Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.3%

Time: 4.9s

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: 99.4% 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: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Taylor expanded in x around inf 99.9%

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

8. Final simplification 99.9%

   \[\leadsto \frac{100}{1 + \frac{y}{x}} \]
9. Add Preprocessing

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-10} \lor \neg \left(x \leq -2.5 \cdot 10^{-40}\right) \land x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.45e+57)
   100.0
   (if (or (<= x -5.2e-10) (and (not (<= x -2.5e-40)) (<= x 3.1e-97)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.45e+57) {
		tmp = 100.0;
	} else if ((x <= -5.2e-10) || (!(x <= -2.5e-40) && (x <= 3.1e-97))) {
		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 <= (-1.45d+57)) then
        tmp = 100.0d0
    else if ((x <= (-5.2d-10)) .or. (.not. (x <= (-2.5d-40))) .and. (x <= 3.1d-97)) 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 <= -1.45e+57) {
		tmp = 100.0;
	} else if ((x <= -5.2e-10) || (!(x <= -2.5e-40) && (x <= 3.1e-97))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.45e+57:
		tmp = 100.0
	elif (x <= -5.2e-10) or (not (x <= -2.5e-40) and (x <= 3.1e-97)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.45e+57)
		tmp = 100.0;
	elseif ((x <= -5.2e-10) || (!(x <= -2.5e-40) && (x <= 3.1e-97)))
		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 <= -1.45e+57)
		tmp = 100.0;
	elseif ((x <= -5.2e-10) || (~((x <= -2.5e-40)) && (x <= 3.1e-97)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.45e+57], 100.0, If[Or[LessEqual[x, -5.2e-10], And[N[Not[LessEqual[x, -2.5e-40]], $MachinePrecision], LessEqual[x, 3.1e-97]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4500000000000001e57 or -5.19999999999999962e-10 < x < -2.49999999999999982e-40 or 3.10000000000000002e-97 < x

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -1.4500000000000001e57 < x < -5.19999999999999962e-10 or -2.49999999999999982e-40 < x < 3.10000000000000002e-97

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 78.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-10} \lor \neg \left(x \leq -2.5 \cdot 10^{-40}\right) \land x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+51}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-47}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.2e+51)
   100.0
   (if (<= x -8.5e-10)
     (* 100.0 (/ x y))
     (if (<= x -9.5e-47) 100.0 (if (<= x 3.1e-97) (* x (/ 100.0 y)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.2e+51) {
		tmp = 100.0;
	} else if (x <= -8.5e-10) {
		tmp = 100.0 * (x / y);
	} else if (x <= -9.5e-47) {
		tmp = 100.0;
	} else if (x <= 3.1e-97) {
		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+51)) then
        tmp = 100.0d0
    else if (x <= (-8.5d-10)) then
        tmp = 100.0d0 * (x / y)
    else if (x <= (-9.5d-47)) then
        tmp = 100.0d0
    else if (x <= 3.1d-97) 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+51) {
		tmp = 100.0;
	} else if (x <= -8.5e-10) {
		tmp = 100.0 * (x / y);
	} else if (x <= -9.5e-47) {
		tmp = 100.0;
	} else if (x <= 3.1e-97) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.2e+51:
		tmp = 100.0
	elif x <= -8.5e-10:
		tmp = 100.0 * (x / y)
	elif x <= -9.5e-47:
		tmp = 100.0
	elif x <= 3.1e-97:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.2e+51)
		tmp = 100.0;
	elseif (x <= -8.5e-10)
		tmp = Float64(100.0 * Float64(x / y));
	elseif (x <= -9.5e-47)
		tmp = 100.0;
	elseif (x <= 3.1e-97)
		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+51)
		tmp = 100.0;
	elseif (x <= -8.5e-10)
		tmp = 100.0 * (x / y);
	elseif (x <= -9.5e-47)
		tmp = 100.0;
	elseif (x <= 3.1e-97)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.2e+51], 100.0, If[LessEqual[x, -8.5e-10], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-47], 100.0, If[LessEqual[x, 3.1e-97], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1999999999999999e51 or -8.4999999999999996e-10 < x < -9.4999999999999991e-47 or 3.10000000000000002e-97 < x

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -1.1999999999999999e51 < x < -8.4999999999999996e-10

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 66.3%

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

   if -9.4999999999999991e-47 < x < 3.10000000000000002e-97

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0 79.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+51}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-47}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+75}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-9}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e+75)
   100.0
   (if (<= x -1.76e-9)
     (/ 100.0 (/ y x))
     (if (<= x -2.9e-40) 100.0 (if (<= x 3.1e-97) (* x (/ 100.0 y)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e+75) {
		tmp = 100.0;
	} else if (x <= -1.76e-9) {
		tmp = 100.0 / (y / x);
	} else if (x <= -2.9e-40) {
		tmp = 100.0;
	} else if (x <= 3.1e-97) {
		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 <= (-7d+75)) then
        tmp = 100.0d0
    else if (x <= (-1.76d-9)) then
        tmp = 100.0d0 / (y / x)
    else if (x <= (-2.9d-40)) then
        tmp = 100.0d0
    else if (x <= 3.1d-97) 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 <= -7e+75) {
		tmp = 100.0;
	} else if (x <= -1.76e-9) {
		tmp = 100.0 / (y / x);
	} else if (x <= -2.9e-40) {
		tmp = 100.0;
	} else if (x <= 3.1e-97) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e+75:
		tmp = 100.0
	elif x <= -1.76e-9:
		tmp = 100.0 / (y / x)
	elif x <= -2.9e-40:
		tmp = 100.0
	elif x <= 3.1e-97:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e+75)
		tmp = 100.0;
	elseif (x <= -1.76e-9)
		tmp = Float64(100.0 / Float64(y / x));
	elseif (x <= -2.9e-40)
		tmp = 100.0;
	elseif (x <= 3.1e-97)
		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 <= -7e+75)
		tmp = 100.0;
	elseif (x <= -1.76e-9)
		tmp = 100.0 / (y / x);
	elseif (x <= -2.9e-40)
		tmp = 100.0;
	elseif (x <= 3.1e-97)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e+75], 100.0, If[LessEqual[x, -1.76e-9], N[(100.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e-40], 100.0, If[LessEqual[x, 3.1e-97], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999997e75 or -1.75999999999999992e-9 < x < -2.8999999999999999e-40 or 3.10000000000000002e-97 < x

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -6.9999999999999997e75 < x < -1.75999999999999992e-9

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 66.3%

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

      1. associate-*r/ 65.9%

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

      2. associate-*l/ 66.3%

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

      3. associate-/r/ 66.4%

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

   9. Simplified 66.4%

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

   if -2.8999999999999999e-40 < x < 3.10000000000000002e-97

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0 79.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+75}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-9}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+60}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-47}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.9e+60)
   100.0
   (if (<= x -4.9e-9)
     (/ x (* y 0.01))
     (if (<= x -7.2e-47) 100.0 (if (<= x 8.6e-98) (* x (/ 100.0 y)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.9e+60) {
		tmp = 100.0;
	} else if (x <= -4.9e-9) {
		tmp = x / (y * 0.01);
	} else if (x <= -7.2e-47) {
		tmp = 100.0;
	} else if (x <= 8.6e-98) {
		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 <= (-1.9d+60)) then
        tmp = 100.0d0
    else if (x <= (-4.9d-9)) then
        tmp = x / (y * 0.01d0)
    else if (x <= (-7.2d-47)) then
        tmp = 100.0d0
    else if (x <= 8.6d-98) 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 <= -1.9e+60) {
		tmp = 100.0;
	} else if (x <= -4.9e-9) {
		tmp = x / (y * 0.01);
	} else if (x <= -7.2e-47) {
		tmp = 100.0;
	} else if (x <= 8.6e-98) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.9e+60:
		tmp = 100.0
	elif x <= -4.9e-9:
		tmp = x / (y * 0.01)
	elif x <= -7.2e-47:
		tmp = 100.0
	elif x <= 8.6e-98:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.9e+60)
		tmp = 100.0;
	elseif (x <= -4.9e-9)
		tmp = Float64(x / Float64(y * 0.01));
	elseif (x <= -7.2e-47)
		tmp = 100.0;
	elseif (x <= 8.6e-98)
		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 <= -1.9e+60)
		tmp = 100.0;
	elseif (x <= -4.9e-9)
		tmp = x / (y * 0.01);
	elseif (x <= -7.2e-47)
		tmp = 100.0;
	elseif (x <= 8.6e-98)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.9e+60], 100.0, If[LessEqual[x, -4.9e-9], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-47], 100.0, If[LessEqual[x, 8.6e-98], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000005e60 or -4.90000000000000004e-9 < x < -7.19999999999999982e-47 or 8.59999999999999977e-98 < x

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -1.90000000000000005e60 < x < -4.90000000000000004e-9

   1. Initial program 99.3%

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

      1. associate-/l* 99.6%

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

      2. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around 0 66.3%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. associate-*r/ 65.9%

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

      2. associate-*l/ 66.3%

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

      3. associate-/r/ 66.4%

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

      4. metadata-eval 66.4%

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

      5. associate-/r* 66.4%

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

      6. associate-/l/ 66.3%

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

      7. associate-/r/ 66.4%

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

      8. *-commutative 66.4%

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

      9. associate-*r/ 66.4%

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

      10. associate-*l/ 66.4%

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

      11. *-rgt-identity 66.4%

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

      12. associate-/r* 66.5%

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

   8. Simplified 66.5%

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

   if -7.19999999999999982e-47 < x < 8.59999999999999977e-98

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0 79.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+60}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-47}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

   \[\leadsto 100 \cdot \frac{x}{y + x} \]
6. Add Preprocessing

Alternative 7: 51.9% 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 99.3%

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

   2. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf 55.4%

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

6. Final simplification 55.4%

   \[\leadsto 100 \]
7. Add Preprocessing

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 2024079 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :alt
  (* (/ x 1.0) (/ 100.0 (+ x y)))

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