Development.Shake.Progress:message from shake-0.15.5

Average Accuracy: 99.5% → 99.7%

Time: 5.3s

Precision: binary64

Cost: 448

Math

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

↓

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

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(x / Float64(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[(x / N[(N[(x + y), $MachinePrecision] / 100.0), $MachinePrecision]), $MachinePrecision]

Target

Original	99.5%
Target	99.7%
Herbie	99.7%

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

Derivation

1. Initial program 99.5%

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

2. Simplified 99.7%

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

   [Start] 99.5	\[ \frac{x \cdot 100}{x + y} \]
   associate-/l* [=>] 99.7	\[ \color{blue}{\frac{x}{\frac{x + y}{100}}} \]

3. Final simplification 99.7%

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

Alternatives

Alternative 1
Accuracy	73.4%
Cost	1114

\[\begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-12} \lor \neg \left(x \leq -1.6 \cdot 10^{-38}\right) \land \left(x \leq 3.4 \cdot 10^{-193} \lor \neg \left(x \leq 9.5 \cdot 10^{-181}\right) \land x \leq 1.3 \cdot 10^{+34}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 2
Accuracy	73.5%
Cost	1114

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-12} \lor \neg \left(x \leq -2.2 \cdot 10^{-38}\right) \land \left(x \leq 3.4 \cdot 10^{-193} \lor \neg \left(x \leq 9.5 \cdot 10^{-181}\right) \land x \leq 1.95 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3
Accuracy	73.5%
Cost	1113

\[\begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{+16}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-39}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-193} \lor \neg \left(x \leq 9.5 \cdot 10^{-181}\right) \land x \leq 2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4
Accuracy	73.4%
Cost	1112

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+18}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5
Accuracy	99.7%
Cost	448

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

Alternative 6
Accuracy	50.1%
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2023151 
(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)))