Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 5.4s

Alternatives: 7

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

   5. +-lowering-+.f64 99.7%

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 99.7%

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

   1. associate-*r/ N/A

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

   2. *-commutative N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{x + y}{100}\right)}\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(x + y\right), \color{blue}{100}\right)\right) \]

   8. +-lowering-+.f64 99.8%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), 100\right)\right) \]

6. Applied egg-rr 99.8%

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

Alternative 2: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+115}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.1e-13)
   (/ (* x 100.0) y)
   (if (<= y 9e+115) 100.0 (/ x (* y 0.01)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.1e-13) {
		tmp = (x * 100.0) / y;
	} else if (y <= 9e+115) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.1d-13)) then
        tmp = (x * 100.0d0) / y
    else if (y <= 9d+115) then
        tmp = 100.0d0
    else
        tmp = x / (y * 0.01d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.1e-13) {
		tmp = (x * 100.0) / y;
	} else if (y <= 9e+115) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.1e-13:
		tmp = (x * 100.0) / y
	elif y <= 9e+115:
		tmp = 100.0
	else:
		tmp = x / (y * 0.01)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.1e-13)
		tmp = Float64(Float64(x * 100.0) / y);
	elseif (y <= 9e+115)
		tmp = 100.0;
	else
		tmp = Float64(x / Float64(y * 0.01));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.1e-13)
		tmp = (x * 100.0) / y;
	elseif (y <= 9e+115)
		tmp = 100.0;
	else
		tmp = x / (y * 0.01);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.1e-13], N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 9e+115], 100.0, N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0999999999999999e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 100\right), \color{blue}{y}\right) \]
   4. Step-by-step derivation

   5. Simplified 86.1%

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

   if -3.0999999999999999e-13 < y < 8.99999999999999927e115

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 79.4%

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

   if 8.99999999999999927e115 < y

   1. Initial program 99.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.6%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.6%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{x + y}{100}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(x + y\right), \color{blue}{100}\right)\right) \]

      8. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), 100\right)\right) \]

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{100} \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\frac{1}{100}}\right)\right) \]

      2. *-lowering-*.f64 88.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{1}{100}}\right)\right) \]

   9. Simplified 88.9%

      \[\leadsto \frac{x}{\color{blue}{y \cdot 0.01}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 0.01}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+115}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 0.01))))
   (if (<= y -3.3e-15) t_0 (if (<= y 9e+115) 100.0 t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 0.01);
	double tmp;
	if (y <= -3.3e-15) {
		tmp = t_0;
	} else if (y <= 9e+115) {
		tmp = 100.0;
	} else {
		tmp = t_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 / (y * 0.01d0)
    if (y <= (-3.3d-15)) then
        tmp = t_0
    else if (y <= 9d+115) then
        tmp = 100.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 0.01);
	double tmp;
	if (y <= -3.3e-15) {
		tmp = t_0;
	} else if (y <= 9e+115) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * 0.01)
	tmp = 0
	if y <= -3.3e-15:
		tmp = t_0
	elif y <= 9e+115:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 0.01))
	tmp = 0.0
	if (y <= -3.3e-15)
		tmp = t_0;
	elseif (y <= 9e+115)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * 0.01);
	tmp = 0.0;
	if (y <= -3.3e-15)
		tmp = t_0;
	elseif (y <= 9e+115)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-15], t$95$0, If[LessEqual[y, 9e+115], 100.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e-15 or 8.99999999999999927e115 < y

   1. Initial program 99.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.6%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.6%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{x + y}{100}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(x + y\right), \color{blue}{100}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), 100\right)\right) \]

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{100} \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\frac{1}{100}}\right)\right) \]

      2. *-lowering-*.f64 87.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{1}{100}}\right)\right) \]

   9. Simplified 87.0%

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

   if -3.3e-15 < y < 8.99999999999999927e115

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 79.4%

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

Alternative 4: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+115}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 100.0 y))))
   (if (<= y -1.35e-14) t_0 (if (<= y 9e+115) 100.0 t_0))))

C

double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -1.35e-14) {
		tmp = t_0;
	} else if (y <= 9e+115) {
		tmp = 100.0;
	} else {
		tmp = t_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 <= (-1.35d-14)) then
        tmp = t_0
    else if (y <= 9d+115) then
        tmp = 100.0d0
    else
        tmp = t_0
    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 <= -1.35e-14) {
		tmp = t_0;
	} else if (y <= 9e+115) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (100.0 / y)
	tmp = 0
	if y <= -1.35e-14:
		tmp = t_0
	elif y <= 9e+115:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(100.0 / y))
	tmp = 0.0
	if (y <= -1.35e-14)
		tmp = t_0;
	elseif (y <= 9e+115)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (100.0 / y);
	tmp = 0.0;
	if (y <= -1.35e-14)
		tmp = t_0;
	elseif (y <= 9e+115)
		tmp = 100.0;
	else
		tmp = t_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, -1.35e-14], t$95$0, If[LessEqual[y, 9e+115], 100.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3499999999999999e-14 or 8.99999999999999927e115 < y

   1. Initial program 99.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.6%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      2. /-lowering-/.f64 86.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 86.9%

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{100}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 86.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(100, y\right), x\right) \]

   9. Applied egg-rr 86.9%

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

   if -1.3499999999999999e-14 < y < 8.99999999999999927e115

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 79.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+115}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+116}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ x y))))
   (if (<= y -1.02e-13) t_0 (if (<= y 1.42e+116) 100.0 t_0))))

C

double code(double x, double y) {
	double t_0 = 100.0 * (x / y);
	double tmp;
	if (y <= -1.02e-13) {
		tmp = t_0;
	} else if (y <= 1.42e+116) {
		tmp = 100.0;
	} else {
		tmp = t_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 = 100.0d0 * (x / y)
    if (y <= (-1.02d-13)) then
        tmp = t_0
    else if (y <= 1.42d+116) then
        tmp = 100.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 100.0 * (x / y);
	double tmp;
	if (y <= -1.02e-13) {
		tmp = t_0;
	} else if (y <= 1.42e+116) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 100.0 * (x / y)
	tmp = 0
	if y <= -1.02e-13:
		tmp = t_0
	elif y <= 1.42e+116:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(100.0 * Float64(x / y))
	tmp = 0.0
	if (y <= -1.02e-13)
		tmp = t_0;
	elseif (y <= 1.42e+116)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 100.0 * (x / y);
	tmp = 0.0;
	if (y <= -1.02e-13)
		tmp = t_0;
	elseif (y <= 1.42e+116)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e-13], t$95$0, If[LessEqual[y, 1.42e+116], 100.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0199999999999999e-13 or 1.4199999999999999e116 < y

   1. Initial program 99.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.6%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      2. /-lowering-/.f64 86.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 86.9%

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

   if -1.0199999999999999e-13 < y < 1.4199999999999999e116

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 79.4%

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

Alternative 6: 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 99.8%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

   5. +-lowering-+.f64 99.7%

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 99.7%

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

Alternative 7: 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 99.8%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

   5. +-lowering-+.f64 99.7%

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 99.7%

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

5. Taylor expanded in x around inf

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

7. Simplified 49.4%

   \[\leadsto \color{blue}{100} \]
8. Add Preprocessing

Developer Target 1: 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 2024155 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (* (/ x 1) (/ 100 (+ x y))))

  (/ (* x 100.0) (+ x y)))