Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 3.9s

Alternatives: 5

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 99.7%

   \[\frac{x \cdot 100}{x + y} \]
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. Final simplification 99.7%

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

Alternative 2: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-46} \lor \neg \left(x \leq -4 \cdot 10^{-111}\right) \land x \leq 36000000:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.5e+58)
   100.0
   (if (or (<= x -3e-46) (and (not (<= x -4e-111)) (<= x 36000000.0)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.5e+58) {
		tmp = 100.0;
	} else if ((x <= -3e-46) || (!(x <= -4e-111) && (x <= 36000000.0))) {
		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 <= (-6.5d+58)) then
        tmp = 100.0d0
    else if ((x <= (-3d-46)) .or. (.not. (x <= (-4d-111))) .and. (x <= 36000000.0d0)) 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 <= -6.5e+58) {
		tmp = 100.0;
	} else if ((x <= -3e-46) || (!(x <= -4e-111) && (x <= 36000000.0))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.5e+58:
		tmp = 100.0
	elif (x <= -3e-46) or (not (x <= -4e-111) and (x <= 36000000.0)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.5e+58)
		tmp = 100.0;
	elseif ((x <= -3e-46) || (!(x <= -4e-111) && (x <= 36000000.0)))
		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 <= -6.5e+58)
		tmp = 100.0;
	elseif ((x <= -3e-46) || (~((x <= -4e-111)) && (x <= 36000000.0)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.5e+58], 100.0, If[Or[LessEqual[x, -3e-46], And[N[Not[LessEqual[x, -4e-111]], $MachinePrecision], LessEqual[x, 36000000.0]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999998e58 or -2.99999999999999987e-46 < x < -4.00000000000000035e-111 or 3.6e7 < 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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -6.49999999999999998e58 < x < -2.99999999999999987e-46 or -4.00000000000000035e-111 < x < 3.6e7

   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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 81.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-46} \lor \neg \left(x \leq -4 \cdot 10^{-111}\right) \land x \leq 36000000:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.2e+61)
   100.0
   (if (<= x -1.08e-47)
     (/ 100.0 (/ y x))
     (if (<= x -4e-111)
       100.0
       (if (<= x 35000000.0) (* 100.0 (/ x y)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.2e+61) {
		tmp = 100.0;
	} else if (x <= -1.08e-47) {
		tmp = 100.0 / (y / x);
	} else if (x <= -4e-111) {
		tmp = 100.0;
	} else if (x <= 35000000.0) {
		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 <= (-4.2d+61)) then
        tmp = 100.0d0
    else if (x <= (-1.08d-47)) then
        tmp = 100.0d0 / (y / x)
    else if (x <= (-4d-111)) then
        tmp = 100.0d0
    else if (x <= 35000000.0d0) 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 <= -4.2e+61) {
		tmp = 100.0;
	} else if (x <= -1.08e-47) {
		tmp = 100.0 / (y / x);
	} else if (x <= -4e-111) {
		tmp = 100.0;
	} else if (x <= 35000000.0) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.2e+61:
		tmp = 100.0
	elif x <= -1.08e-47:
		tmp = 100.0 / (y / x)
	elif x <= -4e-111:
		tmp = 100.0
	elif x <= 35000000.0:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.2e+61)
		tmp = 100.0;
	elseif (x <= -1.08e-47)
		tmp = Float64(100.0 / Float64(y / x));
	elseif (x <= -4e-111)
		tmp = 100.0;
	elseif (x <= 35000000.0)
		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 <= -4.2e+61)
		tmp = 100.0;
	elseif (x <= -1.08e-47)
		tmp = 100.0 / (y / x);
	elseif (x <= -4e-111)
		tmp = 100.0;
	elseif (x <= 35000000.0)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.2e+61], 100.0, If[LessEqual[x, -1.08e-47], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-111], 100.0, If[LessEqual[x, 35000000.0], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000002e61 or -1.08000000000000005e-47 < x < -4.00000000000000035e-111 or 3.5e7 < 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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -4.2000000000000002e61 < x < -1.08000000000000005e-47

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   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 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 62.5%

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

      1. associate-*r/ 62.7%

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

      2. associate-*l/ 62.6%

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

      3. associate-/r/ 62.8%

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

   9. Simplified 62.8%

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

   if -4.00000000000000035e-111 < x < 3.5e7

   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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 84.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-47}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.3e+59)
   100.0
   (if (<= x -1.85e-47)
     (/ 100.0 (/ y x))
     (if (<= x -4e-111)
       100.0
       (if (<= x 35000000.0) (/ (* 100.0 x) y) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.3e+59) {
		tmp = 100.0;
	} else if (x <= -1.85e-47) {
		tmp = 100.0 / (y / x);
	} else if (x <= -4e-111) {
		tmp = 100.0;
	} else if (x <= 35000000.0) {
		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 <= (-3.3d+59)) then
        tmp = 100.0d0
    else if (x <= (-1.85d-47)) then
        tmp = 100.0d0 / (y / x)
    else if (x <= (-4d-111)) then
        tmp = 100.0d0
    else if (x <= 35000000.0d0) 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 <= -3.3e+59) {
		tmp = 100.0;
	} else if (x <= -1.85e-47) {
		tmp = 100.0 / (y / x);
	} else if (x <= -4e-111) {
		tmp = 100.0;
	} else if (x <= 35000000.0) {
		tmp = (100.0 * x) / y;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.3e+59:
		tmp = 100.0
	elif x <= -1.85e-47:
		tmp = 100.0 / (y / x)
	elif x <= -4e-111:
		tmp = 100.0
	elif x <= 35000000.0:
		tmp = (100.0 * x) / y
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.3e+59)
		tmp = 100.0;
	elseif (x <= -1.85e-47)
		tmp = Float64(100.0 / Float64(y / x));
	elseif (x <= -4e-111)
		tmp = 100.0;
	elseif (x <= 35000000.0)
		tmp = Float64(Float64(100.0 * x) / y);
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.3e+59)
		tmp = 100.0;
	elseif (x <= -1.85e-47)
		tmp = 100.0 / (y / x);
	elseif (x <= -4e-111)
		tmp = 100.0;
	elseif (x <= 35000000.0)
		tmp = (100.0 * x) / y;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.3e+59], 100.0, If[LessEqual[x, -1.85e-47], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-111], 100.0, If[LessEqual[x, 35000000.0], N[(N[(100.0 * x), $MachinePrecision] / y), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2999999999999999e59 or -1.85e-47 < x < -4.00000000000000035e-111 or 3.5e7 < 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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -3.2999999999999999e59 < x < -1.85e-47

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   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 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 62.5%

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

      1. associate-*r/ 62.7%

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

      2. associate-*l/ 62.6%

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

      3. associate-/r/ 62.8%

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

   9. Simplified 62.8%

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

   if -4.00000000000000035e-111 < x < 3.5e7

   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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-47}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 99.7%

   \[\frac{x \cdot 100}{x + y} \]
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 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 2024059 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :alt
  (* (/ x 1.0) (/ 100.0 (+ x y)))

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