Average Error: 0.1 → 0.1
Time: 5.6s
Precision: binary64
\[\frac{-\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-63\right) + 252 \cdot u\right) + 1008 \cdot {u}^{2}\right) - 5040 \cdot {u}^{3}\right) - 5040 \cdot {u}^{4}\right) + 40320 \cdot {u}^{5}\right) - 161280 \cdot {u}^{7}\right) + 80640 \cdot {u}^{8}\right) + 322560 \cdot {u}^{9}\right) - 258048 \cdot {u}^{10}\right) - 258048 \cdot {u}^{11}\right) + 258048 \cdot {u}^{12}\right)}{1024}\]
↓
\[\frac{-258048 \cdot {u}^{12}}{1024} - \frac{\left(\left(\left(40320 \cdot {u}^{5} - 161280 \cdot {u}^{7}\right) + \left(252 \cdot u - 63\right)\right) + \left(1008 \cdot {u}^{2} - 5040 \cdot \left({u}^{3} + {u}^{4}\right)\right)\right) + \left(80640 \cdot {u}^{8} + \left(322560 \cdot {u}^{9} - 258048 \cdot \left({u}^{10} + {u}^{11}\right)\right)\right)}{1024}\]

Error

Bits error versus u

Derivation

  1. Initial program 0.1

    \[\frac{-\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-63\right) + 252 \cdot u\right) + 1008 \cdot {u}^{2}\right) - 5040 \cdot {u}^{3}\right) - 5040 \cdot {u}^{4}\right) + 40320 \cdot {u}^{5}\right) - 161280 \cdot {u}^{7}\right) + 80640 \cdot {u}^{8}\right) + 322560 \cdot {u}^{9}\right) - 258048 \cdot {u}^{10}\right) - 258048 \cdot {u}^{11}\right) + 258048 \cdot {u}^{12}\right)}{1024}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{-258048 \cdot {u}^{12}}{1024} - \frac{\left(\left(\left(40320 \cdot {u}^{5} - 161280 \cdot {u}^{7}\right) + \left(252 \cdot u - 63\right)\right) + \left(1008 \cdot {u}^{2} - 5040 \cdot \left({u}^{3} + {u}^{4}\right)\right)\right) + \left(80640 \cdot {u}^{8} + \left(322560 \cdot {u}^{9} - 258048 \cdot \left({u}^{10} + {u}^{11}\right)\right)\right)}{1024}}\]

  3. Final simplification0.1

    \[\leadsto \frac{-258048 \cdot {u}^{12}}{1024} - \frac{\left(\left(\left(40320 \cdot {u}^{5} - 161280 \cdot {u}^{7}\right) + \left(252 \cdot u - 63\right)\right) + \left(1008 \cdot {u}^{2} - 5040 \cdot \left({u}^{3} + {u}^{4}\right)\right)\right) + \left(80640 \cdot {u}^{8} + \left(322560 \cdot {u}^{9} - 258048 \cdot \left({u}^{10} + {u}^{11}\right)\right)\right)}{1024}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (u)
  :name "(/ (- (+ (- (- (+ (+ (- (+ (- (- (+ (+ (- 63) (* 252 u)) (* 1008 (pow u 2))) (* 5040 (pow u 3))) (* 5040 (pow u 4))) (* 40320 (pow u 5))) (* 161280 (pow u 7))) (* 80640 (pow u 8))) (* 322560 (pow u 9))) (* 258048 (pow u 10))) (* 258048 (pow u 11))) (* 258048 (pow u 12)))) 1024)"
  :precision binary64
  (/ (neg (+ (- (- (+ (+ (- (+ (- (- (+ (+ (neg 63.0) (* 252.0 u)) (* 1008.0 (pow u 2.0))) (* 5040.0 (pow u 3.0))) (* 5040.0 (pow u 4.0))) (* 40320.0 (pow u 5.0))) (* 161280.0 (pow u 7.0))) (* 80640.0 (pow u 8.0))) (* 322560.0 (pow u 9.0))) (* 258048.0 (pow u 10.0))) (* 258048.0 (pow u 11.0))) (* 258048.0 (pow u 12.0)))) 1024.0))