(pow (- (+ (- x1) (sqrt (- (pow (+ x1 1) 2) 1))) 1) (/ 1 3))

Average Error: 34.4 → 34.4

Time: 6.9s

Precision: binary64

• could not determine a ground truth for program body

  1. x1 = -4.5470520620794555e-15

Math

\[{\left(\left(\left(-x1\right) + \sqrt{{\left(x1 + 1\right)}^{2} - 1}\right) - 1\right)}^{\left(\frac{1}{3}\right)}\]

↓

\[{\left(\left(\left(-x1\right) + \sqrt{{\left(x1 + 1\right)}^{2} - 1}\right) - 1\right)}^{\left(\frac{1}{3}\right)}\]

Error

Bits error versus x1

Derivation

1. Initial program 34.4

   \[{\left(\left(\left(-x1\right) + \sqrt{{\left(x1 + 1\right)}^{2} - 1}\right) - 1\right)}^{\left(\frac{1}{3}\right)}\]

2. Final simplification 34.4

   \[\leadsto {\left(\left(\left(-x1\right) + \sqrt{{\left(x1 + 1\right)}^{2} - 1}\right) - 1\right)}^{\left(\frac{1}{3}\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x1)
  :name "(pow (- (+ (- x1) (sqrt (- (pow (+ x1 1) 2) 1))) 1) (/ 1 3))"
  :precision binary64
  (pow (- (+ (neg x1) (sqrt (- (pow (+ x1 1.0) 2.0) 1.0))) 1.0) (/ 1.0 3.0)))