If[LessEqual[y, 3.7e+50], x, If[LessEqual[y, 5.8e+149], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+176], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e6 or 4.0999999999999999e176 < y

   1. Initial program 91.3%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

      1. associate-/r/ 94.1%

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

      2. +-commutative 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in z around 0 77.0%

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

      1. associate-/l* 72.4%

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

   8. Simplified 72.4%

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

   if -8e6 < y < 3.7000000000000001e50 or 5.8000000000000004e149 < y < 4.0999999999999999e176

   1. Initial program 78.8%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 79.4%

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

   if 3.7000000000000001e50 < y < 5.8000000000000004e149

   1. Initial program 99.7%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in z around 0 88.5%

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

      1. associate-*r/ 77.6%

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

   6. Simplified 77.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8000000:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 6: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-*r/ 97.0%

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

   2. remove-double-neg 97.0%

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

   3. sub-neg 97.0%

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

   4. div-sub 97.0%

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

   5. distribute-frac-neg 97.0%

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

   6. *-inverses 97.0%

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

   7. metadata-eval 97.0%

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

   8. sub-neg 97.0%

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

   9. metadata-eval 97.0%

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

   10. *-inverses 97.0%

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

   11. distribute-lft-out 97.0%

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

   12. *-inverses 97.0%

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

   13. *-rgt-identity 97.0%

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

   14. fma-def 97.0%

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

3. Simplified 97.0%

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

4. Taylor expanded in x around 0 97.0%

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

5. Final simplification 97.0%

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

Alternative 7: 51.4% 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 84.4%

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

   1. associate-*l/ 83.1%

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

3. Simplified 83.1%

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

4. Taylor expanded in z around inf 55.7%

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

5. Final simplification 55.7%

   \[\leadsto x \]

Developer target: 96.6% 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 2023310 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

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