Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 5.0s

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: 99.5% 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

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

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 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 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-105}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1e+17)
   (/ x (/ y 100.0))
   (if (<= y 3.1e-105) 100.0 (* x (/ 100.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1e+17) {
		tmp = x / (y / 100.0);
	} else if (y <= 3.1e-105) {
		tmp = 100.0;
	} else {
		tmp = x * (100.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1d+17)) then
        tmp = x / (y / 100.0d0)
    else if (y <= 3.1d-105) then
        tmp = 100.0d0
    else
        tmp = x * (100.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1e+17) {
		tmp = x / (y / 100.0);
	} else if (y <= 3.1e-105) {
		tmp = 100.0;
	} else {
		tmp = x * (100.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1e+17:
		tmp = x / (y / 100.0)
	elif y <= 3.1e-105:
		tmp = 100.0
	else:
		tmp = x * (100.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1e+17)
		tmp = Float64(x / Float64(y / 100.0));
	elseif (y <= 3.1e-105)
		tmp = 100.0;
	else
		tmp = Float64(x * Float64(100.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1e+17)
		tmp = x / (y / 100.0);
	elseif (y <= 3.1e-105)
		tmp = 100.0;
	else
		tmp = x * (100.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1e+17], N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-105], 100.0, N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e17

   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 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{x + y}} \]
   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 82.7%

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

   7. Simplified 82.7%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

      7. /-lowering-/.f64 82.8%

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

   9. Applied egg-rr 82.8%

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

   if -1e17 < y < 3.10000000000000014e-105

   1. Initial program 98.8%

      \[\frac{x \cdot 100}{x + y} \]
   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 99.9%

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

   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 83.4%

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

   if 3.10000000000000014e-105 < y

   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 99.6%

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

   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 70.0%

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

   7. Simplified 70.0%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   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 70.1%

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

   9. Applied egg-rr 70.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-105}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-105}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 100.0 y))))
   (if (<= y -6.4e+18) t_0 (if (<= y 4.2e-105) 100.0 t_0))))

C

double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -6.4e+18) {
		tmp = t_0;
	} else if (y <= 4.2e-105) {
		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 <= (-6.4d+18)) then
        tmp = t_0
    else if (y <= 4.2d-105) 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 <= -6.4e+18) {
		tmp = t_0;
	} else if (y <= 4.2e-105) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (100.0 / y)
	tmp = 0
	if y <= -6.4e+18:
		tmp = t_0
	elif y <= 4.2e-105:
		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 <= -6.4e+18)
		tmp = t_0;
	elseif (y <= 4.2e-105)
		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 <= -6.4e+18)
		tmp = t_0;
	elseif (y <= 4.2e-105)
		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, -6.4e+18], t$95$0, If[LessEqual[y, 4.2e-105], 100.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e18 or 4.2e-105 < y

   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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 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 74.5%

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

   7. Simplified 74.5%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   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 74.7%

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

   9. Applied egg-rr 74.7%

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

   if -6.4e18 < y < 4.2e-105

   1. Initial program 98.8%

      \[\frac{x \cdot 100}{x + y} \]
   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 99.9%

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

   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 83.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-105}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-105}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ x y))))
   (if (<= y -2.65e+17) t_0 (if (<= y 4.2e-105) 100.0 t_0))))

C

double code(double x, double y) {
	double t_0 = 100.0 * (x / y);
	double tmp;
	if (y <= -2.65e+17) {
		tmp = t_0;
	} else if (y <= 4.2e-105) {
		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 <= (-2.65d+17)) then
        tmp = t_0
    else if (y <= 4.2d-105) 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 <= -2.65e+17) {
		tmp = t_0;
	} else if (y <= 4.2e-105) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 100.0 * (x / y)
	tmp = 0
	if y <= -2.65e+17:
		tmp = t_0
	elif y <= 4.2e-105:
		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 <= -2.65e+17)
		tmp = t_0;
	elseif (y <= 4.2e-105)
		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 <= -2.65e+17)
		tmp = t_0;
	elseif (y <= 4.2e-105)
		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, -2.65e+17], t$95$0, If[LessEqual[y, 4.2e-105], 100.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65e17 or 4.2e-105 < y

   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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 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 74.5%

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

   7. Simplified 74.5%

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

   if -2.65e17 < y < 4.2e-105

   1. Initial program 98.8%

      \[\frac{x \cdot 100}{x + y} \]
   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 99.9%

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

   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 83.4%

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

Alternative 5: 51.3% 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 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 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf

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

7. Simplified 50.0%

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

Developer Target 1: 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 2024138 
(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)))