Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.3% → 99.3%

Time: 3.5s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% 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 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.8%

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

   3. +-commutative 99.8%

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

   4. remove-double-neg 99.8%

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

   5. unsub-neg 99.8%

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

   6. div-sub 99.8%

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

   7. distribute-frac-neg 99.8%

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

   8. *-inverses 99.8%

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

   9. metadata-eval 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto \frac{100}{\frac{y}{x} - -1} \]
6. Add Preprocessing

Alternative 2: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-16} \lor \neg \left(y \leq 1.52 \cdot 10^{+38}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4e-16) (not (<= y 1.52e+38))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e-16) || !(y <= 1.52e+38)) {
		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 <= (-1.4d-16)) .or. (.not. (y <= 1.52d+38))) 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 <= -1.4e-16) || !(y <= 1.52e+38)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4e-16) or not (y <= 1.52e+38):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4e-16) || !(y <= 1.52e+38))
		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 <= -1.4e-16) || ~((y <= 1.52e+38)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4e-16], N[Not[LessEqual[y, 1.52e+38]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-16 or 1.51999999999999996e38 < 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* 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. div-sub 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.5%

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

   if -1.4000000000000001e-16 < y < 1.51999999999999996e38

   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* 99.9%

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

      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. Add Preprocessing

   5. Taylor expanded in y around 0 76.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-16} \lor \neg \left(y \leq 1.52 \cdot 10^{+38}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+37}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.4e-16)
   (/ x (/ y 100.0))
   (if (<= y 2.75e+37) 100.0 (* 100.0 (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.4e-16) {
		tmp = x / (y / 100.0);
	} else if (y <= 2.75e+37) {
		tmp = 100.0;
	} else {
		tmp = 100.0 * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.4d-16)) then
        tmp = x / (y / 100.0d0)
    else if (y <= 2.75d+37) then
        tmp = 100.0d0
    else
        tmp = 100.0d0 * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.4e-16) {
		tmp = x / (y / 100.0);
	} else if (y <= 2.75e+37) {
		tmp = 100.0;
	} else {
		tmp = 100.0 * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.4e-16:
		tmp = x / (y / 100.0)
	elif y <= 2.75e+37:
		tmp = 100.0
	else:
		tmp = 100.0 * (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.4e-16)
		tmp = Float64(x / Float64(y / 100.0));
	elseif (y <= 2.75e+37)
		tmp = 100.0;
	else
		tmp = Float64(100.0 * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.4e-16)
		tmp = x / (y / 100.0);
	elseif (y <= 2.75e+37)
		tmp = 100.0;
	else
		tmp = 100.0 * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.4e-16], N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+37], 100.0, N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e-16

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

      3. +-commutative 99.7%

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

      4. remove-double-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. div-sub 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. *-inverses 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 77.2%

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

      1. associate-*r/ 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-/l* 77.3%

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

   7. Applied egg-rr 77.3%

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

   if -3.4e-16 < y < 2.75000000000000008e37

   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* 99.9%

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

      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. Add Preprocessing

   5. Taylor expanded in y around 0 76.4%

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

   if 2.75000000000000008e37 < 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* 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. div-sub 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 75.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+37}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.6% 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 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.8%

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

   3. +-commutative 99.8%

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

   4. remove-double-neg 99.8%

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

   5. unsub-neg 99.8%

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

   6. div-sub 99.8%

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

   7. distribute-frac-neg 99.8%

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

   8. *-inverses 99.8%

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

   9. metadata-eval 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 50.5%

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

6. Final simplification 50.5%

   \[\leadsto 100 \]
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 2024019 
(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)))