Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.5% → 96.0%

Time: 4.0s

Alternatives: 4

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: 84.5% 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: 96.0% 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 85.9%

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

   1. associate-/l* 97.7%

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

   2. remove-double-neg 97.7%

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

   3. distribute-frac-neg2 97.7%

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

   4. neg-sub0 97.7%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

   5. remove-double-neg 97.7%

      \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

   6. unsub-neg 97.7%

      \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

   7. div-sub 97.7%

      \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

   8. *-inverses 97.7%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

   9. metadata-eval 97.7%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

   10. associate--r- 97.7%

       \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

   11. neg-sub0 97.7%

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

   12. distribute-frac-neg2 97.7%

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

   13. remove-double-neg 97.7%

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

   14. sub-neg 97.7%

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

3. Simplified 97.7%

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

Alternative 2: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.25e-114) x (if (<= z 2.1e+127) (/ x (/ z y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.25e-114) {
		tmp = x;
	} else if (z <= 2.1e+127) {
		tmp = x / (z / y);
	} 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 <= (-2.25d-114)) then
        tmp = x
    else if (z <= 2.1d+127) then
        tmp = x / (z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.25e-114) {
		tmp = x;
	} else if (z <= 2.1e+127) {
		tmp = x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.25e-114:
		tmp = x
	elif z <= 2.1e+127:
		tmp = x / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.25e-114)
		tmp = x;
	elseif (z <= 2.1e+127)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.25e-114)
		tmp = x;
	elseif (z <= 2.1e+127)
		tmp = x / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.25e-114], x, If[LessEqual[z, 2.1e+127], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999984e-114 or 2.09999999999999992e127 < z

   1. Initial program 78.3%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg2 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 100.0%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 100.0%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 100.0%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 100.0%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 100.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 100.0%

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

      12. distribute-frac-neg2 100.0%

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

      13. remove-double-neg 100.0%

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

      14. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.5%

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

   if -2.24999999999999984e-114 < z < 2.09999999999999992e127

   1. Initial program 92.0%

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

      1. associate-/l* 95.9%

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

      2. remove-double-neg 95.9%

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

      3. distribute-frac-neg2 95.9%

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

      4. neg-sub0 95.9%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 95.9%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 95.9%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 95.9%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 95.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 95.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 95.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 95.9%

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

      12. distribute-frac-neg2 95.9%

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

      13. remove-double-neg 95.9%

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

      14. sub-neg 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 74.4%

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

      1. clear-num 74.3%

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

      2. un-div-inv 74.7%

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

   7. Applied egg-rr 74.7%

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

Alternative 3: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7e-115) x (if (<= z 4.8e+123) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e-115) {
		tmp = x;
	} else if (z <= 4.8e+123) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-7d-115)) then
        tmp = x
    else if (z <= 4.8d+123) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e-115) {
		tmp = x;
	} else if (z <= 4.8e+123) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7e-115:
		tmp = x
	elif z <= 4.8e+123:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7e-115)
		tmp = x;
	elseif (z <= 4.8e+123)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7e-115)
		tmp = x;
	elseif (z <= 4.8e+123)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7e-115], x, If[LessEqual[z, 4.8e+123], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000004e-115 or 4.79999999999999978e123 < z

   1. Initial program 78.3%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg2 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 100.0%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 100.0%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 100.0%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 100.0%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 100.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 100.0%

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

      12. distribute-frac-neg2 100.0%

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

      13. remove-double-neg 100.0%

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

      14. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.5%

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

   if -7.0000000000000004e-115 < z < 4.79999999999999978e123

   1. Initial program 92.0%

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

      1. associate-/l* 95.9%

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

      2. remove-double-neg 95.9%

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

      3. distribute-frac-neg2 95.9%

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

      4. neg-sub0 95.9%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 95.9%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 95.9%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 95.9%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 95.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 95.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 95.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 95.9%

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

      12. distribute-frac-neg2 95.9%

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

      13. remove-double-neg 95.9%

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

      14. sub-neg 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 74.4%

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

Alternative 4: 51.2% 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 85.9%

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

   1. associate-/l* 97.7%

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

   2. remove-double-neg 97.7%

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

   3. distribute-frac-neg2 97.7%

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

   4. neg-sub0 97.7%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

   5. remove-double-neg 97.7%

      \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

   6. unsub-neg 97.7%

      \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

   7. div-sub 97.7%

      \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

   8. *-inverses 97.7%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

   9. metadata-eval 97.7%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

   10. associate--r- 97.7%

       \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

   11. neg-sub0 97.7%

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

   12. distribute-frac-neg2 97.7%

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

   13. remove-double-neg 97.7%

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

   14. sub-neg 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in y around 0 49.5%

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

Developer Target 1: 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 2024135 
(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))