Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 4.6s

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: 99.5% 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

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

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 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.7%

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

3. Simplified 99.7%

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

Alternative 2: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-10}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+26}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.8e-10)
   100.0
   (if (<= x 1.4e-62)
     (* x (/ 100.0 y))
     (if (<= x 2e+26) 100.0 (if (<= x 7.8e+43) (/ 100.0 (/ y x)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-10) {
		tmp = 100.0;
	} else if (x <= 1.4e-62) {
		tmp = x * (100.0 / y);
	} else if (x <= 2e+26) {
		tmp = 100.0;
	} else if (x <= 7.8e+43) {
		tmp = 100.0 / (y / x);
	} 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 <= (-6.8d-10)) then
        tmp = 100.0d0
    else if (x <= 1.4d-62) then
        tmp = x * (100.0d0 / y)
    else if (x <= 2d+26) then
        tmp = 100.0d0
    else if (x <= 7.8d+43) then
        tmp = 100.0d0 / (y / x)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-10) {
		tmp = 100.0;
	} else if (x <= 1.4e-62) {
		tmp = x * (100.0 / y);
	} else if (x <= 2e+26) {
		tmp = 100.0;
	} else if (x <= 7.8e+43) {
		tmp = 100.0 / (y / x);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.8e-10:
		tmp = 100.0
	elif x <= 1.4e-62:
		tmp = x * (100.0 / y)
	elif x <= 2e+26:
		tmp = 100.0
	elif x <= 7.8e+43:
		tmp = 100.0 / (y / x)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.8e-10)
		tmp = 100.0;
	elseif (x <= 1.4e-62)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (x <= 2e+26)
		tmp = 100.0;
	elseif (x <= 7.8e+43)
		tmp = Float64(100.0 / Float64(y / x));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.8e-10)
		tmp = 100.0;
	elseif (x <= 1.4e-62)
		tmp = x * (100.0 / y);
	elseif (x <= 2e+26)
		tmp = 100.0;
	elseif (x <= 7.8e+43)
		tmp = 100.0 / (y / x);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.8e-10], 100.0, If[LessEqual[x, 1.4e-62], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+26], 100.0, If[LessEqual[x, 7.8e+43], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8000000000000003e-10 or 1.40000000000000001e-62 < x < 2.0000000000000001e26 or 7.8000000000000001e43 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 77.9%

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

   if -6.8000000000000003e-10 < x < 1.40000000000000001e-62

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r/ 77.6%

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

   5. Simplified 77.6%

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

   if 2.0000000000000001e26 < x < 7.8000000000000001e43

   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* 99.1%

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

   3. Simplified 99.1%

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

      1. clear-num 99.1%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0 99.7%

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

Alternative 3: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-11}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+26}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+42}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e-11)
   100.0
   (if (<= x 1.65e-62)
     (* x (/ 100.0 y))
     (if (<= x 1.05e+26) 100.0 (if (<= x 6.8e+42) (* 100.0 (/ x y)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e-11) {
		tmp = 100.0;
	} else if (x <= 1.65e-62) {
		tmp = x * (100.0 / y);
	} else if (x <= 1.05e+26) {
		tmp = 100.0;
	} else if (x <= 6.8e+42) {
		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 (x <= (-5d-11)) then
        tmp = 100.0d0
    else if (x <= 1.65d-62) then
        tmp = x * (100.0d0 / y)
    else if (x <= 1.05d+26) then
        tmp = 100.0d0
    else if (x <= 6.8d+42) 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 (x <= -5e-11) {
		tmp = 100.0;
	} else if (x <= 1.65e-62) {
		tmp = x * (100.0 / y);
	} else if (x <= 1.05e+26) {
		tmp = 100.0;
	} else if (x <= 6.8e+42) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e-11:
		tmp = 100.0
	elif x <= 1.65e-62:
		tmp = x * (100.0 / y)
	elif x <= 1.05e+26:
		tmp = 100.0
	elif x <= 6.8e+42:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e-11)
		tmp = 100.0;
	elseif (x <= 1.65e-62)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (x <= 1.05e+26)
		tmp = 100.0;
	elseif (x <= 6.8e+42)
		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 (x <= -5e-11)
		tmp = 100.0;
	elseif (x <= 1.65e-62)
		tmp = x * (100.0 / y);
	elseif (x <= 1.05e+26)
		tmp = 100.0;
	elseif (x <= 6.8e+42)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e-11], 100.0, If[LessEqual[x, 1.65e-62], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+26], 100.0, If[LessEqual[x, 6.8e+42], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.00000000000000018e-11 or 1.65000000000000002e-62 < x < 1.05e26 or 6.7999999999999995e42 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 77.9%

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

   if -5.00000000000000018e-11 < x < 1.65000000000000002e-62

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r/ 77.6%

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

   5. Simplified 77.6%

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

   if 1.05e26 < x < 6.7999999999999995e42

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.1%

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

Alternative 4: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-11}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-53}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e-11) 100.0 (if (<= x 5.8e-53) (* 100.0 (/ x y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e-11) {
		tmp = 100.0;
	} else if (x <= 5.8e-53) {
		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 (x <= (-7d-11)) then
        tmp = 100.0d0
    else if (x <= 5.8d-53) 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 (x <= -7e-11) {
		tmp = 100.0;
	} else if (x <= 5.8e-53) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e-11:
		tmp = 100.0
	elif x <= 5.8e-53:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e-11)
		tmp = 100.0;
	elseif (x <= 5.8e-53)
		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 (x <= -7e-11)
		tmp = 100.0;
	elseif (x <= 5.8e-53)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e-11], 100.0, If[LessEqual[x, 5.8e-53], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -7.00000000000000038e-11 or 5.7999999999999996e-53 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 75.5%

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

   if -7.00000000000000038e-11 < x < 5.7999999999999996e-53

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 77.1%

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

Alternative 5: 49.9% 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. Add Preprocessing

3. Taylor expanded in x around inf 50.6%

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

Alternative 6: 2.7% 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. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 79.9%

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

   2. sqrt-unprod 75.9%

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

   3. associate-*l/ 75.8%

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

   4. associate-*l/ 75.9%

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

   5. swap-sqr 75.9%

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

   6. pow2 75.9%

      \[\leadsto \sqrt{\color{blue}{{\left(\frac{x}{x + y}\right)}^{2}} \cdot \left(100 \cdot 100\right)} \]

   7. metadata-eval 75.9%

      \[\leadsto \sqrt{{\left(\frac{x}{x + y}\right)}^{2} \cdot \color{blue}{10000}} \]

4. Applied egg-rr 75.9%

   \[\leadsto \color{blue}{\sqrt{{\left(\frac{x}{x + y}\right)}^{2} \cdot 10000}} \]

5. Taylor expanded in x around -inf 2.7%

   \[\leadsto \color{blue}{-100} \]
6. 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 2024111 
(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)))