Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 3.6s

Alternatives: 6

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

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.7e+52) 100.0 (if (<= x 1.76e-22) (* x (/ 100.0 y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.7e+52) {
		tmp = 100.0;
	} else if (x <= 1.76e-22) {
		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 (x <= (-3.7d+52)) then
        tmp = 100.0d0
    else if (x <= 1.76d-22) 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 (x <= -3.7e+52) {
		tmp = 100.0;
	} else if (x <= 1.76e-22) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.7e+52:
		tmp = 100.0
	elif x <= 1.76e-22:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.7e+52)
		tmp = 100.0;
	elseif (x <= 1.76e-22)
		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 (x <= -3.7e+52)
		tmp = 100.0;
	elseif (x <= 1.76e-22)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.7e+52], 100.0, If[LessEqual[x, 1.76e-22], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7e52 or 1.76e-22 < x

   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/ 99.9%

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

      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 84.0%

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

   if -3.7e52 < x < 1.76e-22

   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 81.5%

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

      1. associate-*r/ 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-/l* 81.8%

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

   6. Simplified 81.8%

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

      1. div-inv 81.7%

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

      2. clear-num 81.8%

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

      3. *-commutative 81.8%

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

   8. Applied egg-rr 81.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.4e+52) 100.0 (if (<= x 1.76e-22) (/ x (/ y 100.0)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.4e+52) {
		tmp = 100.0;
	} else if (x <= 1.76e-22) {
		tmp = x / (y / 100.0);
	} 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 <= (-4.4d+52)) then
        tmp = 100.0d0
    else if (x <= 1.76d-22) then
        tmp = x / (y / 100.0d0)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.4e+52) {
		tmp = 100.0;
	} else if (x <= 1.76e-22) {
		tmp = x / (y / 100.0);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.4e+52:
		tmp = 100.0
	elif x <= 1.76e-22:
		tmp = x / (y / 100.0)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.4e+52)
		tmp = 100.0;
	elseif (x <= 1.76e-22)
		tmp = Float64(x / Float64(y / 100.0));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.4e+52)
		tmp = 100.0;
	elseif (x <= 1.76e-22)
		tmp = x / (y / 100.0);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.4e+52], 100.0, If[LessEqual[x, 1.76e-22], N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4e52 or 1.76e-22 < x

   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/ 99.9%

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

      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 84.0%

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

   if -4.4e52 < x < 1.76e-22

   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 81.5%

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

      1. associate-*r/ 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-/l* 81.8%

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

   6. Simplified 81.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.5e+52) 100.0 (if (<= x 1.76e-22) (/ (* x 100.0) y) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.5e+52) {
		tmp = 100.0;
	} else if (x <= 1.76e-22) {
		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 (x <= (-6.5d+52)) then
        tmp = 100.0d0
    else if (x <= 1.76d-22) 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 (x <= -6.5e+52) {
		tmp = 100.0;
	} else if (x <= 1.76e-22) {
		tmp = (x * 100.0) / y;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.5e+52:
		tmp = 100.0
	elif x <= 1.76e-22:
		tmp = (x * 100.0) / y
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.5e+52)
		tmp = 100.0;
	elseif (x <= 1.76e-22)
		tmp = Float64(Float64(x * 100.0) / y);
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.5e+52)
		tmp = 100.0;
	elseif (x <= 1.76e-22)
		tmp = (x * 100.0) / y;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.5e+52], 100.0, If[LessEqual[x, 1.76e-22], N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999996e52 or 1.76e-22 < x

   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/ 99.9%

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

      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 84.0%

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

   if -6.49999999999999996e52 < x < 1.76e-22

   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 81.5%

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

      1. associate-*r/ 81.8%

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

   6. Simplified 81.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5: 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%

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

   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. Final simplification 99.7%

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

Alternative 6: 50.5% 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 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-*l/ 99.7%

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

   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 inf 48.7%

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

5. Final simplification 48.7%

   \[\leadsto 100 \]

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 2023320 
(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)))