Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.8%

Time: 3.6s

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: 99.5% 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: 99.8% 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 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-112} \lor \neg \left(x \leq -7.702 \cdot 10^{-163}\right) \land x \leq 3.3 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.15e+80)
   100.0
   (if (or (<= x -2.8e-112) (and (not (<= x -7.702e-163)) (<= x 3.3e-33)))
     (* x (/ 100.0 y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.15e+80) {
		tmp = 100.0;
	} else if ((x <= -2.8e-112) || (!(x <= -7.702e-163) && (x <= 3.3e-33))) {
		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 <= (-1.15d+80)) then
        tmp = 100.0d0
    else if ((x <= (-2.8d-112)) .or. (.not. (x <= (-7.702d-163))) .and. (x <= 3.3d-33)) 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 <= -1.15e+80) {
		tmp = 100.0;
	} else if ((x <= -2.8e-112) || (!(x <= -7.702e-163) && (x <= 3.3e-33))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.15e+80:
		tmp = 100.0
	elif (x <= -2.8e-112) or (not (x <= -7.702e-163) and (x <= 3.3e-33)):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.15e+80)
		tmp = 100.0;
	elseif ((x <= -2.8e-112) || (!(x <= -7.702e-163) && (x <= 3.3e-33)))
		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 <= -1.15e+80)
		tmp = 100.0;
	elseif ((x <= -2.8e-112) || (~((x <= -7.702e-163)) && (x <= 3.3e-33)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.15e+80], 100.0, If[Or[LessEqual[x, -2.8e-112], And[N[Not[LessEqual[x, -7.702e-163]], $MachinePrecision], LessEqual[x, 3.3e-33]]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15000000000000002e80 or -2.80000000000000023e-112 < x < -7.70200000000000006e-163 or 3.3000000000000003e-33 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 80.7%

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

   if -1.15000000000000002e80 < x < -2.80000000000000023e-112 or -7.70200000000000006e-163 < x < 3.3000000000000003e-33

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0 79.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-112} \lor \neg \left(x \leq -7.702 \cdot 10^{-163}\right) \land x \leq 3.3 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-115} \lor \neg \left(x \leq -7.702 \cdot 10^{-163}\right) \land x \leq 5.6 \cdot 10^{-34}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.15e+80)
   100.0
   (if (or (<= x -2.8e-115) (and (not (<= x -7.702e-163)) (<= x 5.6e-34)))
     (* 100.0 (/ x y))
     100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.15e+80) {
		tmp = 100.0;
	} else if ((x <= -2.8e-115) || (!(x <= -7.702e-163) && (x <= 5.6e-34))) {
		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 <= (-1.15d+80)) then
        tmp = 100.0d0
    else if ((x <= (-2.8d-115)) .or. (.not. (x <= (-7.702d-163))) .and. (x <= 5.6d-34)) 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 <= -1.15e+80) {
		tmp = 100.0;
	} else if ((x <= -2.8e-115) || (!(x <= -7.702e-163) && (x <= 5.6e-34))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.15e+80:
		tmp = 100.0
	elif (x <= -2.8e-115) or (not (x <= -7.702e-163) and (x <= 5.6e-34)):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.15e+80)
		tmp = 100.0;
	elseif ((x <= -2.8e-115) || (!(x <= -7.702e-163) && (x <= 5.6e-34)))
		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 <= -1.15e+80)
		tmp = 100.0;
	elseif ((x <= -2.8e-115) || (~((x <= -7.702e-163)) && (x <= 5.6e-34)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.15e+80], 100.0, If[Or[LessEqual[x, -2.8e-115], And[N[Not[LessEqual[x, -7.702e-163]], $MachinePrecision], LessEqual[x, 5.6e-34]]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15000000000000002e80 or -2.79999999999999987e-115 < x < -7.70200000000000006e-163 or 5.59999999999999994e-34 < x

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 80.7%

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

   if -1.15000000000000002e80 < x < -2.79999999999999987e-115 or -7.70200000000000006e-163 < x < 5.59999999999999994e-34

   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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 79.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-115} \lor \neg \left(x \leq -7.702 \cdot 10^{-163}\right) \land x \leq 5.6 \cdot 10^{-34}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf 47.5%

   \[\leadsto \color{blue}{100} \]
6. Add Preprocessing

Developer target: 99.8% 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 2024101 
(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)))