Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.56% → 0.26%

Time: 3.4s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

↓

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);
}

↓

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)

↓

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

↓

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

↓

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]

↓

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

Target

Original	0.56%
Target	0.26%
Herbie	0.26%

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

Derivation

1. Initial program 0.56

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

2. Simplified 0.27

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

   [Start] 0.56	\[ \frac{x \cdot 100}{x + y} \]
   associate-/l* [=>] 0.27	\[ \color{blue}{\frac{x}{\frac{x + y}{100}}} \]

3. Applied egg-rr 0.26

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

4. Final simplification 0.26

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

Alternatives

Alternative 1
Error	25.58%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+21} \lor \neg \left(y \leq 62\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 2
Error	25.53%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+22} \lor \neg \left(y \leq 250\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3
Error	25.51%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 52:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]

Alternative 4
Error	49.53%
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2023088 
(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)))