Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 83.9% → 95.1%

Time: 3.8s

Alternatives: 7

Speedup: 0.8×

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: 83.9% 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: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+166}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e+166) (/ (* y x) z) (/ x (/ z (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+166) {
		tmp = (y * x) / z;
	} else {
		tmp = x / (z / (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 <= (-3.6d+166)) then
        tmp = (y * x) / z
    else
        tmp = x / (z / (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+166) {
		tmp = (y * x) / z;
	} else {
		tmp = x / (z / (y + z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e+166:
		tmp = (y * x) / z
	else:
		tmp = x / (z / (y + z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e+166)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(x / Float64(z / Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e+166)
		tmp = (y * x) / z;
	else
		tmp = x / (z / (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e+166], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999997e166

   1. Initial program 96.6%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around 0 96.6%

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

   if -3.5999999999999997e166 < y

   1. Initial program 80.8%

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

      1. associate-*l/ 81.3%

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

   3. Simplified 81.3%

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

      1. associate-/r/ 97.8%

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

      2. +-commutative 97.8%

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

   5. Applied egg-rr 97.8%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+166}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \]

Alternative 2: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+117}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ y z) (/ x z))))
   (if (<= z -4e+158)
     x
     (if (<= z -1.75e-147)
       t_0
       (if (<= z -2.5e-284) (/ (* y x) z) (if (<= z 3.6e+117) t_0 x))))))

C

double code(double x, double y, double z) {
	double t_0 = (y + z) * (x / z);
	double tmp;
	if (z <= -4e+158) {
		tmp = x;
	} else if (z <= -1.75e-147) {
		tmp = t_0;
	} else if (z <= -2.5e-284) {
		tmp = (y * x) / z;
	} else if (z <= 3.6e+117) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (y + z) * (x / z)
    if (z <= (-4d+158)) then
        tmp = x
    else if (z <= (-1.75d-147)) then
        tmp = t_0
    else if (z <= (-2.5d-284)) then
        tmp = (y * x) / z
    else if (z <= 3.6d+117) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y + z) * (x / z);
	double tmp;
	if (z <= -4e+158) {
		tmp = x;
	} else if (z <= -1.75e-147) {
		tmp = t_0;
	} else if (z <= -2.5e-284) {
		tmp = (y * x) / z;
	} else if (z <= 3.6e+117) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + z) * (x / z)
	tmp = 0
	if z <= -4e+158:
		tmp = x
	elif z <= -1.75e-147:
		tmp = t_0
	elif z <= -2.5e-284:
		tmp = (y * x) / z
	elif z <= 3.6e+117:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + z) * Float64(x / z))
	tmp = 0.0
	if (z <= -4e+158)
		tmp = x;
	elseif (z <= -1.75e-147)
		tmp = t_0;
	elseif (z <= -2.5e-284)
		tmp = Float64(Float64(y * x) / z);
	elseif (z <= 3.6e+117)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + z) * (x / z);
	tmp = 0.0;
	if (z <= -4e+158)
		tmp = x;
	elseif (z <= -1.75e-147)
		tmp = t_0;
	elseif (z <= -2.5e-284)
		tmp = (y * x) / z;
	elseif (z <= 3.6e+117)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+158], x, If[LessEqual[z, -1.75e-147], t$95$0, If[LessEqual[z, -2.5e-284], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.6e+117], t$95$0, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999981e158 or 3.60000000000000013e117 < z

   1. Initial program 62.2%

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

      1. associate-*l/ 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in z around inf 92.0%

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

   if -3.99999999999999981e158 < z < -1.75000000000000002e-147 or -2.49999999999999987e-284 < z < 3.60000000000000013e117

   1. Initial program 90.5%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   if -1.75000000000000002e-147 < z < -2.49999999999999987e-284

   1. Initial program 93.4%

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

      1. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in z around 0 90.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+117}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 67.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+118} \lor \neg \left(y \leq 3 \cdot 10^{+172}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+118) (not (<= y 3e+172))) (* x (/ y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+118) || !(y <= 3e+172)) {
		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 <= (-3d+118)) .or. (.not. (y <= 3d+172))) 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 <= -3e+118) || !(y <= 3e+172)) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+118) or not (y <= 3e+172):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+118) || !(y <= 3e+172))
		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 <= -3e+118) || ~((y <= 3e+172)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+118], N[Not[LessEqual[y, 3e+172]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3e118 or 2.9999999999999999e172 < y

   1. Initial program 91.2%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in z around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*r/ 80.5%

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

   6. Simplified 80.5%

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

   if -3e118 < y < 2.9999999999999999e172

   1. Initial program 79.8%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in z around inf 72.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+118} \lor \neg \left(y \leq 3 \cdot 10^{+172}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+94} \lor \neg \left(y \leq 1.05 \cdot 10^{+173}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e+94) (not (<= y 1.05e+173))) (* y (/ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+94) || !(y <= 1.05e+173)) {
		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 <= (-1.05d+94)) .or. (.not. (y <= 1.05d+173))) 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 <= -1.05e+94) || !(y <= 1.05e+173)) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e+94) or not (y <= 1.05e+173):
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e+94) || !(y <= 1.05e+173))
		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 <= -1.05e+94) || ~((y <= 1.05e+173)))
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e+94], N[Not[LessEqual[y, 1.05e+173]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999995e94 or 1.05e173 < y

   1. Initial program 89.7%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in z around 0 83.1%

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

      1. associate-*r/ 86.3%

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

   6. Simplified 86.3%

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

   if -1.04999999999999995e94 < y < 1.05e173

   1. Initial program 79.9%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in z around inf 73.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+94} \lor \neg \left(y \leq 1.05 \cdot 10^{+173}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+88) (* y (/ x z)) (if (<= y 3e+172) x (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+88) {
		tmp = y * (x / z);
	} else if (y <= 3e+172) {
		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 <= (-1.05d+88)) then
        tmp = y * (x / z)
    else if (y <= 3d+172) 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 <= -1.05e+88) {
		tmp = y * (x / z);
	} else if (y <= 3e+172) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+88:
		tmp = y * (x / z)
	elif y <= 3e+172:
		tmp = x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+88)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 3e+172)
		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 <= -1.05e+88)
		tmp = y * (x / z);
	elseif (y <= 3e+172)
		tmp = x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+88], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+172], x, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e88

   1. Initial program 92.3%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around 0 86.1%

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

      1. associate-*r/ 84.0%

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

   6. Simplified 84.0%

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

   if -1.05e88 < y < 2.9999999999999999e172

   1. Initial program 79.9%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in z around inf 73.6%

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

   if 2.9999999999999999e172 < y

   1. Initial program 84.7%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*r/ 83.5%

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

   6. Simplified 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/r/ 91.1%

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

   8. Applied egg-rr 91.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+88) (/ (* y x) z) (if (<= y 3e+172) x (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+88) {
		tmp = (y * x) / z;
	} else if (y <= 3e+172) {
		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 <= (-4d+88)) then
        tmp = (y * x) / z
    else if (y <= 3d+172) 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 <= -4e+88) {
		tmp = (y * x) / z;
	} else if (y <= 3e+172) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+88:
		tmp = (y * x) / z
	elif y <= 3e+172:
		tmp = x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+88)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= 3e+172)
		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 <= -4e+88)
		tmp = (y * x) / z;
	elseif (y <= 3e+172)
		tmp = x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+88], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3e+172], x, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999984e88

   1. Initial program 92.3%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around 0 86.1%

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

   if -3.99999999999999984e88 < y < 2.9999999999999999e172

   1. Initial program 79.9%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in z around inf 73.6%

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

   if 2.9999999999999999e172 < y

   1. Initial program 84.7%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*r/ 83.5%

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

   6. Simplified 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/r/ 91.1%

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

   8. Applied egg-rr 91.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 51.8% 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 82.8%

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

   1. associate-*l/ 82.4%

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

3. Simplified 82.4%

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

4. Taylor expanded in z around inf 55.2%

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

5. Final simplification 55.2%

   \[\leadsto x \]

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 2023230 
(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))