Development.Shake.Progress:message from shake-0.15.5

Average Accuracy: 99.4% → 99.7%

Time: 5.7s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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 * 100.0d0) / (x + y)
end function

↓

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 * 100.0) / (x + y);
}

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	99.4%
Target	99.7%
Herbie	99.7%

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

Derivation

1. Initial program 99.4%

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

2. Simplified 99.7%

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

   [Start] 99.4	\[ \frac{x \cdot 100}{x + y} \]
   associate-/l* [=>] 99.7	\[ \color{blue}{\frac{x}{\frac{x + y}{100}}} \]

3. Applied egg-rr 99.7%

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

   [Start] 99.7	\[ \frac{x}{\frac{x + y}{100}} \]
   associate-/r/ [=>] 99.7	\[ \color{blue}{\frac{x}{x + y} \cdot 100} \]

4. Final simplification 99.7%

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

Alternatives

Alternative 1
Accuracy	73.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-101}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 2
Accuracy	73.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-101}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3
Accuracy	73.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-101}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4
Accuracy	99.7%
Cost	448

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

Alternative 5
Accuracy	50.5%
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2023133 
(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)))