Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.3% → 99.7%

Time: 3.3s

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: 99.3% 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

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

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(Float64(x / Float64(x + y)) * 100.0)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. +-commutative 99.7%

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

   2. associate-*l/ 99.8%

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

   3. +-commutative 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+105} \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.1e+105) (not (<= y 3600000000000.0)))
   (* x (/ 100.0 y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.1e+105) || !(y <= 3600000000000.0)) {
		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 <= (-2.1d+105)) .or. (.not. (y <= 3600000000000.0d0))) 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 <= -2.1e+105) || !(y <= 3600000000000.0)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.1e+105) or not (y <= 3600000000000.0):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.1e+105) || !(y <= 3600000000000.0))
		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 <= -2.1e+105) || ~((y <= 3600000000000.0)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.1e+105], N[Not[LessEqual[y, 3600000000000.0]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e105 or 3.6e12 < y

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l/ 99.6%

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

      3. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 79.6%

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

      1. associate-*r/ 79.8%

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

      2. *-commutative 79.8%

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

      3. /-rgt-identity 79.8%

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

      4. associate-/l* 79.6%

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

      5. metadata-eval 79.6%

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

      6. associate-/l/ 79.6%

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

   6. Simplified 79.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]
   7. Step-by-step derivation

      1. clear-num 79.5%

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

      2. associate-/r/ 79.7%

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

      3. *-commutative 79.7%

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

      4. associate-/r* 79.8%

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

      5. metadata-eval 79.8%

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

   8. Applied egg-rr 79.8%

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

   if -2.1000000000000001e105 < y < 3.6e12

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l/ 99.9%

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

      3. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 81.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+105} \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 220000000000:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.2e+105)
   (* x (/ 100.0 y))
   (if (<= y 220000000000.0) 100.0 (/ (* x 100.0) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+105) {
		tmp = x * (100.0 / y);
	} else if (y <= 220000000000.0) {
		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 <= (-2.2d+105)) then
        tmp = x * (100.0d0 / y)
    else if (y <= 220000000000.0d0) 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 <= -2.2e+105) {
		tmp = x * (100.0 / y);
	} else if (y <= 220000000000.0) {
		tmp = 100.0;
	} else {
		tmp = (x * 100.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.2e+105:
		tmp = x * (100.0 / y)
	elif y <= 220000000000.0:
		tmp = 100.0
	else:
		tmp = (x * 100.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.2e+105)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (y <= 220000000000.0)
		tmp = 100.0;
	else
		tmp = Float64(Float64(x * 100.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.2e+105)
		tmp = x * (100.0 / y);
	elseif (y <= 220000000000.0)
		tmp = 100.0;
	else
		tmp = (x * 100.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.2e+105], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 220000000000.0], 100.0, N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000007e105

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l/ 99.7%

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

      3. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 80.2%

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

      1. associate-*r/ 80.3%

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

      2. *-commutative 80.3%

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

      3. /-rgt-identity 80.3%

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

      4. associate-/l* 80.2%

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

      5. metadata-eval 80.2%

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

      6. associate-/l/ 80.2%

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

   6. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]
   7. Step-by-step derivation

      1. clear-num 79.9%

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

      2. associate-/r/ 80.3%

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

      3. *-commutative 80.3%

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

      4. associate-/r* 80.4%

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

      5. metadata-eval 80.4%

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

   8. Applied egg-rr 80.4%

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

   if -2.20000000000000007e105 < y < 2.2e11

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l/ 99.9%

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

      3. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 81.0%

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

   if 2.2e11 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.6%

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

      3. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 79.0%

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

      1. associate-*r/ 79.3%

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

   6. Simplified 79.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 220000000000:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \]

Alternative 4: 51.7% 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 99.7%

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

   1. +-commutative 99.7%

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

   2. associate-*l/ 99.8%

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

   3. +-commutative 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 59.1%

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

5. Final simplification 59.1%

   \[\leadsto 100 \]

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 2023308 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

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