(+ (+ (/ x 3) (/ x 5)) (/ x 6))

Average Error: 0.3 → 0.3

Time: 602.0ms

Precision: binary64

• could not determine a ground truth for program body

  1. x = -6.29987895111135e-96

Math

\[\left(\frac{x}{3} + \frac{x}{5}\right) + \frac{x}{6}\]

↓

\[\left(\frac{x}{3} + \frac{x}{5}\right) + \frac{x}{6}\]

C

double code(double x) {
	return ((double) (((double) (((double) (x / 3.0)) + ((double) (x / 5.0)))) + ((double) (x / 6.0))));
}

↓

double code(double x) {
	return ((double) (((double) (((double) (x / 3.0)) + ((double) (x / 5.0)))) + ((double) (x / 6.0))));
}

Error

Bits error versus x

Derivation

1. Initial program 0.3

   \[\left(\frac{x}{3} + \frac{x}{5}\right) + \frac{x}{6}\]

2. Final simplification 0.3

   \[\leadsto \left(\frac{x}{3} + \frac{x}{5}\right) + \frac{x}{6}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (+ (/ x 3) (/ x 5)) (/ x 6))"
  :precision binary64
  (+ (+ (/ x 3.0) (/ x 5.0)) (/ x 6.0)))