Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.4%

Time: 3.0s

Alternatives: 7

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: 99.4% 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]

Derivation

1. Initial program 99.8%

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

Alternative 2: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+30} \lor \neg \left(y \leq 29500\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3e+30) (not (<= y 29500.0))) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3e+30) || !(y <= 29500.0)) {
		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 <= (-3d+30)) .or. (.not. (y <= 29500.0d0))) 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 <= -3e+30) || !(y <= 29500.0)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3e+30) or not (y <= 29500.0):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3e+30) || !(y <= 29500.0))
		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 <= -3e+30) || ~((y <= 29500.0)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3e+30], N[Not[LessEqual[y, 29500.0]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999978e30 or 29500 < 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* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 76.7%

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

      1. associate-*r/ 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r/ 77.1%

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

   7. Simplified 77.1%

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

   if -2.99999999999999978e30 < y < 29500

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 78.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+30} \lor \neg \left(y \leq 29500\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+30} \lor \neg \left(y \leq 720000\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3e+30) (not (<= y 720000.0))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3e+30) || !(y <= 720000.0)) {
		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 ((y <= (-3d+30)) .or. (.not. (y <= 720000.0d0))) 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 ((y <= -3e+30) || !(y <= 720000.0)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3e+30) or not (y <= 720000.0):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3e+30) || !(y <= 720000.0))
		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 <= -3e+30) || ~((y <= 720000.0)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3e+30], N[Not[LessEqual[y, 720000.0]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999978e30 or 7.2e5 < 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* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 76.7%

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

   if -2.99999999999999978e30 < y < 7.2e5

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 78.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+30} \lor \neg \left(y \leq 720000\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.1e+30)
   (* x (/ 100.0 y))
   (if (<= y 2.0) 100.0 (/ (* x 100.0) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.1e+30) {
		tmp = x * (100.0 / y);
	} else if (y <= 2.0) {
		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 <= (-3.1d+30)) then
        tmp = x * (100.0d0 / y)
    else if (y <= 2.0d0) 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 <= -3.1e+30) {
		tmp = x * (100.0 / y);
	} else if (y <= 2.0) {
		tmp = 100.0;
	} else {
		tmp = (x * 100.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.1e+30:
		tmp = x * (100.0 / y)
	elif y <= 2.0:
		tmp = 100.0
	else:
		tmp = (x * 100.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.1e+30)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (y <= 2.0)
		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 <= -3.1e+30)
		tmp = x * (100.0 / y);
	elseif (y <= 2.0)
		tmp = 100.0;
	else
		tmp = (x * 100.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.1e+30], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.0], 100.0, N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0999999999999998e30

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 80.2%

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

      1. associate-*r/ 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-*r/ 80.5%

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

   7. Simplified 80.5%

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

   if -3.0999999999999998e30 < y < 2

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 78.9%

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

   if 2 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.9%

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

Alternative 5: 99.7% 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 99.8%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

4. Applied egg-rr 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 6: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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* 99.6%

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

3. Simplified 99.6%

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

Alternative 7: 50.7% 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 99.8%

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

   1. *-commutative 99.8%

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

   2. associate-/l* 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 50.6%

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

Developer Target 1: 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 2024121 
(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)))