Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.6% → 99.3%

Time: 5.8s

Alternatives: 8

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: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Simplified 99.8%

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

   1. clear-num 99.7%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-67}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25e+24) (not (<= y 3.2e-67))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25e+24) || !(y <= 3.2e-67)) {
		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 <= (-1.25d+24)) .or. (.not. (y <= 3.2d-67))) 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 <= -1.25e+24) || !(y <= 3.2e-67)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.25e+24) or not (y <= 3.2e-67):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.25e+24) || !(y <= 3.2e-67))
		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 <= -1.25e+24) || ~((y <= 3.2e-67)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.25e+24], N[Not[LessEqual[y, 3.2e-67]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000011e24 or 3.20000000000000021e-67 < 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* 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 0 76.0%

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

   if -1.25000000000000011e24 < y < 3.20000000000000021e-67

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 77.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-67}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+23} \lor \neg \left(y \leq 5.2 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.4e+23) (not (<= y 5.2e-62))) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.4e+23) || !(y <= 5.2e-62)) {
		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 <= (-7.4d+23)) .or. (.not. (y <= 5.2d-62))) 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 <= -7.4e+23) || !(y <= 5.2e-62)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.4e+23) or not (y <= 5.2e-62):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.4e+23) || !(y <= 5.2e-62))
		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 <= -7.4e+23) || ~((y <= 5.2e-62)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.4e+23], N[Not[LessEqual[y, 5.2e-62]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -7.40000000000000025e23 or 5.1999999999999999e-62 < 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* 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. Step-by-step derivation

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-*l/ 76.1%

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

      3. associate-*r/ 76.1%

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

   9. Simplified 76.1%

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

   if -7.40000000000000025e23 < y < 5.1999999999999999e-62

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 77.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+23} \lor \neg \left(y \leq 5.2 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-63}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+23)
   (* x (/ 100.0 y))
   (if (<= y 9.8e-63) 100.0 (/ 100.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+23) {
		tmp = x * (100.0 / y);
	} else if (y <= 9.8e-63) {
		tmp = 100.0;
	} else {
		tmp = 100.0 / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.2d+23)) then
        tmp = x * (100.0d0 / y)
    else if (y <= 9.8d-63) then
        tmp = 100.0d0
    else
        tmp = 100.0d0 / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+23) {
		tmp = x * (100.0 / y);
	} else if (y <= 9.8e-63) {
		tmp = 100.0;
	} else {
		tmp = 100.0 / (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+23:
		tmp = x * (100.0 / y)
	elif y <= 9.8e-63:
		tmp = 100.0
	else:
		tmp = 100.0 / (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+23)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (y <= 9.8e-63)
		tmp = 100.0;
	else
		tmp = Float64(100.0 / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e+23)
		tmp = x * (100.0 / y);
	elseif (y <= 9.8e-63)
		tmp = 100.0;
	else
		tmp = 100.0 / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+23], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-63], 100.0, N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000003e23

   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. Step-by-step derivation

      1. clear-num 99.5%

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

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 79.1%

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

      3. associate-*r/ 79.1%

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

   9. Simplified 79.1%

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

   if -4.2000000000000003e23 < y < 9.8000000000000003e-63

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 77.6%

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

   if 9.8000000000000003e-63 < 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* 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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 73.8%

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

      1. associate-*r/ 73.7%

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

      2. metadata-eval 73.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{0.01}} \cdot x}{y} \]

      3. associate-/r/ 73.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{0.01}{x}}}}{y} \]

      4. associate-/r* 73.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{0.01}{x} \cdot y}} \]

      5. *-commutative 73.7%

         \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{0.01}{x}}} \]

      6. associate-*r/ 73.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{y \cdot 0.01}{x}}} \]

      7. *-commutative 73.7%

         \[\leadsto \frac{1}{\frac{\color{blue}{0.01 \cdot y}}{x}} \]

      8. associate-*r/ 73.7%

         \[\leadsto \frac{1}{\color{blue}{0.01 \cdot \frac{y}{x}}} \]

      9. associate-/r* 73.9%

         \[\leadsto \color{blue}{\frac{\frac{1}{0.01}}{\frac{y}{x}}} \]

      10. metadata-eval 73.9%

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

   9. Simplified 73.9%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-63}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.8e+23)
   (/ x (* y 0.01))
   (if (<= y 1.4e-61) 100.0 (/ 100.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.8e+23) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.4e-61) {
		tmp = 100.0;
	} else {
		tmp = 100.0 / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6.8d+23)) then
        tmp = x / (y * 0.01d0)
    else if (y <= 1.4d-61) then
        tmp = 100.0d0
    else
        tmp = 100.0d0 / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.8e+23) {
		tmp = x / (y * 0.01);
	} else if (y <= 1.4e-61) {
		tmp = 100.0;
	} else {
		tmp = 100.0 / (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.8e+23:
		tmp = x / (y * 0.01)
	elif y <= 1.4e-61:
		tmp = 100.0
	else:
		tmp = 100.0 / (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.8e+23)
		tmp = Float64(x / Float64(y * 0.01));
	elseif (y <= 1.4e-61)
		tmp = 100.0;
	else
		tmp = Float64(100.0 / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.8e+23)
		tmp = x / (y * 0.01);
	elseif (y <= 1.4e-61)
		tmp = 100.0;
	else
		tmp = 100.0 / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.8e+23], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-61], 100.0, N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.79999999999999983e23

   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. Taylor expanded in x around 0 78.9%

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

      1. associate-*r/ 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*r/ 79.1%

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

      4. metadata-eval 79.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{0.01}}}{y} \]

      5. associate-/r* 79.1%

         \[\leadsto x \cdot \color{blue}{\frac{1}{0.01 \cdot y}} \]

      6. *-commutative 79.1%

         \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot 0.01}} \]

      7. associate-*r/ 79.1%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{y \cdot 0.01}} \]

      8. *-rgt-identity 79.1%

         \[\leadsto \frac{\color{blue}{x}}{y \cdot 0.01} \]

   7. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]

   if -6.79999999999999983e23 < y < 1.4000000000000001e-61

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 77.6%

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

   if 1.4000000000000001e-61 < 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* 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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 73.8%

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

      1. associate-*r/ 73.7%

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

      2. metadata-eval 73.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{0.01}} \cdot x}{y} \]

      3. associate-/r/ 73.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{0.01}{x}}}}{y} \]

      4. associate-/r* 73.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{0.01}{x} \cdot y}} \]

      5. *-commutative 73.7%

         \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{0.01}{x}}} \]

      6. associate-*r/ 73.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{y \cdot 0.01}{x}}} \]

      7. *-commutative 73.7%

         \[\leadsto \frac{1}{\frac{\color{blue}{0.01 \cdot y}}{x}} \]

      8. associate-*r/ 73.7%

         \[\leadsto \frac{1}{\color{blue}{0.01 \cdot \frac{y}{x}}} \]

      9. associate-/r* 73.9%

         \[\leadsto \color{blue}{\frac{\frac{1}{0.01}}{\frac{y}{x}}} \]

      10. metadata-eval 73.9%

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

   9. Simplified 73.9%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.8% 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 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 7: 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 99.3%

   \[\frac{x \cdot 100}{x + y} \]
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 8: 51.0% 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 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf 51.4%

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

6. Final simplification 51.4%

   \[\leadsto 100 \]
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 2024115 
(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)))