Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 6.3s

Alternatives: 6

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: 99.7% 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 99.0%

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

   1. *-commutative 99.0%

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

   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. Final simplification 99.7%

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

Alternative 2: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3800:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-53} \lor \neg \left(x \leq 8.1 \cdot 10^{+43}\right) \land x \leq 1.95 \cdot 10^{+61}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3800.0)
   100.0
   (if (or (<= x 1.04e-53) (and (not (<= x 8.1e+43)) (<= x 1.95e+61)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3800.0) {
		tmp = 100.0;
	} else if ((x <= 1.04e-53) || (!(x <= 8.1e+43) && (x <= 1.95e+61))) {
		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 (x <= (-3800.0d0)) then
        tmp = 100.0d0
    else if ((x <= 1.04d-53) .or. (.not. (x <= 8.1d+43)) .and. (x <= 1.95d+61)) 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 (x <= -3800.0) {
		tmp = 100.0;
	} else if ((x <= 1.04e-53) || (!(x <= 8.1e+43) && (x <= 1.95e+61))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3800.0:
		tmp = 100.0
	elif (x <= 1.04e-53) or (not (x <= 8.1e+43) and (x <= 1.95e+61)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3800.0)
		tmp = 100.0;
	elseif ((x <= 1.04e-53) || (!(x <= 8.1e+43) && (x <= 1.95e+61)))
		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 (x <= -3800.0)
		tmp = 100.0;
	elseif ((x <= 1.04e-53) || (~((x <= 8.1e+43)) && (x <= 1.95e+61)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3800.0], 100.0, If[Or[LessEqual[x, 1.04e-53], And[N[Not[LessEqual[x, 8.1e+43]], $MachinePrecision], LessEqual[x, 1.95e+61]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3800 or 1.04000000000000001e-53 < x < 8.0999999999999996e43 or 1.94999999999999994e61 < x

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 75.3%

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

   if -3800 < x < 1.04000000000000001e-53 or 8.0999999999999996e43 < x < 1.94999999999999994e61

   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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 78.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3800:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-53} \lor \neg \left(x \leq 8.1 \cdot 10^{+43}\right) \land x \leq 1.95 \cdot 10^{+61}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -840:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-54} \lor \neg \left(x \leq 8.8 \cdot 10^{+43}\right) \land x \leq 1.9 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -840.0)
   100.0
   (if (or (<= x 8.5e-54) (and (not (<= x 8.8e+43)) (<= x 1.9e+61)))
     (* x (/ 100.0 y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -840.0) {
		tmp = 100.0;
	} else if ((x <= 8.5e-54) || (!(x <= 8.8e+43) && (x <= 1.9e+61))) {
		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 (x <= (-840.0d0)) then
        tmp = 100.0d0
    else if ((x <= 8.5d-54) .or. (.not. (x <= 8.8d+43)) .and. (x <= 1.9d+61)) 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 (x <= -840.0) {
		tmp = 100.0;
	} else if ((x <= 8.5e-54) || (!(x <= 8.8e+43) && (x <= 1.9e+61))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -840.0:
		tmp = 100.0
	elif (x <= 8.5e-54) or (not (x <= 8.8e+43) and (x <= 1.9e+61)):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -840.0)
		tmp = 100.0;
	elseif ((x <= 8.5e-54) || (!(x <= 8.8e+43) && (x <= 1.9e+61)))
		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 (x <= -840.0)
		tmp = 100.0;
	elseif ((x <= 8.5e-54) || (~((x <= 8.8e+43)) && (x <= 1.9e+61)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -840.0], 100.0, If[Or[LessEqual[x, 8.5e-54], And[N[Not[LessEqual[x, 8.8e+43]], $MachinePrecision], LessEqual[x, 1.9e+61]]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -840 or 8.5e-54 < x < 8.80000000000000002e43 or 1.89999999999999998e61 < x

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 75.3%

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

   if -840 < x < 8.5e-54 or 8.80000000000000002e43 < x < 1.89999999999999998e61

   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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 78.1%

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

      1. associate-*r/ 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -840:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-54} \lor \neg \left(x \leq 8.8 \cdot 10^{+43}\right) \land x \leq 1.9 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4200:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 8.1 \cdot 10^{+43}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4200.0)
   100.0
   (if (<= x 1.9e-56)
     (* x (/ 100.0 y))
     (if (<= x 8.1e+43) 100.0 (if (<= x 1.85e+61) (/ 100.0 (/ y x)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4200.0) {
		tmp = 100.0;
	} else if (x <= 1.9e-56) {
		tmp = x * (100.0 / y);
	} else if (x <= 8.1e+43) {
		tmp = 100.0;
	} else if (x <= 1.85e+61) {
		tmp = 100.0 / (y / x);
	} 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 (x <= (-4200.0d0)) then
        tmp = 100.0d0
    else if (x <= 1.9d-56) then
        tmp = x * (100.0d0 / y)
    else if (x <= 8.1d+43) then
        tmp = 100.0d0
    else if (x <= 1.85d+61) then
        tmp = 100.0d0 / (y / x)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4200.0) {
		tmp = 100.0;
	} else if (x <= 1.9e-56) {
		tmp = x * (100.0 / y);
	} else if (x <= 8.1e+43) {
		tmp = 100.0;
	} else if (x <= 1.85e+61) {
		tmp = 100.0 / (y / x);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4200.0:
		tmp = 100.0
	elif x <= 1.9e-56:
		tmp = x * (100.0 / y)
	elif x <= 8.1e+43:
		tmp = 100.0
	elif x <= 1.85e+61:
		tmp = 100.0 / (y / x)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4200.0)
		tmp = 100.0;
	elseif (x <= 1.9e-56)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (x <= 8.1e+43)
		tmp = 100.0;
	elseif (x <= 1.85e+61)
		tmp = Float64(100.0 / Float64(y / x));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4200.0)
		tmp = 100.0;
	elseif (x <= 1.9e-56)
		tmp = x * (100.0 / y);
	elseif (x <= 8.1e+43)
		tmp = 100.0;
	elseif (x <= 1.85e+61)
		tmp = 100.0 / (y / x);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4200.0], 100.0, If[LessEqual[x, 1.9e-56], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.1e+43], 100.0, If[LessEqual[x, 1.85e+61], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4200 or 1.9000000000000001e-56 < x < 8.0999999999999996e43 or 1.85000000000000001e61 < x

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 75.3%

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

   if -4200 < x < 1.9000000000000001e-56

   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 76.8%

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

      1. associate-*r/ 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   if 8.0999999999999996e43 < x < 1.85000000000000001e61

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.6%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4200:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 8.1 \cdot 10^{+43}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -114:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+43}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -114.0)
   100.0
   (if (<= x 1.35e-53)
     (/ (* 100.0 x) y)
     (if (<= x 7.4e+43) 100.0 (if (<= x 1.85e+61) (/ 100.0 (/ y x)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -114.0) {
		tmp = 100.0;
	} else if (x <= 1.35e-53) {
		tmp = (100.0 * x) / y;
	} else if (x <= 7.4e+43) {
		tmp = 100.0;
	} else if (x <= 1.85e+61) {
		tmp = 100.0 / (y / x);
	} 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 (x <= (-114.0d0)) then
        tmp = 100.0d0
    else if (x <= 1.35d-53) then
        tmp = (100.0d0 * x) / y
    else if (x <= 7.4d+43) then
        tmp = 100.0d0
    else if (x <= 1.85d+61) then
        tmp = 100.0d0 / (y / x)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -114.0) {
		tmp = 100.0;
	} else if (x <= 1.35e-53) {
		tmp = (100.0 * x) / y;
	} else if (x <= 7.4e+43) {
		tmp = 100.0;
	} else if (x <= 1.85e+61) {
		tmp = 100.0 / (y / x);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -114.0:
		tmp = 100.0
	elif x <= 1.35e-53:
		tmp = (100.0 * x) / y
	elif x <= 7.4e+43:
		tmp = 100.0
	elif x <= 1.85e+61:
		tmp = 100.0 / (y / x)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -114.0)
		tmp = 100.0;
	elseif (x <= 1.35e-53)
		tmp = Float64(Float64(100.0 * x) / y);
	elseif (x <= 7.4e+43)
		tmp = 100.0;
	elseif (x <= 1.85e+61)
		tmp = Float64(100.0 / Float64(y / x));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -114.0)
		tmp = 100.0;
	elseif (x <= 1.35e-53)
		tmp = (100.0 * x) / y;
	elseif (x <= 7.4e+43)
		tmp = 100.0;
	elseif (x <= 1.85e+61)
		tmp = 100.0 / (y / x);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -114.0], 100.0, If[LessEqual[x, 1.35e-53], N[(N[(100.0 * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 7.4e+43], 100.0, If[LessEqual[x, 1.85e+61], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -114 or 1.35e-53 < x < 7.4000000000000002e43 or 1.85000000000000001e61 < x

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 75.3%

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

   if -114 < x < 1.35e-53

   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 76.8%

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

      1. associate-*r/ 76.9%

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

   7. Simplified 76.9%

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

   if 7.4000000000000002e43 < x < 1.85000000000000001e61

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.6%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -114:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+43}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% 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 99.0%

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

   1. *-commutative 99.0%

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

   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 51.1%

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

6. Final simplification 51.1%

   \[\leadsto 100 \]
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 2024039 
(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)))