Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.8%

Time: 7.7s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

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. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 99.7

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

4. Applied rewrites 99.7%

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

5. Final simplification 99.7%

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

Alternative 2: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{100 \cdot x}{x + y} \leq 1:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-100}{x}, 100\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (* 100.0 x) (+ x y)) 1.0)
   (/ (* 100.0 x) y)
   (fma y (/ -100.0 x) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (((100.0 * x) / (x + y)) <= 1.0) {
		tmp = (100.0 * x) / y;
	} else {
		tmp = fma(y, (-100.0 / x), 100.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(100.0 * x) / Float64(x + y)) <= 1.0)
		tmp = Float64(Float64(100.0 * x) / y);
	else
		tmp = fma(y, Float64(-100.0 / x), 100.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(100.0 * x), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], 1.0], N[(N[(100.0 * x), $MachinePrecision] / y), $MachinePrecision], N[(y * N[(-100.0 / x), $MachinePrecision] + 100.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y)) < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 1 < (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{neg}\left(\frac{\color{blue}{100}}{x}\right), 100\right) \]

      12. distribute-neg-frac N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\mathsf{neg}\left(100\right)}{x}}, 100\right) \]

      13. metadata-eval N/A

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

      14. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{-100}{x}, 100\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{100 \cdot x}{x + y} \leq 1:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-100}{x}, 100\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{100 \cdot x}{x + y} \leq 1:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (* 100.0 x) (+ x y)) 1.0) (/ (* 100.0 x) y) 100.0))

C

double code(double x, double y) {
	double tmp;
	if (((100.0 * x) / (x + y)) <= 1.0) {
		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 (((100.0d0 * x) / (x + y)) <= 1.0d0) 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 (((100.0 * x) / (x + y)) <= 1.0) {
		tmp = (100.0 * x) / y;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((100.0 * x) / (x + y)) <= 1.0:
		tmp = (100.0 * x) / y
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(100.0 * x) / Float64(x + y)) <= 1.0)
		tmp = Float64(Float64(100.0 * x) / y);
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((100.0 * x) / (x + y)) <= 1.0)
		tmp = (100.0 * x) / y;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(100.0 * x), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], 1.0], N[(N[(100.0 * x), $MachinePrecision] / y), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y)) < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 1 < (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{100 \cdot x}{x + y} \leq 1:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 20.0× 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. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Applied rewrites 49.0%

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

Developer Target 1: 99.8% accurate, 0.6× 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 2024233 
(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)))