Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 3.3s

Alternatives: 6

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] * 100.0), $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* 99.6%

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

3. Simplified 99.6%

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

   1. div-inv 99.5%

      \[\leadsto \color{blue}{100 \cdot \frac{1}{\frac{x + y}{x}}} \]

   2. clear-num 99.8%

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

   3. *-commutative 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 0.0008:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.6e+45) 100.0 (if (<= x 0.0008) (* 100.0 (/ x y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e+45) {
		tmp = 100.0;
	} else if (x <= 0.0008) {
		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 <= (-1.6d+45)) then
        tmp = 100.0d0
    else if (x <= 0.0008d0) 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 <= -1.6e+45) {
		tmp = 100.0;
	} else if (x <= 0.0008) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e+45:
		tmp = 100.0
	elif x <= 0.0008:
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e+45)
		tmp = 100.0;
	elseif (x <= 0.0008)
		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 <= -1.6e+45)
		tmp = 100.0;
	elseif (x <= 0.0008)
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e+45], 100.0, If[LessEqual[x, 0.0008], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e45 or 8.00000000000000038e-4 < x

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 82.5%

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

   if -1.6000000000000001e45 < x < 8.00000000000000038e-4

   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* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 77.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 0.0008:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 0.00027:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.15e+45) 100.0 (if (<= x 0.00027) (* x (/ 100.0 y)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.15e+45) {
		tmp = 100.0;
	} else if (x <= 0.00027) {
		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 <= (-2.15d+45)) then
        tmp = 100.0d0
    else if (x <= 0.00027d0) 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 <= -2.15e+45) {
		tmp = 100.0;
	} else if (x <= 0.00027) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.15e+45:
		tmp = 100.0
	elif x <= 0.00027:
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.15e+45)
		tmp = 100.0;
	elseif (x <= 0.00027)
		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 <= -2.15e+45)
		tmp = 100.0;
	elseif (x <= 0.00027)
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.15e+45], 100.0, If[LessEqual[x, 0.00027], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1500000000000002e45 or 2.70000000000000003e-4 < x

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 82.5%

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

   if -2.1500000000000002e45 < x < 2.70000000000000003e-4

   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* 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
   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 77.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 0.00027:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 0.00029:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.5e+45) 100.0 (if (<= x 0.00029) (/ x (* y 0.01)) 100.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.5e+45) {
		tmp = 100.0;
	} else if (x <= 0.00029) {
		tmp = x / (y * 0.01);
	} 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 <= (-8.5d+45)) then
        tmp = 100.0d0
    else if (x <= 0.00029d0) then
        tmp = x / (y * 0.01d0)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8.5e+45) {
		tmp = 100.0;
	} else if (x <= 0.00029) {
		tmp = x / (y * 0.01);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.5e+45:
		tmp = 100.0
	elif x <= 0.00029:
		tmp = x / (y * 0.01)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.5e+45)
		tmp = 100.0;
	elseif (x <= 0.00029)
		tmp = Float64(x / Float64(y * 0.01));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.5e+45)
		tmp = 100.0;
	elseif (x <= 0.00029)
		tmp = x / (y * 0.01);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.5e+45], 100.0, If[LessEqual[x, 0.00029], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], 100.0]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4999999999999996e45 or 2.9e-4 < x

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 82.5%

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

   if -8.4999999999999996e45 < x < 2.9e-4

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 77.1%

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

      1. *-commutative 77.1%

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

   6. Simplified 77.1%

      \[\leadsto \frac{x}{\color{blue}{y \cdot 0.01}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+45}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 0.00029:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5: 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 99.3%

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

   1. *-commutative 99.3%

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

   2. associate-/l* 99.6%

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

3. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
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 6: 50.9% 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* 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around inf 50.5%

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

5. Final simplification 50.5%

   \[\leadsto 100 \]

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 2023196 
(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)))