Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.8%

Time: 5.8s

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: 99.8% 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 99.0%

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

   1. associate-/l* 99.8%

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

   2. *-commutative 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-37} \lor \neg \left(y \leq 4 \cdot 10^{-32}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.8e-37) (not (<= y 4e-32))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.8e-37) || !(y <= 4e-32)) {
		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 ((y <= (-3.8d-37)) .or. (.not. (y <= 4d-32))) 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 ((y <= -3.8e-37) || !(y <= 4e-32)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.8e-37) or not (y <= 4e-32):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.8e-37) || !(y <= 4e-32))
		tmp = Float64(100.0 * Float64(x / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.8e-37) || ~((y <= 4e-32)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.8e-37], N[Not[LessEqual[y, 4e-32]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000004e-37 or 4.00000000000000022e-32 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 75.5%

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

   if -3.8000000000000004e-37 < y < 4.00000000000000022e-32

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 79.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-37} \lor \neg \left(y \leq 4 \cdot 10^{-32}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-37} \lor \neg \left(y \leq 4.2 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.6e-37) (not (<= y 4.2e-33))) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.6e-37) || !(y <= 4.2e-33)) {
		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 <= (-5.6d-37)) .or. (.not. (y <= 4.2d-33))) 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 <= -5.6e-37) || !(y <= 4.2e-33)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.6e-37) or not (y <= 4.2e-33):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.6e-37) || !(y <= 4.2e-33))
		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 <= -5.6e-37) || ~((y <= 4.2e-33)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.6e-37], N[Not[LessEqual[y, 4.2e-33]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000002e-37 or 4.2e-33 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

   if -5.6000000000000002e-37 < y < 4.2e-33

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 79.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-37} \lor \neg \left(y \leq 4.2 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-32}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.7e-37)
   (* x (/ 100.0 y))
   (if (<= y 2e-32) 100.0 (/ x (* y 0.01)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.7e-37) {
		tmp = x * (100.0 / y);
	} else if (y <= 2e-32) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.7d-37)) then
        tmp = x * (100.0d0 / y)
    else if (y <= 2d-32) then
        tmp = 100.0d0
    else
        tmp = x / (y * 0.01d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.7e-37) {
		tmp = x * (100.0 / y);
	} else if (y <= 2e-32) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.7e-37:
		tmp = x * (100.0 / y)
	elif y <= 2e-32:
		tmp = 100.0
	else:
		tmp = x / (y * 0.01)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.7e-37)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (y <= 2e-32)
		tmp = 100.0;
	else
		tmp = Float64(x / Float64(y * 0.01));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.7e-37)
		tmp = x * (100.0 / y);
	elseif (y <= 2e-32)
		tmp = 100.0;
	else
		tmp = x / (y * 0.01);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.7e-37], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-32], 100.0, N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e-37

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 77.2%

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

      1. associate-*r/ 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-/l* 77.5%

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

   5. Simplified 77.5%

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

   if -3.7e-37 < y < 2.00000000000000011e-32

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 79.0%

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

   if 2.00000000000000011e-32 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

      1. add0 74.1%

         \[\leadsto \color{blue}{x \cdot \frac{100}{y} + 0} \]

      2. clear-num 74.0%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{100}}} + 0 \]

      3. un-div-inv 74.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} + 0 \]

      4. div-inv 74.1%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{100}}} + 0 \]

      5. metadata-eval 74.1%

         \[\leadsto \frac{x}{y \cdot \color{blue}{0.01}} + 0 \]

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01} + 0} \]
   8. Step-by-step derivation

      1. add0 74.1%

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

   9. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 0.01}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-32}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.5% 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 99.0%

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

3. Taylor expanded in x around inf 48.1%

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

4. Final simplification 48.1%

   \[\leadsto 100 \]
5. Add Preprocessing

Developer target: 99.8% 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 2024046 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :alt
  (* (/ x 1.0) (/ 100.0 (+ x y)))

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