Average Error: 39.5 → 39.5
Time: 8.6s
Precision: binary64
\[\frac{\sqrt{\frac{\sqrt{5} \cdot \sqrt{\left(-{h}^{5}\right) \cdot \left(\left(h + 6 \cdot T\right) - 6 \cdot x\right)} - 5 \cdot {h}^{3}}{\left(h + T\right) - x}}}{4 \cdot \sqrt{15}}\]
↓
\[\frac{\sqrt{\frac{\sqrt{5} \cdot \sqrt{\left(-{h}^{5}\right) \cdot \left(\left(h + 6 \cdot T\right) - 6 \cdot x\right)} - 5 \cdot {h}^{3}}{\left(h + T\right) - x}}}{4 \cdot \sqrt{15}}\]

Error

Bits error versus h

Bits error versus T

Bits error versus x

Derivation

  1. Initial program 39.5

    \[\frac{\sqrt{\frac{\sqrt{5} \cdot \sqrt{\left(-{h}^{5}\right) \cdot \left(\left(h + 6 \cdot T\right) - 6 \cdot x\right)} - 5 \cdot {h}^{3}}{\left(h + T\right) - x}}}{4 \cdot \sqrt{15}}\]

  2. Final simplification39.5

    \[\leadsto \frac{\sqrt{\frac{\sqrt{5} \cdot \sqrt{\left(-{h}^{5}\right) \cdot \left(\left(h + 6 \cdot T\right) - 6 \cdot x\right)} - 5 \cdot {h}^{3}}{\left(h + T\right) - x}}}{4 \cdot \sqrt{15}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (h T x)
  :name "(/ (sqrt (/ (- (* (sqrt 5) (sqrt (* (- (pow h 5)) (- (+ h (* 6 T)) (* 6 x))))) (* 5 (pow h 3))) (- (+ h T) x))) (* 4 (sqrt 15)))"
  :precision binary64
  (/ (sqrt (/ (- (* (sqrt 5.0) (sqrt (* (neg (pow h 5.0)) (- (+ h (* 6.0 T)) (* 6.0 x))))) (* 5.0 (pow h 3.0))) (- (+ h T) x))) (* 4.0 (sqrt 15.0))))