Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.3% → 99.3%

Time: 3.4s

Alternatives: 5

Speedup: N/A×

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: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{100}{\frac{y}{x} - -1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 100.0 (- (/ y x) -1.0)))

C

double code(double x, double y) {
	return 100.0 / ((y / x) - -1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0 / ((y / x) - (-1.0d0))
end function

Java

public static double code(double x, double y) {
	return 100.0 / ((y / x) - -1.0);
}

Python

def code(x, y):
	return 100.0 / ((y / x) - -1.0)

Julia

function code(x, y)
	return Float64(100.0 / Float64(Float64(y / x) - -1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0 / ((y / x) - -1.0);
end

Wolfram

code[x_, y_] := N[(100.0 / N[(N[(y / x), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.8%

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

   3. +-commutative 99.8%

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

   4. remove-double-neg 99.8%

      \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

   5. unsub-neg 99.8%

      \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

   6. div-sub 99.9%

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

   7. distribute-frac-neg 99.9%

      \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

   8. *-inverses 99.9%

      \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

   9. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \frac{100}{\frac{y}{x} - -1} \]
6. Add Preprocessing

Alternative 2: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+109}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -0.00018 \lor \neg \left(x \leq -4.6 \cdot 10^{-108}\right) \land x \leq 1.06 \cdot 10^{+53}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.65e+109)
   100.0
   (if (or (<= x -0.00018) (and (not (<= x -4.6e-108)) (<= x 1.06e+53)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.65e+109) {
		tmp = 100.0;
	} else if ((x <= -0.00018) || (!(x <= -4.6e-108) && (x <= 1.06e+53))) {
		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 <= (-1.65d+109)) then
        tmp = 100.0d0
    else if ((x <= (-0.00018d0)) .or. (.not. (x <= (-4.6d-108))) .and. (x <= 1.06d+53)) 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 <= -1.65e+109) {
		tmp = 100.0;
	} else if ((x <= -0.00018) || (!(x <= -4.6e-108) && (x <= 1.06e+53))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.65e+109:
		tmp = 100.0
	elif (x <= -0.00018) or (not (x <= -4.6e-108) and (x <= 1.06e+53)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.65e+109)
		tmp = 100.0;
	elseif ((x <= -0.00018) || (!(x <= -4.6e-108) && (x <= 1.06e+53)))
		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 <= -1.65e+109)
		tmp = 100.0;
	elseif ((x <= -0.00018) || (~((x <= -4.6e-108)) && (x <= 1.06e+53)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.65e+109], 100.0, If[Or[LessEqual[x, -0.00018], And[N[Not[LessEqual[x, -4.6e-108]], $MachinePrecision], LessEqual[x, 1.06e+53]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6499999999999999e109 or -1.80000000000000011e-4 < x < -4.59999999999999992e-108 or 1.05999999999999999e53 < x

   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* 99.9%

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

      3. +-commutative 99.9%

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

      4. remove-double-neg 99.9%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.9%

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

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.7%

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

   if -1.6499999999999999e109 < x < -1.80000000000000011e-4 or -4.59999999999999992e-108 < x < 1.05999999999999999e53

   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%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.8%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.8%

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

      7. distribute-frac-neg 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+109}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -0.00018 \lor \neg \left(x \leq -4.6 \cdot 10^{-108}\right) \land x \leq 1.06 \cdot 10^{+53}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+109}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -0.02:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-108}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+53}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+109)
   100.0
   (if (<= x -0.02)
     (* 100.0 (/ x y))
     (if (<= x -4.8e-108)
       100.0
       (if (<= x 1.15e+53) (/ 100.0 (/ y x)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+109) {
		tmp = 100.0;
	} else if (x <= -0.02) {
		tmp = 100.0 * (x / y);
	} else if (x <= -4.8e-108) {
		tmp = 100.0;
	} else if (x <= 1.15e+53) {
		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 <= (-1.85d+109)) then
        tmp = 100.0d0
    else if (x <= (-0.02d0)) then
        tmp = 100.0d0 * (x / y)
    else if (x <= (-4.8d-108)) then
        tmp = 100.0d0
    else if (x <= 1.15d+53) 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 <= -1.85e+109) {
		tmp = 100.0;
	} else if (x <= -0.02) {
		tmp = 100.0 * (x / y);
	} else if (x <= -4.8e-108) {
		tmp = 100.0;
	} else if (x <= 1.15e+53) {
		tmp = 100.0 / (y / x);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+109:
		tmp = 100.0
	elif x <= -0.02:
		tmp = 100.0 * (x / y)
	elif x <= -4.8e-108:
		tmp = 100.0
	elif x <= 1.15e+53:
		tmp = 100.0 / (y / x)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+109)
		tmp = 100.0;
	elseif (x <= -0.02)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (x <= -4.8e-108)
		tmp = 100.0;
	elseif (x <= 1.15e+53)
		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 <= -1.85e+109)
		tmp = 100.0;
	elseif (x <= -0.02)
		tmp = 100.0 * (x / y);
	elseif (x <= -4.8e-108)
		tmp = 100.0;
	elseif (x <= 1.15e+53)
		tmp = 100.0 / (y / x);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+109], 100.0, If[LessEqual[x, -0.02], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-108], 100.0, If[LessEqual[x, 1.15e+53], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8500000000000001e109 or -0.0200000000000000004 < x < -4.80000000000000034e-108 or 1.1500000000000001e53 < x

   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* 99.9%

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

      3. +-commutative 99.9%

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

      4. remove-double-neg 99.9%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.9%

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

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.7%

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

   if -1.8500000000000001e109 < x < -0.0200000000000000004

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.8%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.8%

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

      7. distribute-frac-neg 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 65.0%

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

   if -4.80000000000000034e-108 < x < 1.1500000000000001e53

   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* 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.8%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.8%

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

      7. distribute-frac-neg 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.7%

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

      1. associate-*r/ 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-/l* 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in x around 0 82.7%

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

      1. associate-*r/ 82.8%

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

      2. associate-/l* 82.8%

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

   10. Simplified 82.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+109}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -0.02:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-108}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+53}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -0.16:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-108}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e+111)
   100.0
   (if (<= x -0.16)
     (* 100.0 (/ x y))
     (if (<= x -6.2e-108) 100.0 (if (<= x 1.5e+53) (/ (* 100.0 x) y) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+111) {
		tmp = 100.0;
	} else if (x <= -0.16) {
		tmp = 100.0 * (x / y);
	} else if (x <= -6.2e-108) {
		tmp = 100.0;
	} else if (x <= 1.5e+53) {
		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 <= (-2.5d+111)) then
        tmp = 100.0d0
    else if (x <= (-0.16d0)) then
        tmp = 100.0d0 * (x / y)
    else if (x <= (-6.2d-108)) then
        tmp = 100.0d0
    else if (x <= 1.5d+53) 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 <= -2.5e+111) {
		tmp = 100.0;
	} else if (x <= -0.16) {
		tmp = 100.0 * (x / y);
	} else if (x <= -6.2e-108) {
		tmp = 100.0;
	} else if (x <= 1.5e+53) {
		tmp = (100.0 * x) / y;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e+111:
		tmp = 100.0
	elif x <= -0.16:
		tmp = 100.0 * (x / y)
	elif x <= -6.2e-108:
		tmp = 100.0
	elif x <= 1.5e+53:
		tmp = (100.0 * x) / y
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e+111)
		tmp = 100.0;
	elseif (x <= -0.16)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (x <= -6.2e-108)
		tmp = 100.0;
	elseif (x <= 1.5e+53)
		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 <= -2.5e+111)
		tmp = 100.0;
	elseif (x <= -0.16)
		tmp = 100.0 * (x / y);
	elseif (x <= -6.2e-108)
		tmp = 100.0;
	elseif (x <= 1.5e+53)
		tmp = (100.0 * x) / y;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e+111], 100.0, If[LessEqual[x, -0.16], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-108], 100.0, If[LessEqual[x, 1.5e+53], N[(N[(100.0 * x), $MachinePrecision] / y), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4999999999999998e111 or -0.160000000000000003 < x < -6.20000000000000028e-108 or 1.49999999999999999e53 < x

   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* 99.9%

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

      3. +-commutative 99.9%

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

      4. remove-double-neg 99.9%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.9%

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

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.7%

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

   if -2.4999999999999998e111 < x < -0.160000000000000003

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.8%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.8%

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

      7. distribute-frac-neg 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 65.0%

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

   if -6.20000000000000028e-108 < x < 1.49999999999999999e53

   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* 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.8%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.8%

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

      7. distribute-frac-neg 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.8%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.7%

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

      1. associate-*r/ 82.8%

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

   7. Applied egg-rr 82.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -0.16:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-108}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% 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 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.8%

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

   3. +-commutative 99.8%

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

   4. remove-double-neg 99.8%

      \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

   5. unsub-neg 99.8%

      \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

   6. div-sub 99.9%

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

   7. distribute-frac-neg 99.9%

      \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

   8. *-inverses 99.9%

      \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

   9. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 51.3%

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

6. Final simplification 51.3%

   \[\leadsto 100 \]
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 2024020 
(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)))