Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.4%

Time: 4.8s

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: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-41} \lor \neg \left(x \leq 8 \cdot 10^{+90}\right) \land x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.2e+18)
   100.0
   (if (or (<= x 5e-41) (and (not (<= x 8e+90)) (<= x 1.55e+95)))
     (* x (/ 100.0 y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.2e+18) {
		tmp = 100.0;
	} else if ((x <= 5e-41) || (!(x <= 8e+90) && (x <= 1.55e+95))) {
		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 <= (-7.2d+18)) then
        tmp = 100.0d0
    else if ((x <= 5d-41) .or. (.not. (x <= 8d+90)) .and. (x <= 1.55d+95)) 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 <= -7.2e+18) {
		tmp = 100.0;
	} else if ((x <= 5e-41) || (!(x <= 8e+90) && (x <= 1.55e+95))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.2e+18:
		tmp = 100.0
	elif (x <= 5e-41) or (not (x <= 8e+90) and (x <= 1.55e+95)):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.2e+18)
		tmp = 100.0;
	elseif ((x <= 5e-41) || (!(x <= 8e+90) && (x <= 1.55e+95)))
		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 <= -7.2e+18)
		tmp = 100.0;
	elseif ((x <= 5e-41) || (~((x <= 8e+90)) && (x <= 1.55e+95)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.2e+18], 100.0, If[Or[LessEqual[x, 5e-41], And[N[Not[LessEqual[x, 8e+90]], $MachinePrecision], LessEqual[x, 1.55e+95]]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2e18 or 4.9999999999999996e-41 < x < 7.99999999999999973e90 or 1.5500000000000001e95 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 83.5%

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

   if -7.2e18 < x < 4.9999999999999996e-41 or 7.99999999999999973e90 < x < 1.5500000000000001e95

   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 77.4%

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

      1. associate-*r/ 77.7%

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

      2. associate-/l* 76.2%

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

      3. associate-/r/ 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-41} \lor \neg \left(x \leq 8 \cdot 10^{+90}\right) \land x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+90}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.5e+18)
   100.0
   (if (<= x 3.2e-34)
     (* x (/ 100.0 y))
     (if (<= x 1.2e+90) 100.0 (if (<= x 1.55e+95) (/ 100.0 (/ y x)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.5e+18) {
		tmp = 100.0;
	} else if (x <= 3.2e-34) {
		tmp = x * (100.0 / y);
	} else if (x <= 1.2e+90) {
		tmp = 100.0;
	} else if (x <= 1.55e+95) {
		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 <= (-1.5d+18)) then
        tmp = 100.0d0
    else if (x <= 3.2d-34) then
        tmp = x * (100.0d0 / y)
    else if (x <= 1.2d+90) then
        tmp = 100.0d0
    else if (x <= 1.55d+95) 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 <= -1.5e+18) {
		tmp = 100.0;
	} else if (x <= 3.2e-34) {
		tmp = x * (100.0 / y);
	} else if (x <= 1.2e+90) {
		tmp = 100.0;
	} else if (x <= 1.55e+95) {
		tmp = 100.0 / (y / x);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.5e+18:
		tmp = 100.0
	elif x <= 3.2e-34:
		tmp = x * (100.0 / y)
	elif x <= 1.2e+90:
		tmp = 100.0
	elif x <= 1.55e+95:
		tmp = 100.0 / (y / x)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.5e+18)
		tmp = 100.0;
	elseif (x <= 3.2e-34)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (x <= 1.2e+90)
		tmp = 100.0;
	elseif (x <= 1.55e+95)
		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 <= -1.5e+18)
		tmp = 100.0;
	elseif (x <= 3.2e-34)
		tmp = x * (100.0 / y);
	elseif (x <= 1.2e+90)
		tmp = 100.0;
	elseif (x <= 1.55e+95)
		tmp = 100.0 / (y / x);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.5e+18], 100.0, If[LessEqual[x, 3.2e-34], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+90], 100.0, If[LessEqual[x, 1.55e+95], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5e18 or 3.20000000000000003e-34 < x < 1.20000000000000005e90 or 1.5500000000000001e95 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 83.5%

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

   if -1.5e18 < x < 3.20000000000000003e-34

   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 76.6%

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

      1. associate-*r/ 76.8%

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

      2. associate-/l* 75.3%

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

      3. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

   if 1.20000000000000005e90 < x < 1.5500000000000001e95

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. 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 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+90}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+90}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4e+17)
   100.0
   (if (<= x 9e-40)
     (/ x (/ y 100.0))
     (if (<= x 6.8e+90) 100.0 (if (<= x 1.55e+95) (/ 100.0 (/ y x)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4e+17) {
		tmp = 100.0;
	} else if (x <= 9e-40) {
		tmp = x / (y / 100.0);
	} else if (x <= 6.8e+90) {
		tmp = 100.0;
	} else if (x <= 1.55e+95) {
		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 <= (-2.4d+17)) then
        tmp = 100.0d0
    else if (x <= 9d-40) then
        tmp = x / (y / 100.0d0)
    else if (x <= 6.8d+90) then
        tmp = 100.0d0
    else if (x <= 1.55d+95) 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 <= -2.4e+17) {
		tmp = 100.0;
	} else if (x <= 9e-40) {
		tmp = x / (y / 100.0);
	} else if (x <= 6.8e+90) {
		tmp = 100.0;
	} else if (x <= 1.55e+95) {
		tmp = 100.0 / (y / x);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4e+17:
		tmp = 100.0
	elif x <= 9e-40:
		tmp = x / (y / 100.0)
	elif x <= 6.8e+90:
		tmp = 100.0
	elif x <= 1.55e+95:
		tmp = 100.0 / (y / x)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4e+17)
		tmp = 100.0;
	elseif (x <= 9e-40)
		tmp = Float64(x / Float64(y / 100.0));
	elseif (x <= 6.8e+90)
		tmp = 100.0;
	elseif (x <= 1.55e+95)
		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 <= -2.4e+17)
		tmp = 100.0;
	elseif (x <= 9e-40)
		tmp = x / (y / 100.0);
	elseif (x <= 6.8e+90)
		tmp = 100.0;
	elseif (x <= 1.55e+95)
		tmp = 100.0 / (y / x);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4e+17], 100.0, If[LessEqual[x, 9e-40], N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+90], 100.0, If[LessEqual[x, 1.55e+95], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e17 or 9.0000000000000002e-40 < x < 6.80000000000000036e90 or 1.5500000000000001e95 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 83.5%

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

   if -2.4e17 < x < 9.0000000000000002e-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* 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 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

   if 6.80000000000000036e90 < x < 1.5500000000000001e95

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. 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 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+90}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(100.0 / N[(N[(x + y), $MachinePrecision] / x), $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* 99.1%

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

3. Simplified 99.1%

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

5. Final simplification 99.1%

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

Alternative 6: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\left(x + y\right) \cdot 0.01} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* (+ x y) 0.01)))

C

double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / ((x + y) * 0.01d0)
end function

Java

public static double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Python

def code(x, y):
	return x / ((x + y) * 0.01)

Julia

function code(x, y)
	return Float64(x / Float64(Float64(x + y) * 0.01))
end

MATLAB

function tmp = code(x, y)
	tmp = x / ((x + y) * 0.01);
end

Wolfram

code[x_, y_] := N[(x / N[(N[(x + y), $MachinePrecision] * 0.01), $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* 99.1%

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

3. Simplified 99.1%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

   3. expm1-log1p-u 98.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

   4. expm1-udef 66.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

   5. associate-/l* 66.2%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

   6. div-inv 66.2%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

   7. metadata-eval 66.2%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

6. Applied egg-rr 66.2%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot 0.01}\right)} - 1} \]
7. Step-by-step derivation

   1. expm1-def 98.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot 0.01}\right)\right)} \]

   2. expm1-log1p 99.7%

      \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

8. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

9. Final simplification 99.7%

   \[\leadsto \frac{x}{\left(x + y\right) \cdot 0.01} \]
10. Add Preprocessing

Alternative 7: 51.8% 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* 99.1%

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

3. Simplified 99.1%

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

5. Taylor expanded in x around inf 52.4%

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

6. Final simplification 52.4%

   \[\leadsto 100 \]
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 2024027 
(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)))