Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 4.4s

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

\[\begin{array}{l} \\ \frac{x}{\left(x + y\right) \cdot 0.01} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* (+ x y) 0.01)))

C

double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / ((x + y) * 0.01d0)
end function

Java

public static double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Python

def code(x, y):
	return x / ((x + y) * 0.01)

Julia

function code(x, y)
	return Float64(x / Float64(Float64(x + y) * 0.01))
end

MATLAB

function tmp = code(x, y)
	tmp = x / ((x + y) * 0.01);
end

Wolfram

code[x_, y_] := N[(x / N[(N[(x + y), $MachinePrecision] * 0.01), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 98.6%

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

3. Simplified 98.6%

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

   1. associate-/l* 99.4%

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

   2. *-commutative 99.4%

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

   3. expm1-log1p-u 98.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

   4. expm1-udef 64.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

   5. associate-/l* 64.5%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

   6. div-inv 64.5%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

   7. metadata-eval 64.5%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

6. Applied egg-rr 64.5%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot 0.01}\right)} - 1} \]
7. Step-by-step derivation

   1. expm1-def 98.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot 0.01}\right)\right)} \]

   2. expm1-log1p 99.7%

      \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

8. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

9. Final simplification 99.7%

   \[\leadsto \frac{x}{\left(x + y\right) \cdot 0.01} \]
10. Add Preprocessing

Alternative 2: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+15} \lor \neg \left(y \leq 3.8 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.5e+15) (not (<= y 3.8e+86))) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.5e+15) || !(y <= 3.8e+86)) {
		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 <= (-3.5d+15)) .or. (.not. (y <= 3.8d+86))) 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 <= -3.5e+15) || !(y <= 3.8e+86)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.5e+15) or not (y <= 3.8e+86):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.5e+15) || !(y <= 3.8e+86))
		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 <= -3.5e+15) || ~((y <= 3.8e+86)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.5e+15], N[Not[LessEqual[y, 3.8e+86]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e15 or 3.79999999999999978e86 < y

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0 84.1%

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

      1. associate-*r/ 84.4%

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

      2. associate-/l* 82.3%

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

      3. associate-/r/ 84.4%

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

   7. Simplified 84.4%

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

   if -3.5e15 < y < 3.79999999999999978e86

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 77.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+15} \lor \neg \left(y \leq 3.8 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+85}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.8e+15)
   (/ x (/ y 100.0))
   (if (<= y 5.4e+85) 100.0 (* x (/ 100.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.8e+15) {
		tmp = x / (y / 100.0);
	} else if (y <= 5.4e+85) {
		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 <= (-2.8d+15)) then
        tmp = x / (y / 100.0d0)
    else if (y <= 5.4d+85) 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 <= -2.8e+15) {
		tmp = x / (y / 100.0);
	} else if (y <= 5.4e+85) {
		tmp = 100.0;
	} else {
		tmp = x * (100.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.8e+15:
		tmp = x / (y / 100.0)
	elif y <= 5.4e+85:
		tmp = 100.0
	else:
		tmp = x * (100.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.8e+15)
		tmp = Float64(x / Float64(y / 100.0));
	elseif (y <= 5.4e+85)
		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 <= -2.8e+15)
		tmp = x / (y / 100.0);
	elseif (y <= 5.4e+85)
		tmp = 100.0;
	else
		tmp = x * (100.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.8e+15], N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+85], 100.0, N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e15

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-/r/ 78.3%

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

   7. Simplified 78.3%

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

   if -2.8e15 < y < 5.39999999999999966e85

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 77.6%

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

   if 5.39999999999999966e85 < y

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around 0 92.6%

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

      1. associate-*r/ 93.1%

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

      2. associate-/l* 89.6%

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

      3. associate-/r/ 93.2%

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

   7. Simplified 93.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+85}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 98.6%

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

3. Simplified 98.6%

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

5. Final simplification 98.6%

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

Alternative 5: 51.2% 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 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 98.6%

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

3. Simplified 98.6%

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

5. Taylor expanded in x around inf 50.8%

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

6. Final simplification 50.8%

   \[\leadsto 100 \]
7. Add Preprocessing

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 2024036 
(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)))