Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.8%

Time: 3.6s

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: 99.4% 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: 99.8% 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 99.8%

   \[\frac{x \cdot 100}{x + y} \]
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 99.8%

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

   4. +-commutative 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+136} \lor \neg \left(y \leq -4.1 \cdot 10^{+128} \lor \neg \left(y \leq -2.9 \cdot 10^{+45}\right) \land y \leq 1.6 \cdot 10^{+31}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.15e+136)
         (not
          (or (<= y -4.1e+128) (and (not (<= y -2.9e+45)) (<= y 1.6e+31)))))
   (* 100.0 (/ x y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.15e+136) || !((y <= -4.1e+128) || (!(y <= -2.9e+45) && (y <= 1.6e+31)))) {
		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 <= (-2.15d+136)) .or. (.not. (y <= (-4.1d+128)) .or. (.not. (y <= (-2.9d+45))) .and. (y <= 1.6d+31))) 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 <= -2.15e+136) || !((y <= -4.1e+128) || (!(y <= -2.9e+45) && (y <= 1.6e+31)))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.15e+136) or not ((y <= -4.1e+128) or (not (y <= -2.9e+45) and (y <= 1.6e+31))):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.15e+136) || !((y <= -4.1e+128) || (!(y <= -2.9e+45) && (y <= 1.6e+31))))
		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 <= -2.15e+136) || ~(((y <= -4.1e+128) || (~((y <= -2.9e+45)) && (y <= 1.6e+31)))))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.15e+136], N[Not[Or[LessEqual[y, -4.1e+128], And[N[Not[LessEqual[y, -2.9e+45]], $MachinePrecision], LessEqual[y, 1.6e+31]]]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e136 or -4.10000000000000012e128 < y < -2.8999999999999997e45 or 1.6e31 < 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. +-commutative 99.7%

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

      3. associate-/l* 97.8%

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

      4. remove-double-neg 97.8%

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

      5. unsub-neg 97.8%

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

      6. div-sub 97.8%

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

      7. distribute-frac-neg 97.8%

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

      8. *-inverses 97.8%

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

      9. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 77.1%

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

   if -2.1499999999999999e136 < y < -4.10000000000000012e128 or -2.8999999999999997e45 < y < 1.6e31

   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. +-commutative 99.8%

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

      3. associate-/l* 99.5%

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

      4. remove-double-neg 99.5%

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

      5. unsub-neg 99.5%

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

      6. div-sub 99.5%

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

      7. distribute-frac-neg 99.5%

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

      8. *-inverses 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 76.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+136} \lor \neg \left(y \leq -4.1 \cdot 10^{+128} \lor \neg \left(y \leq -2.9 \cdot 10^{+45}\right) \land y \leq 1.6 \cdot 10^{+31}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+135} \lor \neg \left(y \leq -4 \cdot 10^{+128} \lor \neg \left(y \leq -2.1 \cdot 10^{+46}\right) \land y \leq 2.95 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.2e+135)
         (not (or (<= y -4e+128) (and (not (<= y -2.1e+46)) (<= y 2.95e+31)))))
   (* x (/ 100.0 y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.2e+135) || !((y <= -4e+128) || (!(y <= -2.1e+46) && (y <= 2.95e+31)))) {
		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 <= (-3.2d+135)) .or. (.not. (y <= (-4d+128)) .or. (.not. (y <= (-2.1d+46))) .and. (y <= 2.95d+31))) 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 <= -3.2e+135) || !((y <= -4e+128) || (!(y <= -2.1e+46) && (y <= 2.95e+31)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.2e+135) or not ((y <= -4e+128) or (not (y <= -2.1e+46) and (y <= 2.95e+31))):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.2e+135) || !((y <= -4e+128) || (!(y <= -2.1e+46) && (y <= 2.95e+31))))
		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 <= -3.2e+135) || ~(((y <= -4e+128) || (~((y <= -2.1e+46)) && (y <= 2.95e+31)))))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.2e+135], N[Not[Or[LessEqual[y, -4e+128], And[N[Not[LessEqual[y, -2.1e+46]], $MachinePrecision], LessEqual[y, 2.95e+31]]]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999975e135 or -4.0000000000000003e128 < y < -2.1e46 or 2.9500000000000002e31 < y

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   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/ 99.6%

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

      3. clear-num 99.9%

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

      4. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 77.5%

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

   if -3.19999999999999975e135 < y < -4.0000000000000003e128 or -2.1e46 < y < 2.9500000000000002e31

   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. +-commutative 99.8%

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

      3. associate-/l* 99.5%

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

      4. remove-double-neg 99.5%

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

      5. unsub-neg 99.5%

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

      6. div-sub 99.5%

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

      7. distribute-frac-neg 99.5%

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

      8. *-inverses 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 76.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+135} \lor \neg \left(y \leq -4 \cdot 10^{+128} \lor \neg \left(y \leq -2.1 \cdot 10^{+46}\right) \land y \leq 2.95 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{100 \cdot x}{x}\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+47} \lor \neg \left(y \leq 3.7 \cdot 10^{+32}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 100.0 y))))
   (if (<= y -4.9e+135)
     t_0
     (if (<= y -4.1e+128)
       (/ (* 100.0 x) x)
       (if (or (<= y -2.95e+47) (not (<= y 3.7e+32))) t_0 100.0)))))

C

double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -4.9e+135) {
		tmp = t_0;
	} else if (y <= -4.1e+128) {
		tmp = (100.0 * x) / x;
	} else if ((y <= -2.95e+47) || !(y <= 3.7e+32)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (100.0d0 / y)
    if (y <= (-4.9d+135)) then
        tmp = t_0
    else if (y <= (-4.1d+128)) then
        tmp = (100.0d0 * x) / x
    else if ((y <= (-2.95d+47)) .or. (.not. (y <= 3.7d+32))) then
        tmp = t_0
    else
        tmp = 100.0d0
    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 <= -4.9e+135) {
		tmp = t_0;
	} else if (y <= -4.1e+128) {
		tmp = (100.0 * x) / x;
	} else if ((y <= -2.95e+47) || !(y <= 3.7e+32)) {
		tmp = t_0;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (100.0 / y)
	tmp = 0
	if y <= -4.9e+135:
		tmp = t_0
	elif y <= -4.1e+128:
		tmp = (100.0 * x) / x
	elif (y <= -2.95e+47) or not (y <= 3.7e+32):
		tmp = t_0
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(100.0 / y))
	tmp = 0.0
	if (y <= -4.9e+135)
		tmp = t_0;
	elseif (y <= -4.1e+128)
		tmp = Float64(Float64(100.0 * x) / x);
	elseif ((y <= -2.95e+47) || !(y <= 3.7e+32))
		tmp = t_0;
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (100.0 / y);
	tmp = 0.0;
	if (y <= -4.9e+135)
		tmp = t_0;
	elseif (y <= -4.1e+128)
		tmp = (100.0 * x) / x;
	elseif ((y <= -2.95e+47) || ~((y <= 3.7e+32)))
		tmp = t_0;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.9e+135], t$95$0, If[LessEqual[y, -4.1e+128], N[(N[(100.0 * x), $MachinePrecision] / x), $MachinePrecision], If[Or[LessEqual[y, -2.95e+47], N[Not[LessEqual[y, 3.7e+32]], $MachinePrecision]], t$95$0, 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9000000000000001e135 or -4.10000000000000012e128 < y < -2.95000000000000017e47 or 3.7e32 < y

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   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/ 99.6%

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

      3. clear-num 99.9%

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

      4. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 77.5%

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

   if -4.9000000000000001e135 < y < -4.10000000000000012e128

   1. Initial program 99.7%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

      1. clear-num 99.4%

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

      2. associate-/r/ 98.8%

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

      3. clear-num 99.7%

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

      4. +-commutative 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 88.1%

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

      1. associate-*l/ 88.4%

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

   8. Applied egg-rr 88.4%

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

   if -2.95000000000000017e47 < y < 3.7e32

   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. +-commutative 99.8%

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

      3. associate-/l* 99.5%

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

      4. remove-double-neg 99.5%

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

      5. unsub-neg 99.5%

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

      6. div-sub 99.5%

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

      7. distribute-frac-neg 99.5%

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

      8. *-inverses 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 75.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{100 \cdot x}{x}\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+47} \lor \neg \left(y \leq 3.7 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5: 50.0% 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 99.8%

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

   1. *-commutative 99.8%

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

   2. +-commutative 99.8%

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

   3. associate-/l* 98.9%

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

   4. remove-double-neg 98.9%

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

   5. unsub-neg 98.9%

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

   6. div-sub 98.9%

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

   7. distribute-frac-neg 98.9%

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

   8. *-inverses 98.9%

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

   9. metadata-eval 98.9%

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

3. Simplified 98.9%

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

4. Taylor expanded in y around 0 56.0%

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

5. Final simplification 56.0%

   \[\leadsto 100 \]

Developer target: 99.8% 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 2023318 
(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)))