Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 6.3s

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: 99.4% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

3. Taylor expanded in x around inf

   \[\leadsto \frac{x \cdot 100}{\color{blue}{x \cdot \left(1 + \frac{y}{x}\right)}} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. distribute-rgt-in N/A

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

   3. *-lft-identity N/A

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

   4. lower-fma.f64 N/A

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

   5. lower-/.f64 99.1

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

5. Applied rewrites 99.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 99.6

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

7. Applied rewrites 99.6%

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

9. Applied rewrites 99.8%

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

Alternative 2: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot 100}{x + y} \leq 0.1:\\ \;\;\;\;\frac{100}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, -100, 100\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (* x 100.0) (+ x y)) 0.1)
   (* (/ 100.0 y) x)
   (fma (/ y x) -100.0 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (((x * 100.0) / (x + y)) <= 0.1) {
		tmp = (100.0 / y) * x;
	} else {
		tmp = fma((y / x), -100.0, 100.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x * 100.0) / Float64(x + y)) <= 0.1)
		tmp = Float64(Float64(100.0 / y) * x);
	else
		tmp = fma(Float64(y / x), -100.0, 100.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], 0.1], N[(N[(100.0 / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * -100.0 + 100.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y)) < 0.10000000000000001

   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. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 95.2

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

   5. Applied rewrites 95.2%

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

   if 0.10000000000000001 < (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y))

   1. Initial program 99.0%

      \[\frac{x \cdot 100}{x + y} \]
   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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 99.1

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

   5. Applied rewrites 99.1%

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

Alternative 3: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot 100}{x + y} \leq 0.1:\\ \;\;\;\;\frac{100}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (* x 100.0) (+ x y)) 0.1) (* (/ 100.0 y) x) 100.0))

C

double code(double x, double y) {
	double tmp;
	if (((x * 100.0) / (x + y)) <= 0.1) {
		tmp = (100.0 / y) * x;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x * 100.0d0) / (x + y)) <= 0.1d0) then
        tmp = (100.0d0 / y) * x
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x * 100.0) / (x + y)) <= 0.1) {
		tmp = (100.0 / y) * x;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x * 100.0) / (x + y)) <= 0.1:
		tmp = (100.0 / y) * x
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x * 100.0) / Float64(x + y)) <= 0.1)
		tmp = Float64(Float64(100.0 / y) * x);
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x * 100.0) / (x + y)) <= 0.1)
		tmp = (100.0 / y) * x;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], 0.1], N[(N[(100.0 / y), $MachinePrecision] * x), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y)) < 0.10000000000000001

   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. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 95.2

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

   5. Applied rewrites 95.2%

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

   if 0.10000000000000001 < (/.f64 (*.f64 x #s(literal 100 binary64)) (+.f64 x y))

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 97.9%

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

Alternative 4: 50.9% 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 99.3%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 54.0%

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

Alternative 5: 2.7% 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 99.3%

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

4. Applied rewrites 45.0%

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

5. Taylor expanded in x around inf

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

7. Applied rewrites 2.9%

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

Developer Target 1: 99.7% 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 2024320 
(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)))