Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 4.6s

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: 99.4% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-50} \lor \neg \left(x \leq 2.75 \cdot 10^{-6}\right) \land x \leq 1.4 \cdot 10^{+30}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.7e-77)
   100.0
   (if (or (<= x 3.4e-50) (and (not (<= x 2.75e-6)) (<= x 1.4e+30)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.7e-77) {
		tmp = 100.0;
	} else if ((x <= 3.4e-50) || (!(x <= 2.75e-6) && (x <= 1.4e+30))) {
		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 <= (-1.7d-77)) then
        tmp = 100.0d0
    else if ((x <= 3.4d-50) .or. (.not. (x <= 2.75d-6)) .and. (x <= 1.4d+30)) 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 <= -1.7e-77) {
		tmp = 100.0;
	} else if ((x <= 3.4e-50) || (!(x <= 2.75e-6) && (x <= 1.4e+30))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.7e-77:
		tmp = 100.0
	elif (x <= 3.4e-50) or (not (x <= 2.75e-6) and (x <= 1.4e+30)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.7e-77)
		tmp = 100.0;
	elseif ((x <= 3.4e-50) || (!(x <= 2.75e-6) && (x <= 1.4e+30)))
		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 <= -1.7e-77)
		tmp = 100.0;
	elseif ((x <= 3.4e-50) || (~((x <= 2.75e-6)) && (x <= 1.4e+30)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.7e-77], 100.0, If[Or[LessEqual[x, 3.4e-50], And[N[Not[LessEqual[x, 2.75e-6]], $MachinePrecision], LessEqual[x, 1.4e+30]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999991e-77 or 3.40000000000000014e-50 < x < 2.7499999999999999e-6 or 1.39999999999999992e30 < x

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.9%

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

   if -1.69999999999999991e-77 < x < 3.40000000000000014e-50 or 2.7499999999999999e-6 < x < 1.39999999999999992e30

   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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 82.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-50} \lor \neg \left(x \leq 2.75 \cdot 10^{-6}\right) \land x \leq 1.4 \cdot 10^{+30}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-79}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-51} \lor \neg \left(x \leq 1.4 \cdot 10^{-6}\right) \land x \leq 1.12 \cdot 10^{+28}:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.12e-79)
   100.0
   (if (or (<= x 5.4e-51) (and (not (<= x 1.4e-6)) (<= x 1.12e+28)))
     (/ (* 100.0 x) y)
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.12e-79) {
		tmp = 100.0;
	} else if ((x <= 5.4e-51) || (!(x <= 1.4e-6) && (x <= 1.12e+28))) {
		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 <= (-1.12d-79)) then
        tmp = 100.0d0
    else if ((x <= 5.4d-51) .or. (.not. (x <= 1.4d-6)) .and. (x <= 1.12d+28)) 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 <= -1.12e-79) {
		tmp = 100.0;
	} else if ((x <= 5.4e-51) || (!(x <= 1.4e-6) && (x <= 1.12e+28))) {
		tmp = (100.0 * x) / y;
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.12e-79:
		tmp = 100.0
	elif (x <= 5.4e-51) or (not (x <= 1.4e-6) and (x <= 1.12e+28)):
		tmp = (100.0 * x) / y
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.12e-79)
		tmp = 100.0;
	elseif ((x <= 5.4e-51) || (!(x <= 1.4e-6) && (x <= 1.12e+28)))
		tmp = Float64(Float64(100.0 * x) / y);
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.12e-79)
		tmp = 100.0;
	elseif ((x <= 5.4e-51) || (~((x <= 1.4e-6)) && (x <= 1.12e+28)))
		tmp = (100.0 * x) / y;
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.12e-79], 100.0, If[Or[LessEqual[x, 5.4e-51], And[N[Not[LessEqual[x, 1.4e-6]], $MachinePrecision], LessEqual[x, 1.12e+28]]], N[(N[(100.0 * x), $MachinePrecision] / y), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.11999999999999996e-79 or 5.3999999999999994e-51 < x < 1.39999999999999994e-6 or 1.12e28 < x

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.9%

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

   if -1.11999999999999996e-79 < x < 5.3999999999999994e-51 or 1.39999999999999994e-6 < x < 1.12e28

   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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 82.1%

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

      1. associate-/l* 82.3%

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

   7. Simplified 82.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-79}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-51} \lor \neg \left(x \leq 1.4 \cdot 10^{-6}\right) \land x \leq 1.12 \cdot 10^{+28}:\\ \;\;\;\;\frac{100 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.8% 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 53.1%

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

6. Final simplification 53.1%

   \[\leadsto 100 \]
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 2024078 
(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)))