Average Error: 43.4 → 43.4
Time: 2.1s
Precision: binary64
\[\frac{\left(-1\right) + \sqrt{1 + \left(\left(4 \cdot \left(\left(-1\right) + x\right)\right) \cdot x\right) \cdot \left(1 - 4 \cdot y\right)}}{\left(-1\right) + 4 \cdot y}\]
↓
\[\frac{\left(-1\right) + \sqrt{1 + \left(\left(4 \cdot \left(\left(-1\right) + x\right)\right) \cdot x\right) \cdot \left(1 - 4 \cdot y\right)}}{\left(-1\right) + 4 \cdot y}\]

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 43.4

    \[\frac{\left(-1\right) + \sqrt{1 + \left(\left(4 \cdot \left(\left(-1\right) + x\right)\right) \cdot x\right) \cdot \left(1 - 4 \cdot y\right)}}{\left(-1\right) + 4 \cdot y}\]

  2. Final simplification43.4

    \[\leadsto \frac{\left(-1\right) + \sqrt{1 + \left(\left(4 \cdot \left(\left(-1\right) + x\right)\right) \cdot x\right) \cdot \left(1 - 4 \cdot y\right)}}{\left(-1\right) + 4 \cdot y}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(/ (+ (- 1) (sqrt (+ 1 (* (* (* 4 (+ (- 1) x)) x) (- 1 (* 4 y)))))) (+ (- 1) (* 4 y)))"
  :precision binary64
  (/ (+ (neg 1.0) (sqrt (+ 1.0 (* (* (* 4.0 (+ (neg 1.0) x)) x) (- 1.0 (* 4.0 y)))))) (+ (neg 1.0) (* 4.0 y))))