Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 3.8s

Alternatives: 4

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

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

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 99.4%

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

   1. +-commutative 99.4%

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

   2. associate-*r/ 99.8%

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

   3. +-commutative 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+135}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.12e+135) 100.0 (if (<= x 4.8e-90) (* x (/ 100.0 y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+135) {
		tmp = 100.0;
	} else if (x <= 4.8e-90) {
		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 <= (-1.12d+135)) then
        tmp = 100.0d0
    else if (x <= 4.8d-90) 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 <= -1.12e+135) {
		tmp = 100.0;
	} else if (x <= 4.8e-90) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.12e+135:
		tmp = 100.0
	elif x <= 4.8e-90:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.12e+135)
		tmp = 100.0;
	elseif (x <= 4.8e-90)
		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 <= -1.12e+135)
		tmp = 100.0;
	elseif (x <= 4.8e-90)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.12e+135], 100.0, If[LessEqual[x, 4.8e-90], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1199999999999999e135 or 4.8000000000000003e-90 < x

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-*r/ 99.7%

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

      3. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.2%

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

   if -1.1199999999999999e135 < x < 4.8000000000000003e-90

   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-*r/ 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 73.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+135}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+135}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.12e+135) 100.0 (if (<= x 1.22e-90) (/ (* x 100.0) y) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+135) {
		tmp = 100.0;
	} else if (x <= 1.22e-90) {
		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 <= (-1.12d+135)) then
        tmp = 100.0d0
    else if (x <= 1.22d-90) 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 <= -1.12e+135) {
		tmp = 100.0;
	} else if (x <= 1.22e-90) {
		tmp = (x * 100.0) / y;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.12e+135:
		tmp = 100.0
	elif x <= 1.22e-90:
		tmp = (x * 100.0) / y
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.12e+135)
		tmp = 100.0;
	elseif (x <= 1.22e-90)
		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 <= -1.12e+135)
		tmp = 100.0;
	elseif (x <= 1.22e-90)
		tmp = (x * 100.0) / y;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.12e+135], 100.0, If[LessEqual[x, 1.22e-90], N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1199999999999999e135 or 1.2199999999999999e-90 < x

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-*r/ 99.7%

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

      3. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.2%

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

   if -1.1199999999999999e135 < x < 1.2199999999999999e-90

   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-*r/ 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 73.3%

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

      1. associate-*r/ 73.5%

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

   6. Simplified 73.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+135}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 50.2% 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 99.4%

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

   1. +-commutative 99.4%

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

   2. associate-*r/ 99.8%

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

   3. +-commutative 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 55.5%

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

5. Final simplification 55.5%

   \[\leadsto 100 \]

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 2023301 
(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)))