Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 3.7s

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: 99.5% 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

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

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 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.0%

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

3. Simplified 99.0%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+81}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-65} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.35e+81)
   100.0
   (if (or (<= x -5e-65) (and (not (<= x -3.6e-145)) (<= x 6.2e-19)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.35e+81) {
		tmp = 100.0;
	} else if ((x <= -5e-65) || (!(x <= -3.6e-145) && (x <= 6.2e-19))) {
		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 <= (-2.35d+81)) then
        tmp = 100.0d0
    else if ((x <= (-5d-65)) .or. (.not. (x <= (-3.6d-145))) .and. (x <= 6.2d-19)) 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 <= -2.35e+81) {
		tmp = 100.0;
	} else if ((x <= -5e-65) || (!(x <= -3.6e-145) && (x <= 6.2e-19))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.35e+81:
		tmp = 100.0
	elif (x <= -5e-65) or (not (x <= -3.6e-145) and (x <= 6.2e-19)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.35e+81)
		tmp = 100.0;
	elseif ((x <= -5e-65) || (!(x <= -3.6e-145) && (x <= 6.2e-19)))
		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 <= -2.35e+81)
		tmp = 100.0;
	elseif ((x <= -5e-65) || (~((x <= -3.6e-145)) && (x <= 6.2e-19)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.35e+81], 100.0, If[Or[LessEqual[x, -5e-65], And[N[Not[LessEqual[x, -3.6e-145]], $MachinePrecision], LessEqual[x, 6.2e-19]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3500000000000001e81 or -4.99999999999999983e-65 < x < -3.6e-145 or 6.1999999999999998e-19 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 76.0%

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

   if -2.3500000000000001e81 < x < -4.99999999999999983e-65 or -3.6e-145 < x < 6.1999999999999998e-19

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around 0 82.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+81}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-65} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-67} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 4.4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+80)
   100.0
   (if (or (<= x -2.9e-67) (and (not (<= x -3.6e-145)) (<= x 4.4e-15)))
     (* x (/ 100.0 y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+80) {
		tmp = 100.0;
	} else if ((x <= -2.9e-67) || (!(x <= -3.6e-145) && (x <= 4.4e-15))) {
		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 <= (-9d+80)) then
        tmp = 100.0d0
    else if ((x <= (-2.9d-67)) .or. (.not. (x <= (-3.6d-145))) .and. (x <= 4.4d-15)) 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 <= -9e+80) {
		tmp = 100.0;
	} else if ((x <= -2.9e-67) || (!(x <= -3.6e-145) && (x <= 4.4e-15))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+80:
		tmp = 100.0
	elif (x <= -2.9e-67) or (not (x <= -3.6e-145) and (x <= 4.4e-15)):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+80)
		tmp = 100.0;
	elseif ((x <= -2.9e-67) || (!(x <= -3.6e-145) && (x <= 4.4e-15)))
		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 <= -9e+80)
		tmp = 100.0;
	elseif ((x <= -2.9e-67) || (~((x <= -3.6e-145)) && (x <= 4.4e-15)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+80], 100.0, If[Or[LessEqual[x, -2.9e-67], And[N[Not[LessEqual[x, -3.6e-145]], $MachinePrecision], LessEqual[x, 4.4e-15]]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000013e80 or -2.90000000000000005e-67 < x < -3.6e-145 or 4.39999999999999971e-15 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 76.0%

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

   if -9.00000000000000013e80 < x < -2.90000000000000005e-67 or -3.6e-145 < x < 4.39999999999999971e-15

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 82.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-67} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 4.4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-65} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+80)
   100.0
   (if (or (<= x -4.8e-65) (and (not (<= x -3.6e-145)) (<= x 2.5e-16)))
     (/ x (* y 0.01))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+80) {
		tmp = 100.0;
	} else if ((x <= -4.8e-65) || (!(x <= -3.6e-145) && (x <= 2.5e-16))) {
		tmp = x / (y * 0.01);
	} 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 <= (-9d+80)) then
        tmp = 100.0d0
    else if ((x <= (-4.8d-65)) .or. (.not. (x <= (-3.6d-145))) .and. (x <= 2.5d-16)) then
        tmp = x / (y * 0.01d0)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9e+80) {
		tmp = 100.0;
	} else if ((x <= -4.8e-65) || (!(x <= -3.6e-145) && (x <= 2.5e-16))) {
		tmp = x / (y * 0.01);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+80:
		tmp = 100.0
	elif (x <= -4.8e-65) or (not (x <= -3.6e-145) and (x <= 2.5e-16)):
		tmp = x / (y * 0.01)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+80)
		tmp = 100.0;
	elseif ((x <= -4.8e-65) || (!(x <= -3.6e-145) && (x <= 2.5e-16)))
		tmp = Float64(x / Float64(y * 0.01));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9e+80)
		tmp = 100.0;
	elseif ((x <= -4.8e-65) || (~((x <= -3.6e-145)) && (x <= 2.5e-16)))
		tmp = x / (y * 0.01);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+80], 100.0, If[Or[LessEqual[x, -4.8e-65], And[N[Not[LessEqual[x, -3.6e-145]], $MachinePrecision], LessEqual[x, 2.5e-16]]], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000013e80 or -4.8000000000000003e-65 < x < -3.6e-145 or 2.5000000000000002e-16 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 76.0%

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

   if -9.00000000000000013e80 < x < -4.8000000000000003e-65 or -3.6e-145 < x < 2.5000000000000002e-16

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 82.2%

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

      1. *-commutative 82.2%

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

   6. Simplified 82.2%

      \[\leadsto \frac{x}{\color{blue}{y \cdot 0.01}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-65} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5: 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 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.0%

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

3. Simplified 99.0%

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

4. Taylor expanded in x around inf 49.8%

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

5. Final simplification 49.8%

   \[\leadsto 100 \]

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 2023240 
(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)))