Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.3% → 99.7%

Time: 4.2s

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: 99.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 2: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120} \lor \neg \left(y \leq 3.9 \cdot 10^{+37}\right) \land \left(y \leq 4.4 \cdot 10^{+102} \lor \neg \left(y \leq 3.8 \cdot 10^{+142}\right)\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.7e-120)
         (and (not (<= y 3.9e+37)) (or (<= y 4.4e+102) (not (<= y 3.8e+142)))))
   (* x (/ 100.0 y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.7e-120) || (!(y <= 3.9e+37) && ((y <= 4.4e+102) || !(y <= 3.8e+142)))) {
		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 <= (-2.7d-120)) .or. (.not. (y <= 3.9d+37)) .and. (y <= 4.4d+102) .or. (.not. (y <= 3.8d+142))) 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 <= -2.7e-120) || (!(y <= 3.9e+37) && ((y <= 4.4e+102) || !(y <= 3.8e+142)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.7e-120) or (not (y <= 3.9e+37) and ((y <= 4.4e+102) or not (y <= 3.8e+142))):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.7e-120) || (!(y <= 3.9e+37) && ((y <= 4.4e+102) || !(y <= 3.8e+142))))
		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 <= -2.7e-120) || (~((y <= 3.9e+37)) && ((y <= 4.4e+102) || ~((y <= 3.8e+142)))))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.7e-120], And[N[Not[LessEqual[y, 3.9e+37]], $MachinePrecision], Or[LessEqual[y, 4.4e+102], N[Not[LessEqual[y, 3.8e+142]], $MachinePrecision]]]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999999e-120 or 3.8999999999999999e37 < y < 4.40000000000000015e102 or 3.7999999999999999e142 < y

   1. Initial program 99.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 98.4%

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

      2. associate-/r/ 99.5%

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

      3. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 79.3%

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

   if -2.6999999999999999e-120 < y < 3.8999999999999999e37 or 4.40000000000000015e102 < y < 3.7999999999999999e142

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.6%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120} \lor \neg \left(y \leq 3.9 \cdot 10^{+37}\right) \land \left(y \leq 4.4 \cdot 10^{+102} \lor \neg \left(y \leq 3.8 \cdot 10^{+142}\right)\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+101}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 100.0 y))))
   (if (<= y -2.7e-120)
     t_0
     (if (<= y 2.4e+45)
       100.0
       (if (<= y 3.2e+101)
         (* 100.0 (/ x y))
         (if (<= y 2.6e+142) 100.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -2.7e-120) {
		tmp = t_0;
	} else if (y <= 2.4e+45) {
		tmp = 100.0;
	} else if (y <= 3.2e+101) {
		tmp = 100.0 * (x / y);
	} else if (y <= 2.6e+142) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (100.0d0 / y)
    if (y <= (-2.7d-120)) then
        tmp = t_0
    else if (y <= 2.4d+45) then
        tmp = 100.0d0
    else if (y <= 3.2d+101) then
        tmp = 100.0d0 * (x / y)
    else if (y <= 2.6d+142) then
        tmp = 100.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -2.7e-120) {
		tmp = t_0;
	} else if (y <= 2.4e+45) {
		tmp = 100.0;
	} else if (y <= 3.2e+101) {
		tmp = 100.0 * (x / y);
	} else if (y <= 2.6e+142) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (100.0 / y)
	tmp = 0
	if y <= -2.7e-120:
		tmp = t_0
	elif y <= 2.4e+45:
		tmp = 100.0
	elif y <= 3.2e+101:
		tmp = 100.0 * (x / y)
	elif y <= 2.6e+142:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(100.0 / y))
	tmp = 0.0
	if (y <= -2.7e-120)
		tmp = t_0;
	elseif (y <= 2.4e+45)
		tmp = 100.0;
	elseif (y <= 3.2e+101)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (y <= 2.6e+142)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (100.0 / y);
	tmp = 0.0;
	if (y <= -2.7e-120)
		tmp = t_0;
	elseif (y <= 2.4e+45)
		tmp = 100.0;
	elseif (y <= 3.2e+101)
		tmp = 100.0 * (x / y);
	elseif (y <= 2.6e+142)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-120], t$95$0, If[LessEqual[y, 2.4e+45], 100.0, If[LessEqual[y, 3.2e+101], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+142], 100.0, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999999e-120 or 2.60000000000000021e142 < y

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 98.3%

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

      2. associate-/r/ 99.5%

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

      3. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 79.4%

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

   if -2.6999999999999999e-120 < y < 2.39999999999999989e45 or 3.20000000000000005e101 < y < 2.60000000000000021e142

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.6%

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

   if 2.39999999999999989e45 < y < 3.20000000000000005e101

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+101}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]

Alternative 4: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.7e-120)
   (* x (/ 100.0 y))
   (if (<= y 6.5e+38)
     100.0
     (if (<= y 3.4e+101)
       (* 100.0 (/ x y))
       (if (<= y 2.6e+142) 100.0 (/ (* x 100.0) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.7e-120) {
		tmp = x * (100.0 / y);
	} else if (y <= 6.5e+38) {
		tmp = 100.0;
	} else if (y <= 3.4e+101) {
		tmp = 100.0 * (x / y);
	} else if (y <= 2.6e+142) {
		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 <= (-2.7d-120)) then
        tmp = x * (100.0d0 / y)
    else if (y <= 6.5d+38) then
        tmp = 100.0d0
    else if (y <= 3.4d+101) then
        tmp = 100.0d0 * (x / y)
    else if (y <= 2.6d+142) 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 <= -2.7e-120) {
		tmp = x * (100.0 / y);
	} else if (y <= 6.5e+38) {
		tmp = 100.0;
	} else if (y <= 3.4e+101) {
		tmp = 100.0 * (x / y);
	} else if (y <= 2.6e+142) {
		tmp = 100.0;
	} else {
		tmp = (x * 100.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.7e-120:
		tmp = x * (100.0 / y)
	elif y <= 6.5e+38:
		tmp = 100.0
	elif y <= 3.4e+101:
		tmp = 100.0 * (x / y)
	elif y <= 2.6e+142:
		tmp = 100.0
	else:
		tmp = (x * 100.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.7e-120)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (y <= 6.5e+38)
		tmp = 100.0;
	elseif (y <= 3.4e+101)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (y <= 2.6e+142)
		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 <= -2.7e-120)
		tmp = x * (100.0 / y);
	elseif (y <= 6.5e+38)
		tmp = 100.0;
	elseif (y <= 3.4e+101)
		tmp = 100.0 * (x / y);
	elseif (y <= 2.6e+142)
		tmp = 100.0;
	else
		tmp = (x * 100.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.7e-120], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+38], 100.0, If[LessEqual[y, 3.4e+101], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+142], 100.0, N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6999999999999999e-120

   1. Initial program 98.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 97.6%

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

      2. associate-/r/ 99.5%

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

      3. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 71.4%

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

   if -2.6999999999999999e-120 < y < 6.5e38 or 3.40000000000000017e101 < y < 2.60000000000000021e142

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.6%

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

   if 6.5e38 < y < 3.40000000000000017e101

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.0%

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

   if 2.60000000000000021e142 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l/ 99.6%

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

      3. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 94.1%

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

      1. associate-*r/ 94.4%

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

   6. Simplified 94.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \]

Alternative 5: 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 99.0%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

   1. clear-num 99.0%

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

   2. associate-/r/ 99.5%

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

   3. clear-num 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

Alternative 6: 50.6% 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%

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

   2. associate-*l/ 99.7%

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

   3. +-commutative 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around inf 47.3%

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

5. Final simplification 47.3%

   \[\leadsto 100 \]

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 2023310 
(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)))