Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 3.2s

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: 99.5% 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: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\left(x + y\right) \cdot 0.01} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* (+ x y) 0.01)))

C

double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / ((x + y) * 0.01d0)
end function

Java

public static double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Python

def code(x, y):
	return x / ((x + y) * 0.01)

Julia

function code(x, y)
	return Float64(x / Float64(Float64(x + y) * 0.01))
end

MATLAB

function tmp = code(x, y)
	tmp = x / ((x + y) * 0.01);
end

Wolfram

code[x_, y_] := N[(x / N[(N[(x + y), $MachinePrecision] * 0.01), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. *-commutative 99.2%

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

   2. associate-/l* 99.5%

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

3. Simplified 99.5%

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

   1. associate-/l* 99.2%

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

   2. *-commutative 99.2%

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

   3. expm1-log1p-u 98.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

   4. expm1-udef 54.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

   5. associate-/l* 55.2%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

   6. div-inv 55.2%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

   7. metadata-eval 55.2%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

6. Applied egg-rr 55.2%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot 0.01}\right)} - 1} \]
7. Step-by-step derivation

   1. expm1-def 98.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(x + y\right) \cdot 0.01}\right)\right)} \]

   2. expm1-log1p 99.6%

      \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

8. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

9. Final simplification 99.6%

   \[\leadsto \frac{x}{\left(x + y\right) \cdot 0.01} \]
10. Add Preprocessing

Alternative 2: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.2e+17) 100.0 (if (<= x 2.15e+155) (* 100.0 (/ x y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+17) {
		tmp = 100.0;
	} else if (x <= 2.15e+155) {
		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 <= (-9.2d+17)) then
        tmp = 100.0d0
    else if (x <= 2.15d+155) 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 <= -9.2e+17) {
		tmp = 100.0;
	} else if (x <= 2.15e+155) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.2e+17:
		tmp = 100.0
	elif x <= 2.15e+155:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.2e+17)
		tmp = 100.0;
	elseif (x <= 2.15e+155)
		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 <= -9.2e+17)
		tmp = 100.0;
	elseif (x <= 2.15e+155)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.2e+17], 100.0, If[LessEqual[x, 2.15e+155], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2e17 or 2.1500000000000001e155 < x

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around inf 78.9%

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

   if -9.2e17 < x < 2.1500000000000001e155

   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* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 80.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+17}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.6e+17) 100.0 (if (<= x 2.15e+155) (* x (/ 100.0 y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.6e+17) {
		tmp = 100.0;
	} else if (x <= 2.15e+155) {
		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 <= (-6.6d+17)) then
        tmp = 100.0d0
    else if (x <= 2.15d+155) 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 <= -6.6e+17) {
		tmp = 100.0;
	} else if (x <= 2.15e+155) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.6e+17:
		tmp = 100.0
	elif x <= 2.15e+155:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.6e+17)
		tmp = 100.0;
	elseif (x <= 2.15e+155)
		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 <= -6.6e+17)
		tmp = 100.0;
	elseif (x <= 2.15e+155)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.6e+17], 100.0, If[LessEqual[x, 2.15e+155], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e17 or 2.1500000000000001e155 < x

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around inf 78.9%

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

   if -6.6e17 < x < 2.1500000000000001e155

   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* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 80.9%

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

      1. associate-*r/ 80.8%

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

      2. associate-/l* 80.5%

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

      3. associate-/r/ 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+17}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. *-commutative 99.2%

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

   2. associate-/l* 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 5: 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 99.2%

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

   1. *-commutative 99.2%

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

   2. associate-/l* 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around inf 39.6%

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

6. Final simplification 39.6%

   \[\leadsto 100 \]
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 2024029 
(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)))