Average Error: 52.0 → 0
Time: 2.0s
Precision: binary64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]
↓
\[\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) + \mathsf{fma}\left(-y \cdot y, y \cdot y, {y}^{4}\right)\right) + \left(y \cdot y\right) \cdot 2 \]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) + \mathsf{fma}\left(-y \cdot y, y \cdot y, {y}^{4}\right)\right) + \left(y \cdot y\right) \cdot 2

(FPCore (x y)
 :precision binary64
 (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (+
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (fma (- (* y y)) (* y y) (pow y 4.0)))
  (* (* y y) 2.0)))
double code(double x, double y) {
	return ((9.0 * pow(x, 4.0)) - pow(y, 4.0)) + (2.0 * (y * y));
}
↓
double code(double x, double y) {
	return (((9.0 * pow(x, 4.0)) - pow(y, 4.0)) + fma(-(y * y), (y * y), pow(y, 4.0))) + ((y * y) * 2.0);
}

Error

Derivation

  1. Initial program 52.0

    \[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]

  2. Applied egg-rr0

    \[\leadsto \color{blue}{\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) + \mathsf{fma}\left(-y \cdot y, y \cdot y, {y}^{4}\right)\right)} + 2 \cdot \left(y \cdot y\right) \]

  3. Final simplification0

    \[\leadsto \left(\left(9 \cdot {x}^{4} - {y}^{4}\right) + \mathsf{fma}\left(-y \cdot y, y \cdot y, {y}^{4}\right)\right) + \left(y \cdot y\right) \cdot 2 \]

Reproduce

herbie shell --seed 2022125 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))