Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.4% → 96.3%

Time: 4.0s

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: 96.3% 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 85.1%

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

   1. associate-/l* 95.7%

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

3. Simplified 95.7%

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

4. Final simplification 95.7%

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

Alternative 2: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-61} \lor \neg \left(z \leq -2.05 \cdot 10^{-122}\right) \land z \leq 1.5 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4e+15)
   x
   (if (or (<= z -4.9e-61) (and (not (<= z -2.05e-122)) (<= z 1.5e+98)))
     (* x (/ y z))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+15) {
		tmp = x;
	} else if ((z <= -4.9e-61) || (!(z <= -2.05e-122) && (z <= 1.5e+98))) {
		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 <= (-1.4d+15)) then
        tmp = x
    else if ((z <= (-4.9d-61)) .or. (.not. (z <= (-2.05d-122))) .and. (z <= 1.5d+98)) 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 <= -1.4e+15) {
		tmp = x;
	} else if ((z <= -4.9e-61) || (!(z <= -2.05e-122) && (z <= 1.5e+98))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.4e+15:
		tmp = x
	elif (z <= -4.9e-61) or (not (z <= -2.05e-122) and (z <= 1.5e+98)):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4e+15)
		tmp = x;
	elseif ((z <= -4.9e-61) || (!(z <= -2.05e-122) && (z <= 1.5e+98)))
		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 <= -1.4e+15)
		tmp = x;
	elseif ((z <= -4.9e-61) || (~((z <= -2.05e-122)) && (z <= 1.5e+98)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4e+15], x, If[Or[LessEqual[z, -4.9e-61], And[N[Not[LessEqual[z, -2.05e-122]], $MachinePrecision], LessEqual[z, 1.5e+98]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e15 or -4.90000000000000002e-61 < z < -2.05e-122 or 1.5000000000000001e98 < z

   1. Initial program 77.0%

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

      1. associate-*r/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around 0 80.1%

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

   if -1.4e15 < z < -4.90000000000000002e-61 or -2.05e-122 < z < 1.5000000000000001e98

   1. Initial program 91.1%

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

      1. associate-*r/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around inf 73.7%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-61} \lor \neg \left(z \leq -2.05 \cdot 10^{-122}\right) \land z \leq 1.5 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.15:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -3.8e-86)
     t_0
     (if (<= y 3.2e-83)
       x
       (if (<= y 1.35e-16) (* x (/ y z)) (if (<= y 1.15) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -3.8e-86) {
		tmp = t_0;
	} else if (y <= 3.2e-83) {
		tmp = x;
	} else if (y <= 1.35e-16) {
		tmp = x * (y / z);
	} else if (y <= 1.15) {
		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 = y * (x / z)
    if (y <= (-3.8d-86)) then
        tmp = t_0
    else if (y <= 3.2d-83) then
        tmp = x
    else if (y <= 1.35d-16) then
        tmp = x * (y / z)
    else if (y <= 1.15d0) 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 = y * (x / z);
	double tmp;
	if (y <= -3.8e-86) {
		tmp = t_0;
	} else if (y <= 3.2e-83) {
		tmp = x;
	} else if (y <= 1.35e-16) {
		tmp = x * (y / z);
	} else if (y <= 1.15) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -3.8e-86:
		tmp = t_0
	elif y <= 3.2e-83:
		tmp = x
	elif y <= 1.35e-16:
		tmp = x * (y / z)
	elif y <= 1.15:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -3.8e-86)
		tmp = t_0;
	elseif (y <= 3.2e-83)
		tmp = x;
	elseif (y <= 1.35e-16)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 1.15)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (y <= -3.8e-86)
		tmp = t_0;
	elseif (y <= 3.2e-83)
		tmp = x;
	elseif (y <= 1.35e-16)
		tmp = x * (y / z);
	elseif (y <= 1.15)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-86], t$95$0, If[LessEqual[y, 3.2e-83], x, If[LessEqual[y, 1.35e-16], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8e-86 or 1.1499999999999999 < y

   1. Initial program 90.7%

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

      1. associate-*r/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around inf 74.6%

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

      1. associate-*r/ 76.4%

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

   6. Simplified 76.4%

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

   if -3.8e-86 < y < 3.2000000000000001e-83 or 1.35e-16 < y < 1.1499999999999999

   1. Initial program 75.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 0 80.3%

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

   if 3.2000000000000001e-83 < y < 1.35e-16

   1. Initial program 99.7%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 69.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.15:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 96.1% 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 85.1%

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

   1. associate-*r/ 95.5%

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

3. Simplified 95.5%

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

4. Final simplification 95.5%

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

Alternative 5: 50.6% 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 85.1%

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

   1. associate-*r/ 95.5%

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

3. Simplified 95.5%

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

4. Taylor expanded in y around 0 46.3%

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

5. Final simplification 46.3%

   \[\leadsto x \]

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 2023268 
(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))