Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.8% → 94.7%

Time: 2.7s

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: 84.8% 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: 94.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{-28}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1e-28) (* x (/ (+ y z) z)) (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e-28) {
		tmp = x * ((y + z) / z);
	} else {
		tmp = (y + z) * (x / 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 <= 1d-28) then
        tmp = x * ((y + z) / z)
    else
        tmp = (y + z) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e-28) {
		tmp = x * ((y + z) / z);
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1e-28:
		tmp = x * ((y + z) / z)
	else:
		tmp = (y + z) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1e-28)
		tmp = Float64(x * Float64(Float64(y + z) / z));
	else
		tmp = Float64(Float64(y + z) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1e-28)
		tmp = x * ((y + z) / z);
	else
		tmp = (y + z) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1e-28], N[(x * N[(N[(y + z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.99999999999999971e-29

   1. Initial program 87.6%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

   if 9.99999999999999971e-29 < y

   1. Initial program 87.4%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{-28}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+43} \lor \neg \left(y \leq 110000 \lor \neg \left(y \leq 2.25 \cdot 10^{+80}\right) \land y \leq 2.2 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e+43)
         (not
          (or (<= y 110000.0) (and (not (<= y 2.25e+80)) (<= y 2.2e+109)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e+43) || !((y <= 110000.0) || (!(y <= 2.25e+80) && (y <= 2.2e+109)))) {
		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 <= (-2.5d+43)) .or. (.not. (y <= 110000.0d0) .or. (.not. (y <= 2.25d+80)) .and. (y <= 2.2d+109))) 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 <= -2.5e+43) || !((y <= 110000.0) || (!(y <= 2.25e+80) && (y <= 2.2e+109)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e+43) or not ((y <= 110000.0) or (not (y <= 2.25e+80) and (y <= 2.2e+109))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e+43) || !((y <= 110000.0) || (!(y <= 2.25e+80) && (y <= 2.2e+109))))
		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 <= -2.5e+43) || ~(((y <= 110000.0) || (~((y <= 2.25e+80)) && (y <= 2.2e+109)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e+43], N[Not[Or[LessEqual[y, 110000.0], And[N[Not[LessEqual[y, 2.25e+80]], $MachinePrecision], LessEqual[y, 2.2e+109]]]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000002e43 or 1.1e5 < y < 2.25000000000000003e80 or 2.1999999999999999e109 < y

   1. Initial program 91.2%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around inf 77.7%

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

   if -2.5000000000000002e43 < y < 1.1e5 or 2.25000000000000003e80 < y < 2.1999999999999999e109

   1. Initial program 84.3%

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

      1. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 81.5%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+43} \lor \neg \left(y \leq 110000 \lor \neg \left(y \leq 2.25 \cdot 10^{+80}\right) \land y \leq 2.2 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+43} \lor \neg \left(y \leq 780000\right) \land \left(y \leq 2.05 \cdot 10^{+80} \lor \neg \left(y \leq 1.78 \cdot 10^{+109}\right)\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e+43)
         (and (not (<= y 780000.0))
              (or (<= y 2.05e+80) (not (<= y 1.78e+109)))))
   (* y (/ x z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+43) || (!(y <= 780000.0) && ((y <= 2.05e+80) || !(y <= 1.78e+109)))) {
		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 <= (-3.8d+43)) .or. (.not. (y <= 780000.0d0)) .and. (y <= 2.05d+80) .or. (.not. (y <= 1.78d+109))) 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 <= -3.8e+43) || (!(y <= 780000.0) && ((y <= 2.05e+80) || !(y <= 1.78e+109)))) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e+43) or (not (y <= 780000.0) and ((y <= 2.05e+80) or not (y <= 1.78e+109))):
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e+43) || (!(y <= 780000.0) && ((y <= 2.05e+80) || !(y <= 1.78e+109))))
		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 <= -3.8e+43) || (~((y <= 780000.0)) && ((y <= 2.05e+80) || ~((y <= 1.78e+109)))))
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e+43], And[N[Not[LessEqual[y, 780000.0]], $MachinePrecision], Or[LessEqual[y, 2.05e+80], N[Not[LessEqual[y, 1.78e+109]], $MachinePrecision]]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000008e43 or 7.8e5 < y < 2.05000000000000001e80 or 1.7800000000000001e109 < y

   1. Initial program 91.2%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*r/ 85.1%

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

   6. Simplified 85.1%

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

   if -3.80000000000000008e43 < y < 7.8e5 or 2.05000000000000001e80 < y < 1.7800000000000001e109

   1. Initial program 84.3%

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

      1. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 81.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+43} \lor \neg \left(y \leq 780000\right) \land \left(y \leq 2.05 \cdot 10^{+80} \lor \neg \left(y \leq 1.78 \cdot 10^{+109}\right)\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 0.032:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+80} \lor \neg \left(y \leq 1.78 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+45)
   (/ (* y x) z)
   (if (<= y 0.032)
     x
     (if (or (<= y 2.25e+80) (not (<= y 1.78e+109))) (* y (/ x z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+45) {
		tmp = (y * x) / z;
	} else if (y <= 0.032) {
		tmp = x;
	} else if ((y <= 2.25e+80) || !(y <= 1.78e+109)) {
		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 <= (-2.2d+45)) then
        tmp = (y * x) / z
    else if (y <= 0.032d0) then
        tmp = x
    else if ((y <= 2.25d+80) .or. (.not. (y <= 1.78d+109))) 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 <= -2.2e+45) {
		tmp = (y * x) / z;
	} else if (y <= 0.032) {
		tmp = x;
	} else if ((y <= 2.25e+80) || !(y <= 1.78e+109)) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.2e+45:
		tmp = (y * x) / z
	elif y <= 0.032:
		tmp = x
	elif (y <= 2.25e+80) or not (y <= 1.78e+109):
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e+45)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= 0.032)
		tmp = x;
	elseif ((y <= 2.25e+80) || !(y <= 1.78e+109))
		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 <= -2.2e+45)
		tmp = (y * x) / z;
	elseif (y <= 0.032)
		tmp = x;
	elseif ((y <= 2.25e+80) || ~((y <= 1.78e+109)))
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e+45], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 0.032], x, If[Or[LessEqual[y, 2.25e+80], N[Not[LessEqual[y, 1.78e+109]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e45

   1. Initial program 96.1%

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

      1. associate-*r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 83.4%

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

   if -2.2e45 < y < 0.032000000000000001 or 2.25000000000000003e80 < y < 1.7800000000000001e109

   1. Initial program 84.3%

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

      1. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 81.5%

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

   if 0.032000000000000001 < y < 2.25000000000000003e80 or 1.7800000000000001e109 < y

   1. Initial program 87.2%

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

      1. associate-*r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-*r/ 87.0%

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

   6. Simplified 87.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 0.032:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+80} \lor \neg \left(y \leq 1.78 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 96.0% accurate, 1.0× speedup

Math

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

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(x * Float64(Float64(y + z) / z))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

   1. associate-*r/ 95.1%

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

3. Simplified 95.1%

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

4. Final simplification 95.1%

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

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 87.6%

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

   1. associate-*r/ 95.1%

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

3. Simplified 95.1%

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

4. Taylor expanded in y around 0 50.5%

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

5. Final simplification 50.5%

   \[\leadsto x \]

Developer target: 96.5% 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 2023271 
(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))