Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 2.8s

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: 99.5% 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

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.5%

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

3. Simplified 99.5%

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

   1. div-inv 99.5%

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

   2. clear-num 99.7%

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

   3. *-commutative 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

Alternative 2: 73.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-82}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-24}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.8e-82) 100.0 (if (<= x 5.8e-24) (* 100.0 (/ x y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.8e-82) {
		tmp = 100.0;
	} else if (x <= 5.8e-24) {
		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 <= (-8.8d-82)) then
        tmp = 100.0d0
    else if (x <= 5.8d-24) 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 <= -8.8e-82) {
		tmp = 100.0;
	} else if (x <= 5.8e-24) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.8e-82:
		tmp = 100.0
	elif x <= 5.8e-24:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.8e-82)
		tmp = 100.0;
	elseif (x <= 5.8e-24)
		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 <= -8.8e-82)
		tmp = 100.0;
	elseif (x <= 5.8e-24)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.8e-82], 100.0, If[LessEqual[x, 5.8e-24], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999943e-82 or 5.7999999999999997e-24 < x

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      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 76.7%

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

   if -8.79999999999999943e-82 < x < 5.7999999999999997e-24

   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 0 80.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-82}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-24}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-82}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.4e-82) 100.0 (if (<= x 7.5e-33) (/ x (* y 0.01)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.4e-82) {
		tmp = 100.0;
	} else if (x <= 7.5e-33) {
		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 <= (-9.4d-82)) then
        tmp = 100.0d0
    else if (x <= 7.5d-33) 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 <= -9.4e-82) {
		tmp = 100.0;
	} else if (x <= 7.5e-33) {
		tmp = x / (y * 0.01);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.4e-82:
		tmp = 100.0
	elif x <= 7.5e-33:
		tmp = x / (y * 0.01)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.4e-82)
		tmp = 100.0;
	elseif (x <= 7.5e-33)
		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 <= -9.4e-82)
		tmp = 100.0;
	elseif (x <= 7.5e-33)
		tmp = x / (y * 0.01);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.4e-82], 100.0, If[LessEqual[x, 7.5e-33], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4000000000000001e-82 or 7.5000000000000001e-33 < x

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      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 76.7%

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

   if -9.4000000000000001e-82 < x < 7.5000000000000001e-33

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   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 80.8%

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

      1. *-commutative 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-82}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 50.8% 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%

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

   2. associate-/l* 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around inf 53.5%

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

5. Final simplification 53.5%

   \[\leadsto 100 \]

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 2023224 
(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)))