Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.49% → 0.26%

Time: 3.7s

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	0.49%
Target	0.25%
Herbie	0.26%

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

Derivation

1. Initial program 0.49

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

2. Simplified 0.27

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

   [Start] 0.49	\[ \frac{x \cdot 100}{x + y} \]
   associate-/l* [=>] 0.27	\[ \color{blue}{\frac{x}{\frac{x + y}{100}}} \]

3. Applied egg-rr 0.26

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

4. Final simplification 0.26

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

Alternatives

Alternative 1
Error	26.47%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-96}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+16} \lor \neg \left(x \leq 1.55 \cdot 10^{+122}\right) \land x \leq 3.3 \cdot 10^{+145}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 2
Error	26.81%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+145}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3
Error	26.48%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-98}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+145}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4
Error	0.25%
Cost	448

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

Alternative 5
Error	49.01%
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2023121 
(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)))