Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 5.8s

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: 99.4% 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: 99.7% 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 99.7%

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

   1. associate-/l* 99.8%

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

   2. *-commutative 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+64}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+36} \lor \neg \left(x \leq -16500000000\right) \land x \leq 5.8 \cdot 10^{+51}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.2e+64)
   100.0
   (if (or (<= x -1.05e+36) (and (not (<= x -16500000000.0)) (<= x 5.8e+51)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.2e+64) {
		tmp = 100.0;
	} else if ((x <= -1.05e+36) || (!(x <= -16500000000.0) && (x <= 5.8e+51))) {
		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 <= (-3.2d+64)) then
        tmp = 100.0d0
    else if ((x <= (-1.05d+36)) .or. (.not. (x <= (-16500000000.0d0))) .and. (x <= 5.8d+51)) 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 <= -3.2e+64) {
		tmp = 100.0;
	} else if ((x <= -1.05e+36) || (!(x <= -16500000000.0) && (x <= 5.8e+51))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.2e+64:
		tmp = 100.0
	elif (x <= -1.05e+36) or (not (x <= -16500000000.0) and (x <= 5.8e+51)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.2e+64)
		tmp = 100.0;
	elseif ((x <= -1.05e+36) || (!(x <= -16500000000.0) && (x <= 5.8e+51)))
		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 <= -3.2e+64)
		tmp = 100.0;
	elseif ((x <= -1.05e+36) || (~((x <= -16500000000.0)) && (x <= 5.8e+51)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.2e+64], 100.0, If[Or[LessEqual[x, -1.05e+36], And[N[Not[LessEqual[x, -16500000000.0]], $MachinePrecision], LessEqual[x, 5.8e+51]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.20000000000000019e64 or -1.05000000000000002e36 < x < -1.65e10 or 5.7999999999999997e51 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.7%

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

   if -3.20000000000000019e64 < x < -1.05000000000000002e36 or -1.65e10 < x < 5.7999999999999997e51

   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. Taylor expanded in x around 0 80.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+64}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+36} \lor \neg \left(x \leq -16500000000\right) \land x \leq 5.8 \cdot 10^{+51}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+64}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.95 \cdot 10^{+39}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -15500000000:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+64)
   100.0
   (if (<= x -2.95e+39)
     (* 100.0 (/ x y))
     (if (<= x -15500000000.0)
       100.0
       (if (<= x 2.2e+54) (* x (/ 100.0 y)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+64) {
		tmp = 100.0;
	} else if (x <= -2.95e+39) {
		tmp = 100.0 * (x / y);
	} else if (x <= -15500000000.0) {
		tmp = 100.0;
	} else if (x <= 2.2e+54) {
		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 (x <= (-5d+64)) then
        tmp = 100.0d0
    else if (x <= (-2.95d+39)) then
        tmp = 100.0d0 * (x / y)
    else if (x <= (-15500000000.0d0)) then
        tmp = 100.0d0
    else if (x <= 2.2d+54) 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 (x <= -5e+64) {
		tmp = 100.0;
	} else if (x <= -2.95e+39) {
		tmp = 100.0 * (x / y);
	} else if (x <= -15500000000.0) {
		tmp = 100.0;
	} else if (x <= 2.2e+54) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+64:
		tmp = 100.0
	elif x <= -2.95e+39:
		tmp = 100.0 * (x / y)
	elif x <= -15500000000.0:
		tmp = 100.0
	elif x <= 2.2e+54:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+64)
		tmp = 100.0;
	elseif (x <= -2.95e+39)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (x <= -15500000000.0)
		tmp = 100.0;
	elseif (x <= 2.2e+54)
		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 (x <= -5e+64)
		tmp = 100.0;
	elseif (x <= -2.95e+39)
		tmp = 100.0 * (x / y);
	elseif (x <= -15500000000.0)
		tmp = 100.0;
	elseif (x <= 2.2e+54)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+64], 100.0, If[LessEqual[x, -2.95e+39], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -15500000000.0], 100.0, If[LessEqual[x, 2.2e+54], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5e64 or -2.94999999999999983e39 < x < -1.55e10 or 2.1999999999999999e54 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.7%

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

   if -5e64 < x < -2.94999999999999983e39

   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. Taylor expanded in x around 0 86.3%

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

   if -1.55e10 < x < 2.1999999999999999e54

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0 80.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+64}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.95 \cdot 10^{+39}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -15500000000:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+32}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -880000000:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.6e+65)
   100.0
   (if (<= x -2e+32)
     (/ 100.0 (/ y x))
     (if (<= x -880000000.0)
       100.0
       (if (<= x 1.5e+51) (* x (/ 100.0 y)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e+65) {
		tmp = 100.0;
	} else if (x <= -2e+32) {
		tmp = 100.0 / (y / x);
	} else if (x <= -880000000.0) {
		tmp = 100.0;
	} else if (x <= 1.5e+51) {
		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 (x <= (-1.6d+65)) then
        tmp = 100.0d0
    else if (x <= (-2d+32)) then
        tmp = 100.0d0 / (y / x)
    else if (x <= (-880000000.0d0)) then
        tmp = 100.0d0
    else if (x <= 1.5d+51) 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 (x <= -1.6e+65) {
		tmp = 100.0;
	} else if (x <= -2e+32) {
		tmp = 100.0 / (y / x);
	} else if (x <= -880000000.0) {
		tmp = 100.0;
	} else if (x <= 1.5e+51) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e+65:
		tmp = 100.0
	elif x <= -2e+32:
		tmp = 100.0 / (y / x)
	elif x <= -880000000.0:
		tmp = 100.0
	elif x <= 1.5e+51:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e+65)
		tmp = 100.0;
	elseif (x <= -2e+32)
		tmp = Float64(100.0 / Float64(y / x));
	elseif (x <= -880000000.0)
		tmp = 100.0;
	elseif (x <= 1.5e+51)
		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 (x <= -1.6e+65)
		tmp = 100.0;
	elseif (x <= -2e+32)
		tmp = 100.0 / (y / x);
	elseif (x <= -880000000.0)
		tmp = 100.0;
	elseif (x <= 1.5e+51)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e+65], 100.0, If[LessEqual[x, -2e+32], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -880000000.0], 100.0, If[LessEqual[x, 1.5e+51], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.60000000000000003e65 or -2.00000000000000011e32 < x < -8.8e8 or 1.5e51 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.7%

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

   if -1.60000000000000003e65 < x < -2.00000000000000011e32

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around 0 86.3%

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

      1. div-inv 86.3%

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

      2. associate-*l* 85.9%

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

      3. associate-/r/ 86.3%

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

      4. un-div-inv 86.7%

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

   7. Applied egg-rr 86.7%

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

   if -8.8e8 < x < 1.5e51

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0 80.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+32}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -880000000:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 6: 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* 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in x around inf 50.6%

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

6. Final simplification 50.6%

   \[\leadsto 100 \]
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 2024075 
(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)))