Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 5.2s

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

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

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(x * Float64(100.0 / Float64(x + y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-*r/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+46} \lor \neg \left(y \leq -2.9 \cdot 10^{+31}\right) \land \left(y \leq -3.8 \cdot 10^{-70} \lor \neg \left(y \leq 450 \lor \neg \left(y \leq 3.1 \cdot 10^{+29}\right) \land y \leq 10^{+78}\right)\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.5e+46)
         (and (not (<= y -2.9e+31))
              (or (<= y -3.8e-70)
                  (not
                   (or (<= y 450.0)
                       (and (not (<= y 3.1e+29)) (<= y 1e+78)))))))
   (* x (/ 100.0 y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.5e+46) || (!(y <= -2.9e+31) && ((y <= -3.8e-70) || !((y <= 450.0) || (!(y <= 3.1e+29) && (y <= 1e+78)))))) {
		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 ((y <= (-8.5d+46)) .or. (.not. (y <= (-2.9d+31))) .and. (y <= (-3.8d-70)) .or. (.not. (y <= 450.0d0) .or. (.not. (y <= 3.1d+29)) .and. (y <= 1d+78))) 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 ((y <= -8.5e+46) || (!(y <= -2.9e+31) && ((y <= -3.8e-70) || !((y <= 450.0) || (!(y <= 3.1e+29) && (y <= 1e+78)))))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.5e+46) or (not (y <= -2.9e+31) and ((y <= -3.8e-70) or not ((y <= 450.0) or (not (y <= 3.1e+29) and (y <= 1e+78))))):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.5e+46) || (!(y <= -2.9e+31) && ((y <= -3.8e-70) || !((y <= 450.0) || (!(y <= 3.1e+29) && (y <= 1e+78))))))
		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 ((y <= -8.5e+46) || (~((y <= -2.9e+31)) && ((y <= -3.8e-70) || ~(((y <= 450.0) || (~((y <= 3.1e+29)) && (y <= 1e+78)))))))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.5e+46], And[N[Not[LessEqual[y, -2.9e+31]], $MachinePrecision], Or[LessEqual[y, -3.8e-70], N[Not[Or[LessEqual[y, 450.0], And[N[Not[LessEqual[y, 3.1e+29]], $MachinePrecision], LessEqual[y, 1e+78]]]], $MachinePrecision]]]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999996e46 or -2.9e31 < y < -3.7999999999999998e-70 or 450 < y < 3.0999999999999999e29 or 1.00000000000000001e78 < y

   1. Initial program 99.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 85.5%

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

   if -8.4999999999999996e46 < y < -2.9e31 or -3.7999999999999998e-70 < y < 450 or 3.0999999999999999e29 < y < 1.00000000000000001e78

   1. Initial program 99.7%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 80.3%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+46} \lor \neg \left(y \leq -2.9 \cdot 10^{+31}\right) \land \left(y \leq -3.8 \cdot 10^{-70} \lor \neg \left(y \leq 450 \lor \neg \left(y \leq 3.1 \cdot 10^{+29}\right) \land y \leq 10^{+78}\right)\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+31}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-70} \lor \neg \left(y \leq 48 \lor \neg \left(y \leq 2.3 \cdot 10^{+28}\right) \land y \leq 2.2 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.5e+47)
   (/ (* x 100.0) y)
   (if (<= y -2.1e+31)
     100.0
     (if (or (<= y -3.9e-70)
             (not (or (<= y 48.0) (and (not (<= y 2.3e+28)) (<= y 2.2e+80)))))
       (* x (/ 100.0 y))
       100.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.5e+47) {
		tmp = (x * 100.0) / y;
	} else if (y <= -2.1e+31) {
		tmp = 100.0;
	} else if ((y <= -3.9e-70) || !((y <= 48.0) || (!(y <= 2.3e+28) && (y <= 2.2e+80)))) {
		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 (y <= (-1.5d+47)) then
        tmp = (x * 100.0d0) / y
    else if (y <= (-2.1d+31)) then
        tmp = 100.0d0
    else if ((y <= (-3.9d-70)) .or. (.not. (y <= 48.0d0) .or. (.not. (y <= 2.3d+28)) .and. (y <= 2.2d+80))) 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 (y <= -1.5e+47) {
		tmp = (x * 100.0) / y;
	} else if (y <= -2.1e+31) {
		tmp = 100.0;
	} else if ((y <= -3.9e-70) || !((y <= 48.0) || (!(y <= 2.3e+28) && (y <= 2.2e+80)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.5e+47:
		tmp = (x * 100.0) / y
	elif y <= -2.1e+31:
		tmp = 100.0
	elif (y <= -3.9e-70) or not ((y <= 48.0) or (not (y <= 2.3e+28) and (y <= 2.2e+80))):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.5e+47)
		tmp = Float64(Float64(x * 100.0) / y);
	elseif (y <= -2.1e+31)
		tmp = 100.0;
	elseif ((y <= -3.9e-70) || !((y <= 48.0) || (!(y <= 2.3e+28) && (y <= 2.2e+80))))
		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 (y <= -1.5e+47)
		tmp = (x * 100.0) / y;
	elseif (y <= -2.1e+31)
		tmp = 100.0;
	elseif ((y <= -3.9e-70) || ~(((y <= 48.0) || (~((y <= 2.3e+28)) && (y <= 2.2e+80)))))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.5e+47], N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.1e+31], 100.0, If[Or[LessEqual[y, -3.9e-70], N[Not[Or[LessEqual[y, 48.0], And[N[Not[LessEqual[y, 2.3e+28]], $MachinePrecision], LessEqual[y, 2.2e+80]]]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e47

   1. Initial program 99.8%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 81.9%

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

      1. associate-*r/ 81.9%

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

   6. Applied egg-rr 81.9%

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

   if -1.5000000000000001e47 < y < -2.09999999999999979e31 or -3.90000000000000019e-70 < y < 48 or 2.29999999999999984e28 < y < 2.20000000000000003e80

   1. Initial program 99.7%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 80.3%

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

   if -2.09999999999999979e31 < y < -3.90000000000000019e-70 or 48 < y < 2.29999999999999984e28 or 2.20000000000000003e80 < y

   1. Initial program 99.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 87.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+31}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-70} \lor \neg \left(y \leq 48 \lor \neg \left(y \leq 2.3 \cdot 10^{+28}\right) \land y \leq 2.2 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 51.1% 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. associate-*r/ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 49.1%

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

5. Final simplification 49.1%

   \[\leadsto 100 \]

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 2023297 
(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)))