Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.4% → 96.2%

Time: 6.2s

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: 84.4% 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: 96.2% 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 79.4%

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

   1. associate-/l* 95.9%

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

3. Simplified 95.9%

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

4. Final simplification 95.9%

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

Alternative 2: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-145} \lor \neg \left(z \leq 2.1 \cdot 10^{-80}\right) \land z \leq 3.8 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e-75)
   x
   (if (or (<= z 2.45e-145) (and (not (<= z 2.1e-80)) (<= z 3.8e+79)))
     (* x (/ y z))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e-75) {
		tmp = x;
	} else if ((z <= 2.45e-145) || (!(z <= 2.1e-80) && (z <= 3.8e+79))) {
		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 <= (-4.1d-75)) then
        tmp = x
    else if ((z <= 2.45d-145) .or. (.not. (z <= 2.1d-80)) .and. (z <= 3.8d+79)) 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 <= -4.1e-75) {
		tmp = x;
	} else if ((z <= 2.45e-145) || (!(z <= 2.1e-80) && (z <= 3.8e+79))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e-75:
		tmp = x
	elif (z <= 2.45e-145) or (not (z <= 2.1e-80) and (z <= 3.8e+79)):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e-75)
		tmp = x;
	elseif ((z <= 2.45e-145) || (!(z <= 2.1e-80) && (z <= 3.8e+79)))
		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 <= -4.1e-75)
		tmp = x;
	elseif ((z <= 2.45e-145) || (~((z <= 2.1e-80)) && (z <= 3.8e+79)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e-75], x, If[Or[LessEqual[z, 2.45e-145], And[N[Not[LessEqual[z, 2.1e-80]], $MachinePrecision], LessEqual[z, 3.8e+79]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000002e-75 or 2.44999999999999984e-145 < z < 2.10000000000000001e-80 or 3.8000000000000002e79 < z

   1. Initial program 70.7%

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

      1. associate-*r/ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 79.6%

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

   if -4.10000000000000002e-75 < z < 2.44999999999999984e-145 or 2.10000000000000001e-80 < z < 3.8000000000000002e79

   1. Initial program 91.8%

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

      1. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around inf 70.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-145} \lor \neg \left(z \leq 2.1 \cdot 10^{-80}\right) \land z \leq 3.8 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6e-73)
   x
   (if (<= z 2.45e-145)
     (* y (/ x z))
     (if (<= z 1.12e-80) x (if (<= z 2.75e+79) (* x (/ y z)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6e-73) {
		tmp = x;
	} else if (z <= 2.45e-145) {
		tmp = y * (x / z);
	} else if (z <= 1.12e-80) {
		tmp = x;
	} else if (z <= 2.75e+79) {
		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 <= (-6d-73)) then
        tmp = x
    else if (z <= 2.45d-145) then
        tmp = y * (x / z)
    else if (z <= 1.12d-80) then
        tmp = x
    else if (z <= 2.75d+79) 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 <= -6e-73) {
		tmp = x;
	} else if (z <= 2.45e-145) {
		tmp = y * (x / z);
	} else if (z <= 1.12e-80) {
		tmp = x;
	} else if (z <= 2.75e+79) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6e-73:
		tmp = x
	elif z <= 2.45e-145:
		tmp = y * (x / z)
	elif z <= 1.12e-80:
		tmp = x
	elif z <= 2.75e+79:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6e-73)
		tmp = x;
	elseif (z <= 2.45e-145)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.12e-80)
		tmp = x;
	elseif (z <= 2.75e+79)
		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 <= -6e-73)
		tmp = x;
	elseif (z <= 2.45e-145)
		tmp = y * (x / z);
	elseif (z <= 1.12e-80)
		tmp = x;
	elseif (z <= 2.75e+79)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6e-73], x, If[LessEqual[z, 2.45e-145], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-80], x, If[LessEqual[z, 2.75e+79], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e-73 or 2.44999999999999984e-145 < z < 1.12e-80 or 2.75000000000000003e79 < z

   1. Initial program 70.7%

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

      1. associate-*r/ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 79.6%

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

   if -6e-73 < z < 2.44999999999999984e-145

   1. Initial program 90.5%

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

      1. associate-*r/ 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around inf 79.7%

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

      1. associate-*r/ 83.3%

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

   6. Simplified 83.3%

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

   if 1.12e-80 < z < 2.75000000000000003e79

   1. Initial program 96.4%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 95.8% accurate, 1.0× speedup

Math

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.4%

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

   1. associate-*r/ 95.9%

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

3. Simplified 95.9%

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

4. Final simplification 95.9%

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

Alternative 5: 51.6% 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 79.4%

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

   1. associate-*r/ 95.9%

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

3. Simplified 95.9%

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

4. Taylor expanded in y around 0 55.7%

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

5. Final simplification 55.7%

   \[\leadsto x \]

Developer target: 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 2023274 
(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))