Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.4%

Time: 3.8s

Alternatives: 7

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: 99.4% 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: 99.4% 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 99.7%

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

3. Final simplification 99.7%

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

Alternative 2: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+36} \lor \neg \left(y \leq 0.086\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.35e+36) (not (<= y 0.086))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.35e+36) || !(y <= 0.086)) {
		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 <= (-2.35d+36)) .or. (.not. (y <= 0.086d0))) 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 <= -2.35e+36) || !(y <= 0.086)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.35e+36) or not (y <= 0.086):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.35e+36) || !(y <= 0.086))
		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 <= -2.35e+36) || ~((y <= 0.086)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.35e+36], N[Not[LessEqual[y, 0.086]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.34999999999999994e36 or 0.085999999999999993 < y

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around 0 81.5%

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

   if -2.34999999999999994e36 < y < 0.085999999999999993

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+36} \lor \neg \left(y \leq 0.086\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+36}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.013:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+36)
   (* 100.0 (/ x y))
   (if (<= y 0.013) 100.0 (* x (/ 100.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+36) {
		tmp = 100.0 * (x / y);
	} else if (y <= 0.013) {
		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 <= (-4.9d+36)) then
        tmp = 100.0d0 * (x / y)
    else if (y <= 0.013d0) 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 <= -4.9e+36) {
		tmp = 100.0 * (x / y);
	} else if (y <= 0.013) {
		tmp = 100.0;
	} else {
		tmp = x * (100.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+36:
		tmp = 100.0 * (x / y)
	elif y <= 0.013:
		tmp = 100.0
	else:
		tmp = x * (100.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+36)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (y <= 0.013)
		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 <= -4.9e+36)
		tmp = 100.0 * (x / y);
	elseif (y <= 0.013)
		tmp = 100.0;
	else
		tmp = x * (100.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+36], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.013], 100.0, N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.89999999999999981e36

   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* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around 0 74.8%

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

   if -4.89999999999999981e36 < y < 0.0129999999999999994

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.8%

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

   if 0.0129999999999999994 < y

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/r/ 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around 0 86.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+36}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.013:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.4:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.7e+36)
   (* 100.0 (/ x y))
   (if (<= y 3.4) 100.0 (/ x (/ y 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.7e+36) {
		tmp = 100.0 * (x / y);
	} else if (y <= 3.4) {
		tmp = 100.0;
	} else {
		tmp = x / (y / 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 <= (-4.7d+36)) then
        tmp = 100.0d0 * (x / y)
    else if (y <= 3.4d0) then
        tmp = 100.0d0
    else
        tmp = x / (y / 100.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.7e+36) {
		tmp = 100.0 * (x / y);
	} else if (y <= 3.4) {
		tmp = 100.0;
	} else {
		tmp = x / (y / 100.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.7e+36:
		tmp = 100.0 * (x / y)
	elif y <= 3.4:
		tmp = 100.0
	else:
		tmp = x / (y / 100.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.7e+36)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (y <= 3.4)
		tmp = 100.0;
	else
		tmp = Float64(x / Float64(y / 100.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.7e+36)
		tmp = 100.0 * (x / y);
	elseif (y <= 3.4)
		tmp = 100.0;
	else
		tmp = x / (y / 100.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.7e+36], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4], 100.0, N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.69999999999999989e36

   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* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around 0 74.8%

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

   if -4.69999999999999989e36 < y < 3.39999999999999991

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.8%

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

   if 3.39999999999999991 < y

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/r/ 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.4:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;y \leq 0.116:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.45e+36)
   (/ (* x 100.0) y)
   (if (<= y 0.116) 100.0 (/ x (/ y 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.45e+36) {
		tmp = (x * 100.0) / y;
	} else if (y <= 0.116) {
		tmp = 100.0;
	} else {
		tmp = x / (y / 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 <= (-2.45d+36)) then
        tmp = (x * 100.0d0) / y
    else if (y <= 0.116d0) then
        tmp = 100.0d0
    else
        tmp = x / (y / 100.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.45e+36) {
		tmp = (x * 100.0) / y;
	} else if (y <= 0.116) {
		tmp = 100.0;
	} else {
		tmp = x / (y / 100.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.45e+36:
		tmp = (x * 100.0) / y
	elif y <= 0.116:
		tmp = 100.0
	else:
		tmp = x / (y / 100.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.45e+36)
		tmp = Float64(Float64(x * 100.0) / y);
	elseif (y <= 0.116)
		tmp = 100.0;
	else
		tmp = Float64(x / Float64(y / 100.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.45e+36)
		tmp = (x * 100.0) / y;
	elseif (y <= 0.116)
		tmp = 100.0;
	else
		tmp = x / (y / 100.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.45e+36], N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 0.116], 100.0, N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4499999999999999e36

   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* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around 0 74.8%

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

      1. associate-*r/ 74.9%

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

   7. Applied egg-rr 74.9%

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

   if -2.4499999999999999e36 < y < 0.116000000000000006

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.8%

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

   if 0.116000000000000006 < y

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/r/ 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;y \leq 0.116:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 1.0× speedup

Math

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

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(x * Float64(100.0 / Float64(x + y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.4%

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

3. Simplified 99.4%

   \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-/r/ 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 7: 51.0% 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 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in x around inf 53.3%

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

6. Final simplification 53.3%

   \[\leadsto 100 \]
7. Add Preprocessing

Developer target: 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 2024010 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

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