Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.3% → 99.7%

Time: 5.5s

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: 99.3% 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

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

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 99.8%

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

   1. associate-*r/ 99.8%

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

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: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.2e+32) 100.0 (if (<= x 1.26e-50) (* x (/ 100.0 y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.2e+32) {
		tmp = 100.0;
	} else if (x <= 1.26e-50) {
		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 <= (-1.2d+32)) then
        tmp = 100.0d0
    else if (x <= 1.26d-50) 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 <= -1.2e+32) {
		tmp = 100.0;
	} else if (x <= 1.26e-50) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.2e+32:
		tmp = 100.0
	elif x <= 1.26e-50:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.2e+32)
		tmp = 100.0;
	elseif (x <= 1.26e-50)
		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 <= -1.2e+32)
		tmp = 100.0;
	elseif (x <= 1.26e-50)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.2e+32], 100.0, If[LessEqual[x, 1.26e-50], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999996e32 or 1.26e-50 < x

   1. Initial program 99.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.5%

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

   if -1.19999999999999996e32 < x < 1.26e-50

   1. Initial program 99.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 80.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.9e+33) 100.0 (if (<= x 6e-54) (/ x (* y 0.01)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.9e+33) {
		tmp = 100.0;
	} else if (x <= 6e-54) {
		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 <= (-1.9d+33)) then
        tmp = 100.0d0
    else if (x <= 6d-54) 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 <= -1.9e+33) {
		tmp = 100.0;
	} else if (x <= 6e-54) {
		tmp = x / (y * 0.01);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.9e+33:
		tmp = 100.0
	elif x <= 6e-54:
		tmp = x / (y * 0.01)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.9e+33)
		tmp = 100.0;
	elseif (x <= 6e-54)
		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 <= -1.9e+33)
		tmp = 100.0;
	elseif (x <= 6e-54)
		tmp = x / (y * 0.01);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.9e+33], 100.0, If[LessEqual[x, 6e-54], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000001e33 or 6.00000000000000018e-54 < x

   1. Initial program 99.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.5%

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

   if -1.90000000000000001e33 < x < 6.00000000000000018e-54

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. remove-double-neg 99.7%

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

      3. sub0-neg 99.7%

         \[\leadsto \frac{x}{\frac{\color{blue}{\left(0 - \left(-x\right)\right)} + y}{100}} \]

      4. associate-+l- 99.7%

         \[\leadsto \frac{x}{\frac{\color{blue}{0 - \left(\left(-x\right) - y\right)}}{100}} \]

      5. neg-sub0 99.7%

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

      6. distribute-frac-neg 99.7%

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

      7. div-sub 99.7%

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

      8. sub-neg 99.7%

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

      9. distribute-neg-frac 99.7%

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

      10. distribute-neg-out 99.7%

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

      11. neg-mul-1 99.7%

          \[\leadsto \frac{x}{\left(-\frac{\color{blue}{-1 \cdot x}}{100}\right) + \left(-\frac{-y}{100}\right)} \]

      12. associate-/l* 99.7%

          \[\leadsto \frac{x}{\left(-\color{blue}{\frac{-1}{\frac{100}{x}}}\right) + \left(-\frac{-y}{100}\right)} \]

      13. associate-/r/ 99.7%

          \[\leadsto \frac{x}{\left(-\color{blue}{\frac{-1}{100} \cdot x}\right) + \left(-\frac{-y}{100}\right)} \]

      14. metadata-eval 99.7%

          \[\leadsto \frac{x}{\left(-\frac{\color{blue}{-1}}{100} \cdot x\right) + \left(-\frac{-y}{100}\right)} \]

      15. *-inverses 99.7%

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

      16. distribute-frac-neg 99.7%

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

      17. associate-/r* 99.6%

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

      18. distribute-rgt-neg-in 99.6%

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

      19. neg-mul-1 99.6%

          \[\leadsto \frac{x}{\frac{-x}{x \cdot 100} \cdot \left(-x\right) + \left(-\frac{\color{blue}{-1 \cdot y}}{100}\right)} \]

      20. associate-/l* 99.6%

          \[\leadsto \frac{x}{\frac{-x}{x \cdot 100} \cdot \left(-x\right) + \left(-\color{blue}{\frac{-1}{\frac{100}{y}}}\right)} \]

      21. associate-/r/ 99.6%

          \[\leadsto \frac{x}{\frac{-x}{x \cdot 100} \cdot \left(-x\right) + \left(-\color{blue}{\frac{-1}{100} \cdot y}\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

   4. Taylor expanded in x around 0 80.3%

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

      1. *-commutative 80.3%

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

   6. Simplified 80.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+33}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.6e+33) 100.0 (if (<= x 1.26e-50) (/ (* x 100.0) y) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e+33) {
		tmp = 100.0;
	} else if (x <= 1.26e-50) {
		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 <= (-1.6d+33)) then
        tmp = 100.0d0
    else if (x <= 1.26d-50) 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 <= -1.6e+33) {
		tmp = 100.0;
	} else if (x <= 1.26e-50) {
		tmp = (x * 100.0) / y;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e+33:
		tmp = 100.0
	elif x <= 1.26e-50:
		tmp = (x * 100.0) / y
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e+33)
		tmp = 100.0;
	elseif (x <= 1.26e-50)
		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 <= -1.6e+33)
		tmp = 100.0;
	elseif (x <= 1.26e-50)
		tmp = (x * 100.0) / y;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e+33], 100.0, If[LessEqual[x, 1.26e-50], N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000009e33 or 1.26e-50 < x

   1. Initial program 99.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.5%

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

   if -1.60000000000000009e33 < x < 1.26e-50

   1. Initial program 99.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 80.3%

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

      1. associate-*r/ 80.4%

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

   6. Applied egg-rr 80.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+33}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5: 51.3% 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 99.8%

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

   1. associate-*r/ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 53.1%

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

5. Final simplification 53.1%

   \[\leadsto 100 \]

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 2023279 
(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)))