Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 5.0s

Alternatives: 5

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. *-commutative 99.7%

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

   2. associate-/l* 98.5%

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

3. Simplified 98.5%

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

   1. associate-/r/ 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

Alternative 2: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -220000 \lor \neg \left(y \leq 1.5 \cdot 10^{+21}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -220000.0) (not (<= y 1.5e+21))) (* 100.0 (/ x y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -220000.0) || !(y <= 1.5e+21)) {
		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 <= (-220000.0d0)) .or. (.not. (y <= 1.5d+21))) 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 <= -220000.0) || !(y <= 1.5e+21)) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -220000.0) or not (y <= 1.5e+21):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -220000.0) || !(y <= 1.5e+21))
		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 <= -220000.0) || ~((y <= 1.5e+21)))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -220000.0], N[Not[LessEqual[y, 1.5e+21]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e5 or 1.5e21 < 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* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 80.3%

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

   if -2.2e5 < y < 1.5e21

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 80.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -220000 \lor \neg \left(y \leq 1.5 \cdot 10^{+21}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -155000 \lor \neg \left(y \leq 4 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -155000.0) (not (<= y 4e+19))) (* x (/ 100.0 y)) 100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -155000.0) || !(y <= 4e+19)) {
		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 <= (-155000.0d0)) .or. (.not. (y <= 4d+19))) 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 <= -155000.0) || !(y <= 4e+19)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -155000.0) or not (y <= 4e+19):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -155000.0) || !(y <= 4e+19))
		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 <= -155000.0) || ~((y <= 4e+19)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -155000.0], N[Not[LessEqual[y, 4e+19]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -155000 or 4e19 < 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* 97.2%

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

   3. Simplified 97.2%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 80.8%

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

   if -155000 < y < 4e19

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 80.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -155000 \lor \neg \left(y \leq 4 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+16}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1200000.0)
   (* x (/ 100.0 y))
   (if (<= y 4e+16) 100.0 (/ x (* y 0.01)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1200000.0) {
		tmp = x * (100.0 / y);
	} else if (y <= 4e+16) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1200000.0d0)) then
        tmp = x * (100.0d0 / y)
    else if (y <= 4d+16) then
        tmp = 100.0d0
    else
        tmp = x / (y * 0.01d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1200000.0) {
		tmp = x * (100.0 / y);
	} else if (y <= 4e+16) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1200000.0:
		tmp = x * (100.0 / y)
	elif y <= 4e+16:
		tmp = 100.0
	else:
		tmp = x / (y * 0.01)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1200000.0)
		tmp = Float64(x * Float64(100.0 / y));
	elseif (y <= 4e+16)
		tmp = 100.0;
	else
		tmp = Float64(x / Float64(y * 0.01));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1200000.0)
		tmp = x * (100.0 / y);
	elseif (y <= 4e+16)
		tmp = 100.0;
	else
		tmp = x / (y * 0.01);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1200000.0], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+16], 100.0, N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e6

   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* 97.7%

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

   3. Simplified 97.7%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 79.9%

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

   if -1.2e6 < y < 4e16

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 80.2%

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

   if 4e16 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 81.8%

      \[\leadsto \frac{x}{\color{blue}{0.01 \cdot y}} \]
   5. Step-by-step derivation

      1. *-commutative 81.8%

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

   6. Simplified 81.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+16}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]

Alternative 5: 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 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 98.5%

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

3. Simplified 98.5%

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

4. Taylor expanded in x around inf 49.8%

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

5. Final simplification 49.8%

   \[\leadsto 100 \]

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 2023192 
(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)))