Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.6% → 99.7%

Time: 5.3s

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: 99.6% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Simplified 99.1%

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

   1. associate-/r/ 99.7%

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

   2. +-commutative 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 2: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -410000000 \lor \neg \left(y \leq 3.2 \cdot 10^{+130}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -410000000.0) (not (<= y 3.2e+130))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -410000000.0) || !(y <= 3.2e+130)) {
		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 ((y <= (-410000000.0d0)) .or. (.not. (y <= 3.2d+130))) 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 ((y <= -410000000.0) || !(y <= 3.2e+130)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -410000000.0) or not (y <= 3.2e+130):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -410000000.0) || !(y <= 3.2e+130))
		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 ((y <= -410000000.0) || ~((y <= 3.2e+130)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -410000000.0], N[Not[LessEqual[y, 3.2e+130]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e8 or 3.2e130 < y

   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* 98.1%

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

      3. +-commutative 98.1%

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

      4. remove-double-neg 98.1%

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

      5. unsub-neg 98.1%

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

      6. div-sub 98.1%

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

      7. distribute-frac-neg 98.1%

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

      8. *-inverses 98.1%

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

      9. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around inf 80.8%

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

   if -4.1e8 < y < 3.2e130

   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. +-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 99.8%

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

      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 0 74.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -410000000 \lor \neg \left(y \leq 3.2 \cdot 10^{+130}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 4.1 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -32000000.0) (not (<= y 4.1e+95))) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -32000000.0) || !(y <= 4.1e+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 ((y <= (-32000000.0d0)) .or. (.not. (y <= 4.1d+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 ((y <= -32000000.0) || !(y <= 4.1e+95)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -32000000.0) or not (y <= 4.1e+95):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -32000000.0) || !(y <= 4.1e+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 ((y <= -32000000.0) || ~((y <= 4.1e+95)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -32000000.0], N[Not[LessEqual[y, 4.1e+95]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e7 or 4.09999999999999986e95 < y

   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* 98.2%

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

   3. Simplified 98.2%

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

      1. associate-/r/ 99.7%

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

      2. +-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 79.4%

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

   if -3.2e7 < y < 4.09999999999999986e95

   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. +-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 99.8%

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

      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 0 75.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 4.1 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+95}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1200000.0)
   (/ (* 100.0 x) y)
   (if (<= y 4.8e+95) 100.0 (* x (/ 100.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1200000.0) {
		tmp = (100.0 * x) / y;
	} else if (y <= 4.8e+95) {
		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 <= (-1200000.0d0)) then
        tmp = (100.0d0 * x) / y
    else if (y <= 4.8d+95) 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 <= -1200000.0) {
		tmp = (100.0 * x) / y;
	} else if (y <= 4.8e+95) {
		tmp = 100.0;
	} else {
		tmp = x * (100.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1200000.0:
		tmp = (100.0 * x) / y
	elif y <= 4.8e+95:
		tmp = 100.0
	else:
		tmp = x * (100.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1200000.0)
		tmp = Float64(Float64(100.0 * x) / y);
	elseif (y <= 4.8e+95)
		tmp = 100.0;
	else
		tmp = Float64(x * Float64(100.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1200000.0)
		tmp = (100.0 * x) / y;
	elseif (y <= 4.8e+95)
		tmp = 100.0;
	else
		tmp = x * (100.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1200000.0], N[(N[(100.0 * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 4.8e+95], 100.0, N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e6

   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* 98.5%

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

      3. +-commutative 98.5%

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

      4. remove-double-neg 98.5%

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

      5. unsub-neg 98.5%

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

      6. div-sub 98.5%

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

      7. distribute-frac-neg 98.5%

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

      8. *-inverses 98.5%

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

      9. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around inf 72.9%

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

      1. associate-*r/ 73.0%

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

   7. Applied egg-rr 73.0%

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

   if -1.2e6 < y < 4.8000000000000001e95

   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. +-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 99.8%

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

      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 0 75.8%

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

   if 4.8000000000000001e95 < y

   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* 97.9%

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

   3. Simplified 97.9%

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

      1. associate-/r/ 99.8%

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

      2. +-commutative 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 86.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+95}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]
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 99.7%

   \[\frac{x \cdot 100}{x + y} \]
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. +-commutative 99.1%

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

   4. remove-double-neg 99.1%

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

   5. unsub-neg 99.1%

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

   6. div-sub 99.1%

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

   7. distribute-frac-neg 99.1%

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

   8. *-inverses 99.1%

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

   9. metadata-eval 99.1%

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

3. Simplified 99.1%

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

5. Taylor expanded in y around 0 52.1%

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

6. Final simplification 52.1%

   \[\leadsto 100 \]
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 2024024 
(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)))