Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 3.9s

Alternatives: 6

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

\[\begin{array}{l} \\ \frac{x}{\left(x + y\right) \cdot 0.01} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* (+ x y) 0.01)))

C

double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / ((x + y) * 0.01d0)
end function

Java

public static double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Python

def code(x, y):
	return x / ((x + y) * 0.01)

Julia

function code(x, y)
	return Float64(x / Float64(Float64(x + y) * 0.01))
end

MATLAB

function tmp = code(x, y)
	tmp = x / ((x + y) * 0.01);
end

Wolfram

code[x_, y_] := N[(x / N[(N[(x + y), $MachinePrecision] * 0.01), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

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

   1. expm1-log1p-u 98.3%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

   2. expm1-udef 65.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

   3. associate-/l* 66.0%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

   4. div-inv 66.0%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

   5. +-commutative 66.0%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(y + x\right)} \cdot \frac{1}{100}}\right)} - 1 \]

   6. metadata-eval 66.0%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

3. Applied egg-rr 66.0%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)} - 1} \]
4. Step-by-step derivation

   1. expm1-def 98.7%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)\right)} \]

   2. expm1-log1p 99.7%

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

5. Simplified 99.7%

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

6. Final simplification 99.7%

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

Alternative 2: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-79} \lor \neg \left(x \leq 1.02 \cdot 10^{+18}\right) \land x \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.5e+38)
   100.0
   (if (or (<= x 2.8e-79) (and (not (<= x 1.02e+18)) (<= x 1.4e+97)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.5e+38) {
		tmp = 100.0;
	} else if ((x <= 2.8e-79) || (!(x <= 1.02e+18) && (x <= 1.4e+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 <= (-3.5d+38)) then
        tmp = 100.0d0
    else if ((x <= 2.8d-79) .or. (.not. (x <= 1.02d+18)) .and. (x <= 1.4d+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 <= -3.5e+38) {
		tmp = 100.0;
	} else if ((x <= 2.8e-79) || (!(x <= 1.02e+18) && (x <= 1.4e+97))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.5e+38:
		tmp = 100.0
	elif (x <= 2.8e-79) or (not (x <= 1.02e+18) and (x <= 1.4e+97)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.5e+38)
		tmp = 100.0;
	elseif ((x <= 2.8e-79) || (!(x <= 1.02e+18) && (x <= 1.4e+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 <= -3.5e+38)
		tmp = 100.0;
	elseif ((x <= 2.8e-79) || (~((x <= 1.02e+18)) && (x <= 1.4e+97)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.5e+38], 100.0, If[Or[LessEqual[x, 2.8e-79], And[N[Not[LessEqual[x, 1.02e+18]], $MachinePrecision], LessEqual[x, 1.4e+97]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.50000000000000002e38 or 2.80000000000000012e-79 < x < 1.02e18 or 1.4e97 < x

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

      4. remove-double-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. div-sub 99.9%

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

      7. distribute-frac-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 82.7%

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

   if -3.50000000000000002e38 < x < 2.80000000000000012e-79 or 1.02e18 < x < 1.4e97

   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* 98.0%

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

      3. +-commutative 98.0%

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

      4. remove-double-neg 98.0%

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

      5. unsub-neg 98.0%

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

      6. div-sub 98.0%

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

      7. distribute-frac-neg 98.0%

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

      8. *-inverses 98.0%

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

      9. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in y around inf 79.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+38}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-79} \lor \neg \left(x \leq 1.02 \cdot 10^{+18}\right) \land x \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+35}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-79} \lor \neg \left(x \leq 3.7 \cdot 10^{+18}\right) \land x \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e+35)
   100.0
   (if (or (<= x 3.1e-79) (and (not (<= x 3.7e+18)) (<= x 1.3e+97)))
     (/ x (* y 0.01))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e+35) {
		tmp = 100.0;
	} else if ((x <= 3.1e-79) || (!(x <= 3.7e+18) && (x <= 1.3e+97))) {
		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 <= (-4d+35)) then
        tmp = 100.0d0
    else if ((x <= 3.1d-79) .or. (.not. (x <= 3.7d+18)) .and. (x <= 1.3d+97)) 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 <= -4e+35) {
		tmp = 100.0;
	} else if ((x <= 3.1e-79) || (!(x <= 3.7e+18) && (x <= 1.3e+97))) {
		tmp = x / (y * 0.01);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e+35:
		tmp = 100.0
	elif (x <= 3.1e-79) or (not (x <= 3.7e+18) and (x <= 1.3e+97)):
		tmp = x / (y * 0.01)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e+35)
		tmp = 100.0;
	elseif ((x <= 3.1e-79) || (!(x <= 3.7e+18) && (x <= 1.3e+97)))
		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 <= -4e+35)
		tmp = 100.0;
	elseif ((x <= 3.1e-79) || (~((x <= 3.7e+18)) && (x <= 1.3e+97)))
		tmp = x / (y * 0.01);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e+35], 100.0, If[Or[LessEqual[x, 3.1e-79], And[N[Not[LessEqual[x, 3.7e+18]], $MachinePrecision], LessEqual[x, 1.3e+97]]], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999999e35 or 3.0999999999999999e-79 < x < 3.7e18 or 1.3e97 < x

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

      4. remove-double-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. div-sub 99.9%

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

      7. distribute-frac-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 82.7%

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

   if -3.9999999999999999e35 < x < 3.0999999999999999e-79 or 3.7e18 < x < 1.3e97

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

      2. expm1-udef 51.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

      3. associate-/l* 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

      4. div-inv 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

      5. +-commutative 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(y + x\right)} \cdot \frac{1}{100}}\right)} - 1 \]

      6. metadata-eval 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

   3. Applied egg-rr 51.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)} - 1} \]
   4. Step-by-step derivation

      1. expm1-def 99.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)\right)} \]

      2. expm1-log1p 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 79.1%

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

      1. metadata-eval 79.1%

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

      2. times-frac 79.4%

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

      3. *-commutative 79.4%

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

      4. *-lft-identity 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+35}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-79} \lor \neg \left(x \leq 3.7 \cdot 10^{+18}\right) \land x \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+35}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.2e+35)
   100.0
   (if (<= x 3.1e-79)
     (/ (* x 100.0) y)
     (if (<= x 3.7e+18) 100.0 (if (<= x 1.3e+97) (/ x (* y 0.01)) 100.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.2e+35) {
		tmp = 100.0;
	} else if (x <= 3.1e-79) {
		tmp = (x * 100.0) / y;
	} else if (x <= 3.7e+18) {
		tmp = 100.0;
	} else if (x <= 1.3e+97) {
		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 <= (-1.2d+35)) then
        tmp = 100.0d0
    else if (x <= 3.1d-79) then
        tmp = (x * 100.0d0) / y
    else if (x <= 3.7d+18) then
        tmp = 100.0d0
    else if (x <= 1.3d+97) 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 <= -1.2e+35) {
		tmp = 100.0;
	} else if (x <= 3.1e-79) {
		tmp = (x * 100.0) / y;
	} else if (x <= 3.7e+18) {
		tmp = 100.0;
	} else if (x <= 1.3e+97) {
		tmp = x / (y * 0.01);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.2e+35:
		tmp = 100.0
	elif x <= 3.1e-79:
		tmp = (x * 100.0) / y
	elif x <= 3.7e+18:
		tmp = 100.0
	elif x <= 1.3e+97:
		tmp = x / (y * 0.01)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.2e+35)
		tmp = 100.0;
	elseif (x <= 3.1e-79)
		tmp = Float64(Float64(x * 100.0) / y);
	elseif (x <= 3.7e+18)
		tmp = 100.0;
	elseif (x <= 1.3e+97)
		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 <= -1.2e+35)
		tmp = 100.0;
	elseif (x <= 3.1e-79)
		tmp = (x * 100.0) / y;
	elseif (x <= 3.7e+18)
		tmp = 100.0;
	elseif (x <= 1.3e+97)
		tmp = x / (y * 0.01);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.2e+35], 100.0, If[LessEqual[x, 3.1e-79], N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 3.7e+18], 100.0, If[LessEqual[x, 1.3e+97], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], 100.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.20000000000000007e35 or 3.0999999999999999e-79 < x < 3.7e18 or 1.3e97 < x

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

      4. remove-double-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. div-sub 99.9%

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

      7. distribute-frac-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 82.7%

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

   if -1.20000000000000007e35 < x < 3.0999999999999999e-79

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

      2. expm1-udef 53.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

      3. associate-/l* 53.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

      4. div-inv 53.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

      5. +-commutative 53.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(y + x\right)} \cdot \frac{1}{100}}\right)} - 1 \]

      6. metadata-eval 53.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

   3. Applied egg-rr 53.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)} - 1} \]
   4. Step-by-step derivation

      1. expm1-def 99.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)\right)} \]

      2. expm1-log1p 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 80.5%

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

      1. associate-*r/ 80.9%

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

   8. Simplified 80.9%

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

   if 3.7e18 < x < 1.3e97

   1. Initial program 99.6%

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

      1. expm1-log1p-u 98.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

      2. expm1-udef 34.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

      3. associate-/l* 34.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

      4. div-inv 34.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

      5. +-commutative 34.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(y + x\right)} \cdot \frac{1}{100}}\right)} - 1 \]

      6. metadata-eval 34.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

   3. Applied egg-rr 34.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)} - 1} \]
   4. Step-by-step derivation

      1. expm1-def 99.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)\right)} \]

      2. expm1-log1p 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 70.7%

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

      1. metadata-eval 70.7%

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

      2. times-frac 70.7%

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

      3. *-commutative 70.7%

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

      4. *-lft-identity 70.7%

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

   8. Simplified 70.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+35}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5: 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 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 98.9%

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

   3. +-commutative 98.9%

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

   4. remove-double-neg 98.9%

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

   5. unsub-neg 98.9%

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

   6. div-sub 98.9%

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

   7. distribute-frac-neg 98.9%

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

   8. *-inverses 98.9%

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

   9. metadata-eval 98.9%

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

3. Simplified 98.9%

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

4. Final simplification 98.9%

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

Alternative 6: 51.2% 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* 98.9%

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

   3. +-commutative 98.9%

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

   4. remove-double-neg 98.9%

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

   5. unsub-neg 98.9%

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

   6. div-sub 98.9%

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

   7. distribute-frac-neg 98.9%

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

   8. *-inverses 98.9%

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

   9. metadata-eval 98.9%

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

3. Simplified 98.9%

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

4. Taylor expanded in y around 0 51.4%

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

5. Final simplification 51.4%

   \[\leadsto 100 \]

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 2023334 
(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)))