Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.5%

Time: 4.8s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{x \cdot 100}{x + y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-5} \lor \neg \left(y \leq 1.3 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.55e-5) (not (<= y 1.3e-40))) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.55e-5) || !(y <= 1.3e-40)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.55d-5)) .or. (.not. (y <= 1.3d-40))) then
        tmp = x * (100.0d0 / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.55e-5) || !(y <= 1.3e-40)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.55e-5) or not (y <= 1.3e-40):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.55e-5) || !(y <= 1.3e-40))
		tmp = Float64(x * Float64(100.0 / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.55e-5) || ~((y <= 1.3e-40)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.55e-5], N[Not[LessEqual[y, 1.3e-40]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.54999999999999998e-5 or 1.3000000000000001e-40 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.5%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.3%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 76.6%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 76.6%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-*r/ 76.6%

         \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]

   7. Simplified 76.6%

      \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]

   if -2.54999999999999998e-5 < y < 1.3000000000000001e-40

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{100} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-5} \lor \neg \left(y \leq 1.3 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-5} \lor \neg \left(y \leq 1.35 \cdot 10^{-40}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.4e-5) (not (<= y 1.35e-40))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.4e-5) || !(y <= 1.35e-40)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5.4d-5)) .or. (.not. (y <= 1.35d-40))) then
        tmp = 100.0d0 * (x / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.4e-5) || !(y <= 1.35e-40)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.4e-5) or not (y <= 1.35e-40):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.4e-5) || !(y <= 1.35e-40))
		tmp = Float64(100.0 * Float64(x / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.4e-5) || ~((y <= 1.35e-40)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.4e-5], N[Not[LessEqual[y, 1.35e-40]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -5.3999999999999998e-5 or 1.35e-40 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.5%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.3%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]

   if -5.3999999999999998e-5 < y < 1.35e-40

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{100} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-5} \lor \neg \left(y \leq 1.35 \cdot 10^{-40}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-40}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{0.01}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7e-5)
   (/ x (* y 0.01))
   (if (<= y 1.35e-40) 100.0 (/ (/ x 0.01) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7e-5) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.35e-40) {
		tmp = 100.0;
	} else {
		tmp = (x / 0.01) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-7d-5)) then
        tmp = x / (y * 0.01d0)
    else if (y <= 1.35d-40) then
        tmp = 100.0d0
    else
        tmp = (x / 0.01d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7e-5) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.35e-40) {
		tmp = 100.0;
	} else {
		tmp = (x / 0.01) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7e-5:
		tmp = x / (y * 0.01)
	elif y <= 1.35e-40:
		tmp = 100.0
	else:
		tmp = (x / 0.01) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7e-5)
		tmp = Float64(x / Float64(y * 0.01));
	elseif (y <= 1.35e-40)
		tmp = 100.0;
	else
		tmp = Float64(Float64(x / 0.01) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7e-5)
		tmp = x / (y * 0.01);
	elseif (y <= 1.35e-40)
		tmp = 100.0;
	else
		tmp = (x / 0.01) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7e-5], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-40], 100.0, N[(N[(x / 0.01), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999994e-5

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 81.2%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-*r/ 81.1%

         \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]

      4. clear-num 81.0%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{100}}} \]

      5. un-div-inv 81.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

      6. div-inv 81.3%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{100}}} \]

      7. metadata-eval 81.3%

         \[\leadsto \frac{x}{y \cdot \color{blue}{0.01}} \]

   7. Applied egg-rr 81.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]

   if -6.9999999999999994e-5 < y < 1.35e-40

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{100} \]

   if 1.35e-40 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.4%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 72.4%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 72.8%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-*r/ 72.8%

         \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]

      4. clear-num 72.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{100}}} \]

      5. un-div-inv 72.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

      6. div-inv 72.7%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{100}}} \]

      7. metadata-eval 72.7%

         \[\leadsto \frac{x}{y \cdot \color{blue}{0.01}} \]

   7. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]

   8. Taylor expanded in x around 0 72.4%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   9. Step-by-step derivation

      1. metadata-eval 72.4%

         \[\leadsto \color{blue}{\frac{1}{0.01}} \cdot \frac{x}{y} \]

      2. times-frac 72.7%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{0.01 \cdot y}} \]

      3. *-lft-identity 72.7%

         \[\leadsto \frac{\color{blue}{x}}{0.01 \cdot y} \]

      4. associate-/r* 72.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{0.01}}{y}} \]

   10. Simplified 72.8%

       \[\leadsto \color{blue}{\frac{\frac{x}{0.01}}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00031:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-40}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.00031)
   (/ x (* y 0.01))
   (if (<= y 1.35e-40) 100.0 (/ (* x 100.0) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.00031) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.35e-40) {
		tmp = 100.0;
	} else {
		tmp = (x * 100.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.00031d0)) then
        tmp = x / (y * 0.01d0)
    else if (y <= 1.35d-40) then
        tmp = 100.0d0
    else
        tmp = (x * 100.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.00031) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.35e-40) {
		tmp = 100.0;
	} else {
		tmp = (x * 100.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.00031:
		tmp = x / (y * 0.01)
	elif y <= 1.35e-40:
		tmp = 100.0
	else:
		tmp = (x * 100.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.00031)
		tmp = Float64(x / Float64(y * 0.01));
	elseif (y <= 1.35e-40)
		tmp = 100.0;
	else
		tmp = Float64(Float64(x * 100.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.00031)
		tmp = x / (y * 0.01);
	elseif (y <= 1.35e-40)
		tmp = 100.0;
	else
		tmp = (x * 100.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.00031], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-40], 100.0, N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e-4

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 81.2%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-*r/ 81.1%

         \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]

      4. clear-num 81.0%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{100}}} \]

      5. un-div-inv 81.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

      6. div-inv 81.3%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{100}}} \]

      7. metadata-eval 81.3%

         \[\leadsto \frac{x}{y \cdot \color{blue}{0.01}} \]

   7. Applied egg-rr 81.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]

   if -3.1e-4 < y < 1.35e-40

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{100} \]

   if 1.35e-40 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.8%

      \[\leadsto \frac{x \cdot 100}{\color{blue}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00026:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-40}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.00026)
   (/ x (* y 0.01))
   (if (<= y 1.35e-40) 100.0 (* x (/ 100.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.00026) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.35e-40) {
		tmp = 100.0;
	} else {
		tmp = x * (100.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.00026d0)) then
        tmp = x / (y * 0.01d0)
    else if (y <= 1.35d-40) then
        tmp = 100.0d0
    else
        tmp = x * (100.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.00026) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.35e-40) {
		tmp = 100.0;
	} else {
		tmp = x * (100.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.00026:
		tmp = x / (y * 0.01)
	elif y <= 1.35e-40:
		tmp = 100.0
	else:
		tmp = x * (100.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.00026)
		tmp = Float64(x / Float64(y * 0.01));
	elseif (y <= 1.35e-40)
		tmp = 100.0;
	else
		tmp = Float64(x * Float64(100.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.00026)
		tmp = x / (y * 0.01);
	elseif (y <= 1.35e-40)
		tmp = 100.0;
	else
		tmp = x * (100.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.00026], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-40], 100.0, N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.59999999999999977e-4

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 81.2%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-*r/ 81.1%

         \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]

      4. clear-num 81.0%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{100}}} \]

      5. un-div-inv 81.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

      6. div-inv 81.3%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{100}}} \]

      7. metadata-eval 81.3%

         \[\leadsto \frac{x}{y \cdot \color{blue}{0.01}} \]

   7. Applied egg-rr 81.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]

   if -2.59999999999999977e-4 < y < 1.35e-40

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{100} \]

   if 1.35e-40 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.4%

         \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 72.4%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 72.8%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-*r/ 72.8%

         \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{x \cdot \frac{100}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 100 \cdot \frac{x}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 100.0 (/ x (+ x y))))

C

double code(double x, double y) {
	return 100.0 * (x / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0 * (x / (x + y))
end function

Java

public static double code(double x, double y) {
	return 100.0 * (x / (x + y));
}

Python

def code(x, y):
	return 100.0 * (x / (x + y))

Julia

function code(x, y)
	return Float64(100.0 * Float64(x / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0 * (x / (x + y));
end

Wolfram

code[x_, y_] := N[(100.0 * N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{x \cdot 100}{x + y} \]
2. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

   2. associate-/l* 99.7%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 8: 52.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 100 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 100.0)

C

double code(double x, double y) {
	return 100.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0
end function

Java

public static double code(double x, double y) {
	return 100.0;
}

Python

def code(x, y):
	return 100.0

Julia

function code(x, y)
	return 100.0
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0;
end

Wolfram

code[x_, y_] := 100.0

Derivation

1. Initial program 99.8%

   \[\frac{x \cdot 100}{x + y} \]
2. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

   2. associate-/l* 99.7%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 48.2%

   \[\leadsto \color{blue}{100} \]
6. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{1} \cdot \frac{100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ x 1.0) (/ 100.0 (+ x y))))

C

double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / 1.0d0) * (100.0d0 / (x + y))
end function

Java

public static double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}

Python

def code(x, y):
	return (x / 1.0) * (100.0 / (x + y))

Julia

function code(x, y)
	return Float64(Float64(x / 1.0) * Float64(100.0 / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x / 1.0) * (100.0 / (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x / 1.0), $MachinePrecision] * N[(100.0 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (* (/ x 1) (/ 100 (+ x y))))

  (/ (* x 100.0) (+ x y)))