Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.3% → 99.7%

Time: 3.3s

Alternatives: 7

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

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

   \[\frac{x \cdot 100}{x + y} \]
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. Final simplification 99.7%

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

Alternative 2: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+112} \lor \neg \left(y \leq -1.65 \cdot 10^{+39} \lor \neg \left(y \leq -4.5 \cdot 10^{-64}\right) \land \left(y \leq 4.1 \cdot 10^{-12} \lor \neg \left(y \leq 3.3 \cdot 10^{+26}\right) \land y \leq 5.6 \cdot 10^{+53}\right)\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7e+112)
         (not
          (or (<= y -1.65e+39)
              (and (not (<= y -4.5e-64))
                   (or (<= y 4.1e-12)
                       (and (not (<= y 3.3e+26)) (<= y 5.6e+53)))))))
   (* 100.0 (/ x y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7e+112) || !((y <= -1.65e+39) || (!(y <= -4.5e-64) && ((y <= 4.1e-12) || (!(y <= 3.3e+26) && (y <= 5.6e+53)))))) {
		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 ((y <= (-7d+112)) .or. (.not. (y <= (-1.65d+39)) .or. (.not. (y <= (-4.5d-64))) .and. (y <= 4.1d-12) .or. (.not. (y <= 3.3d+26)) .and. (y <= 5.6d+53))) 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 ((y <= -7e+112) || !((y <= -1.65e+39) || (!(y <= -4.5e-64) && ((y <= 4.1e-12) || (!(y <= 3.3e+26) && (y <= 5.6e+53)))))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7e+112) or not ((y <= -1.65e+39) or (not (y <= -4.5e-64) and ((y <= 4.1e-12) or (not (y <= 3.3e+26) and (y <= 5.6e+53))))):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7e+112) || !((y <= -1.65e+39) || (!(y <= -4.5e-64) && ((y <= 4.1e-12) || (!(y <= 3.3e+26) && (y <= 5.6e+53))))))
		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 ((y <= -7e+112) || ~(((y <= -1.65e+39) || (~((y <= -4.5e-64)) && ((y <= 4.1e-12) || (~((y <= 3.3e+26)) && (y <= 5.6e+53)))))))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7e+112], N[Not[Or[LessEqual[y, -1.65e+39], And[N[Not[LessEqual[y, -4.5e-64]], $MachinePrecision], Or[LessEqual[y, 4.1e-12], And[N[Not[LessEqual[y, 3.3e+26]], $MachinePrecision], LessEqual[y, 5.6e+53]]]]]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999994e112 or -1.6500000000000001e39 < y < -4.5000000000000001e-64 or 4.0999999999999999e-12 < y < 3.29999999999999993e26 or 5.6e53 < y

   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* 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in x around 0 81.9%

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

   if -6.99999999999999994e112 < y < -1.6500000000000001e39 or -4.5000000000000001e-64 < y < 4.0999999999999999e-12 or 3.29999999999999993e26 < y < 5.6e53

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      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 82.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+112} \lor \neg \left(y \leq -1.65 \cdot 10^{+39} \lor \neg \left(y \leq -4.5 \cdot 10^{-64}\right) \land \left(y \leq 4.1 \cdot 10^{-12} \lor \neg \left(y \leq 3.3 \cdot 10^{+26}\right) \land y \leq 5.6 \cdot 10^{+53}\right)\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-12}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+57}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ x y))))
   (if (<= y -4.6e+108)
     t_0
     (if (<= y -2.1e+38)
       100.0
       (if (<= y -4e-63)
         t_0
         (if (<= y 4.2e-12)
           100.0
           (if (<= y 7.2e+19)
             (/ 100.0 (/ y x))
             (if (<= y 1.46e+57) 100.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 100.0 * (x / y);
	double tmp;
	if (y <= -4.6e+108) {
		tmp = t_0;
	} else if (y <= -2.1e+38) {
		tmp = 100.0;
	} else if (y <= -4e-63) {
		tmp = t_0;
	} else if (y <= 4.2e-12) {
		tmp = 100.0;
	} else if (y <= 7.2e+19) {
		tmp = 100.0 / (y / x);
	} else if (y <= 1.46e+57) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 100.0d0 * (x / y)
    if (y <= (-4.6d+108)) then
        tmp = t_0
    else if (y <= (-2.1d+38)) then
        tmp = 100.0d0
    else if (y <= (-4d-63)) then
        tmp = t_0
    else if (y <= 4.2d-12) then
        tmp = 100.0d0
    else if (y <= 7.2d+19) then
        tmp = 100.0d0 / (y / x)
    else if (y <= 1.46d+57) then
        tmp = 100.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 100.0 * (x / y);
	double tmp;
	if (y <= -4.6e+108) {
		tmp = t_0;
	} else if (y <= -2.1e+38) {
		tmp = 100.0;
	} else if (y <= -4e-63) {
		tmp = t_0;
	} else if (y <= 4.2e-12) {
		tmp = 100.0;
	} else if (y <= 7.2e+19) {
		tmp = 100.0 / (y / x);
	} else if (y <= 1.46e+57) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 100.0 * (x / y)
	tmp = 0
	if y <= -4.6e+108:
		tmp = t_0
	elif y <= -2.1e+38:
		tmp = 100.0
	elif y <= -4e-63:
		tmp = t_0
	elif y <= 4.2e-12:
		tmp = 100.0
	elif y <= 7.2e+19:
		tmp = 100.0 / (y / x)
	elif y <= 1.46e+57:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(100.0 * Float64(x / y))
	tmp = 0.0
	if (y <= -4.6e+108)
		tmp = t_0;
	elseif (y <= -2.1e+38)
		tmp = 100.0;
	elseif (y <= -4e-63)
		tmp = t_0;
	elseif (y <= 4.2e-12)
		tmp = 100.0;
	elseif (y <= 7.2e+19)
		tmp = Float64(100.0 / Float64(y / x));
	elseif (y <= 1.46e+57)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 100.0 * (x / y);
	tmp = 0.0;
	if (y <= -4.6e+108)
		tmp = t_0;
	elseif (y <= -2.1e+38)
		tmp = 100.0;
	elseif (y <= -4e-63)
		tmp = t_0;
	elseif (y <= 4.2e-12)
		tmp = 100.0;
	elseif (y <= 7.2e+19)
		tmp = 100.0 / (y / x);
	elseif (y <= 1.46e+57)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+108], t$95$0, If[LessEqual[y, -2.1e+38], 100.0, If[LessEqual[y, -4e-63], t$95$0, If[LessEqual[y, 4.2e-12], 100.0, If[LessEqual[y, 7.2e+19], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.46e+57], 100.0, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5999999999999998e108 or -2.1e38 < y < -4.00000000000000027e-63 or 1.46e57 < y

   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* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around 0 81.3%

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

   if -4.5999999999999998e108 < y < -2.1e38 or -4.00000000000000027e-63 < y < 4.19999999999999988e-12 or 7.2e19 < y < 1.46e57

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      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 82.5%

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

   if 4.19999999999999988e-12 < y < 7.2e19

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-63}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-12}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+57}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 0.01}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-14}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+53}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 0.01))))
   (if (<= y -4.6e+108)
     (* 100.0 (/ x y))
     (if (<= y -5.8e+38)
       100.0
       (if (<= y -3.9e-63)
         t_0
         (if (<= y 4e-14)
           100.0
           (if (<= y 1.15e+25)
             (/ 100.0 (/ y x))
             (if (<= y 5.4e+53) 100.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = x / (y * 0.01);
	double tmp;
	if (y <= -4.6e+108) {
		tmp = 100.0 * (x / y);
	} else if (y <= -5.8e+38) {
		tmp = 100.0;
	} else if (y <= -3.9e-63) {
		tmp = t_0;
	} else if (y <= 4e-14) {
		tmp = 100.0;
	} else if (y <= 1.15e+25) {
		tmp = 100.0 / (y / x);
	} else if (y <= 5.4e+53) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (y * 0.01d0)
    if (y <= (-4.6d+108)) then
        tmp = 100.0d0 * (x / y)
    else if (y <= (-5.8d+38)) then
        tmp = 100.0d0
    else if (y <= (-3.9d-63)) then
        tmp = t_0
    else if (y <= 4d-14) then
        tmp = 100.0d0
    else if (y <= 1.15d+25) then
        tmp = 100.0d0 / (y / x)
    else if (y <= 5.4d+53) then
        tmp = 100.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 0.01);
	double tmp;
	if (y <= -4.6e+108) {
		tmp = 100.0 * (x / y);
	} else if (y <= -5.8e+38) {
		tmp = 100.0;
	} else if (y <= -3.9e-63) {
		tmp = t_0;
	} else if (y <= 4e-14) {
		tmp = 100.0;
	} else if (y <= 1.15e+25) {
		tmp = 100.0 / (y / x);
	} else if (y <= 5.4e+53) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * 0.01)
	tmp = 0
	if y <= -4.6e+108:
		tmp = 100.0 * (x / y)
	elif y <= -5.8e+38:
		tmp = 100.0
	elif y <= -3.9e-63:
		tmp = t_0
	elif y <= 4e-14:
		tmp = 100.0
	elif y <= 1.15e+25:
		tmp = 100.0 / (y / x)
	elif y <= 5.4e+53:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 0.01))
	tmp = 0.0
	if (y <= -4.6e+108)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (y <= -5.8e+38)
		tmp = 100.0;
	elseif (y <= -3.9e-63)
		tmp = t_0;
	elseif (y <= 4e-14)
		tmp = 100.0;
	elseif (y <= 1.15e+25)
		tmp = Float64(100.0 / Float64(y / x));
	elseif (y <= 5.4e+53)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * 0.01);
	tmp = 0.0;
	if (y <= -4.6e+108)
		tmp = 100.0 * (x / y);
	elseif (y <= -5.8e+38)
		tmp = 100.0;
	elseif (y <= -3.9e-63)
		tmp = t_0;
	elseif (y <= 4e-14)
		tmp = 100.0;
	elseif (y <= 1.15e+25)
		tmp = 100.0 / (y / x);
	elseif (y <= 5.4e+53)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+108], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e+38], 100.0, If[LessEqual[y, -3.9e-63], t$95$0, If[LessEqual[y, 4e-14], 100.0, If[LessEqual[y, 1.15e+25], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+53], 100.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5999999999999998e108

   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* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 91.8%

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

   if -4.5999999999999998e108 < y < -5.80000000000000013e38 or -3.90000000000000022e-63 < y < 4e-14 or 1.1499999999999999e25 < y < 5.40000000000000039e53

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      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 82.5%

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

   if -5.80000000000000013e38 < y < -3.90000000000000022e-63 or 5.40000000000000039e53 < y

   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 75.3%

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

      1. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   if 4e-14 < y < 1.1499999999999999e25

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-14}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+53}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]

Alternative 5: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{x}{0.01}}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-14}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (/ x 0.01) y)))
   (if (<= y -4.6e+108)
     t_0
     (if (<= y -4.6e+38)
       100.0
       (if (<= y -4.8e-64)
         (/ x (* y 0.01))
         (if (<= y 4e-14)
           100.0
           (if (<= y 7.7e+28)
             (/ 100.0 (/ y x))
             (if (<= y 4.2e+55) 100.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = (x / 0.01) / y;
	double tmp;
	if (y <= -4.6e+108) {
		tmp = t_0;
	} else if (y <= -4.6e+38) {
		tmp = 100.0;
	} else if (y <= -4.8e-64) {
		tmp = x / (y * 0.01);
	} else if (y <= 4e-14) {
		tmp = 100.0;
	} else if (y <= 7.7e+28) {
		tmp = 100.0 / (y / x);
	} else if (y <= 4.2e+55) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / 0.01d0) / y
    if (y <= (-4.6d+108)) then
        tmp = t_0
    else if (y <= (-4.6d+38)) then
        tmp = 100.0d0
    else if (y <= (-4.8d-64)) then
        tmp = x / (y * 0.01d0)
    else if (y <= 4d-14) then
        tmp = 100.0d0
    else if (y <= 7.7d+28) then
        tmp = 100.0d0 / (y / x)
    else if (y <= 4.2d+55) then
        tmp = 100.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / 0.01) / y;
	double tmp;
	if (y <= -4.6e+108) {
		tmp = t_0;
	} else if (y <= -4.6e+38) {
		tmp = 100.0;
	} else if (y <= -4.8e-64) {
		tmp = x / (y * 0.01);
	} else if (y <= 4e-14) {
		tmp = 100.0;
	} else if (y <= 7.7e+28) {
		tmp = 100.0 / (y / x);
	} else if (y <= 4.2e+55) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / 0.01) / y
	tmp = 0
	if y <= -4.6e+108:
		tmp = t_0
	elif y <= -4.6e+38:
		tmp = 100.0
	elif y <= -4.8e-64:
		tmp = x / (y * 0.01)
	elif y <= 4e-14:
		tmp = 100.0
	elif y <= 7.7e+28:
		tmp = 100.0 / (y / x)
	elif y <= 4.2e+55:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / 0.01) / y)
	tmp = 0.0
	if (y <= -4.6e+108)
		tmp = t_0;
	elseif (y <= -4.6e+38)
		tmp = 100.0;
	elseif (y <= -4.8e-64)
		tmp = Float64(x / Float64(y * 0.01));
	elseif (y <= 4e-14)
		tmp = 100.0;
	elseif (y <= 7.7e+28)
		tmp = Float64(100.0 / Float64(y / x));
	elseif (y <= 4.2e+55)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / 0.01) / y;
	tmp = 0.0;
	if (y <= -4.6e+108)
		tmp = t_0;
	elseif (y <= -4.6e+38)
		tmp = 100.0;
	elseif (y <= -4.8e-64)
		tmp = x / (y * 0.01);
	elseif (y <= 4e-14)
		tmp = 100.0;
	elseif (y <= 7.7e+28)
		tmp = 100.0 / (y / x);
	elseif (y <= 4.2e+55)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / 0.01), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.6e+108], t$95$0, If[LessEqual[y, -4.6e+38], 100.0, If[LessEqual[y, -4.8e-64], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-14], 100.0, If[LessEqual[y, 7.7e+28], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+55], 100.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5999999999999998e108 or 4.2000000000000001e55 < y

   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* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. metadata-eval 84.6%

         \[\leadsto \color{blue}{\frac{1}{0.01}} \cdot \frac{x}{y} \]

      2. times-frac 84.6%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{0.01 \cdot y}} \]

      3. *-un-lft-identity 84.6%

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

      4. associate-/r* 84.8%

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

   6. Applied egg-rr 84.8%

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

   if -4.5999999999999998e108 < y < -4.6000000000000002e38 or -4.79999999999999997e-64 < y < 4e-14 or 7.6999999999999997e28 < y < 4.2000000000000001e55

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      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 82.5%

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

   if -4.6000000000000002e38 < y < -4.79999999999999997e-64

   1. Initial program 99.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 64.4%

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

      1. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if 4e-14 < y < 7.6999999999999997e28

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;\frac{\frac{x}{0.01}}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-14}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{0.01}}{y}\\ \end{array} \]

Alternative 6: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{100}{\frac{y}{x} + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 100.0 (+ (/ y x) 1.0)))

C

double code(double x, double y) {
	return 100.0 / ((y / x) + 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0 / ((y / x) + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return 100.0 / ((y / x) + 1.0);
}

Python

def code(x, y):
	return 100.0 / ((y / x) + 1.0)

Julia

function code(x, y)
	return Float64(100.0 / Float64(Float64(y / x) + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0 / ((y / x) + 1.0);
end

Wolfram

code[x_, y_] := N[(100.0 / N[(N[(y / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-/l* 99.3%

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

3. Simplified 99.3%

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

4. Taylor expanded in x around 0 99.3%

   \[\leadsto \frac{100}{\color{blue}{1 + \frac{y}{x}}} \]
5. Step-by-step derivation

   1. +-commutative 99.3%

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

6. Simplified 99.3%

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

7. Final simplification 99.3%

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

Alternative 7: 51.0% 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 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-/l* 99.3%

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

3. Simplified 99.3%

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

4. Taylor expanded in x around inf 51.6%

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

5. Final simplification 51.6%

   \[\leadsto 100 \]

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 2023199 
(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)))