Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.3% → 99.7%

Time: 6.4s

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: 99.3% 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 99.3%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

   5. +-lowering-+.f64 99.9%

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 99.9%

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

Alternative 2: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6e+109) 100.0 (if (<= x 1.9e-45) (/ x (* y 0.01)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6e+109) {
		tmp = 100.0;
	} else if (x <= 1.9e-45) {
		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 <= (-4.6d+109)) then
        tmp = 100.0d0
    else if (x <= 1.9d-45) 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 <= -4.6e+109) {
		tmp = 100.0;
	} else if (x <= 1.9e-45) {
		tmp = x / (y * 0.01);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6e+109:
		tmp = 100.0
	elif x <= 1.9e-45:
		tmp = x / (y * 0.01)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6e+109)
		tmp = 100.0;
	elseif (x <= 1.9e-45)
		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 <= -4.6e+109)
		tmp = 100.0;
	elseif (x <= 1.9e-45)
		tmp = x / (y * 0.01);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6e+109], 100.0, If[LessEqual[x, 1.9e-45], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.60000000000000021e109 or 1.89999999999999999e-45 < x

   1. Initial program 98.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{100} \]
   6. Step-by-step derivation

   7. Simplified 80.8%

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

   if -4.60000000000000021e109 < x < 1.89999999999999999e-45

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{x + y}{100}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(x + y\right), \color{blue}{100}\right)\right) \]

      8. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), 100\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{100} \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\frac{1}{100}}\right)\right) \]

      2. *-lowering-*.f64 75.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{1}{100}}\right)\right) \]

   9. Simplified 75.8%

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

Alternative 3: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-45}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5e+109) 100.0 (if (<= x 7.6e-45) (* 100.0 (/ x y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5e+109) {
		tmp = 100.0;
	} else if (x <= 7.6e-45) {
		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 <= (-4.5d+109)) then
        tmp = 100.0d0
    else if (x <= 7.6d-45) 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 <= -4.5e+109) {
		tmp = 100.0;
	} else if (x <= 7.6e-45) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5e+109:
		tmp = 100.0
	elif x <= 7.6e-45:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5e+109)
		tmp = 100.0;
	elseif (x <= 7.6e-45)
		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 <= -4.5e+109)
		tmp = 100.0;
	elseif (x <= 7.6e-45)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5e+109], 100.0, If[LessEqual[x, 7.6e-45], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999996e109 or 7.59999999999999994e-45 < x

   1. Initial program 98.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{100} \]
   6. Step-by-step derivation

   7. Simplified 80.8%

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

   if -4.4999999999999996e109 < x < 7.59999999999999994e-45

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

      5. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      2. /-lowering-/.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 75.7%

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

Alternative 4: 50.4% 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 99.3%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \color{blue}{\left(\frac{x}{x + y}\right)}\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right)\right) \]

   5. +-lowering-+.f64 99.9%

      \[\leadsto \mathsf{*.f64}\left(100, \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{100} \]
6. Step-by-step derivation

7. Simplified 48.5%

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

Developer Target 1: 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 2024152 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (* (/ x 1) (/ 100 (+ x y))))

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