Average Error: 58.1 → 58.1
Time: 2.5s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}
↓
\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)
double f() {
        double r59044 = 333.75;
        double r59045 = 33096.0;
        double r59046 = 6.0;
        double r59047 = pow(r59045, r59046);
        double r59048 = r59044 * r59047;
        double r59049 = 77617.0;
        double r59050 = r59049 * r59049;
        double r59051 = 11.0;
        double r59052 = r59051 * r59050;
        double r59053 = r59045 * r59045;
        double r59054 = r59052 * r59053;
        double r59055 = -r59047;
        double r59056 = r59054 + r59055;
        double r59057 = -121.0;
        double r59058 = 4.0;
        double r59059 = pow(r59045, r59058);
        double r59060 = r59057 * r59059;
        double r59061 = r59056 + r59060;
        double r59062 = -2.0;
        double r59063 = r59061 + r59062;
        double r59064 = r59050 * r59063;
        double r59065 = r59048 + r59064;
        double r59066 = 5.5;
        double r59067 = 8.0;
        double r59068 = pow(r59045, r59067);
        double r59069 = r59066 * r59068;
        double r59070 = r59065 + r59069;
        double r59071 = 2.0;
        double r59072 = r59071 * r59045;
        double r59073 = r59049 / r59072;
        double r59074 = r59070 + r59073;
        return r59074;
}
↓
double f() {
        double r59075 = 77617.0;
        double r59076 = 11.0;
        double r59077 = r59075 * r59075;
        double r59078 = r59076 * r59077;
        double r59079 = 33096.0;
        double r59080 = r59079 * r59079;
        double r59081 = r59078 * r59080;
        double r59082 = 6.0;
        double r59083 = pow(r59079, r59082);
        double r59084 = 4.0;
        double r59085 = pow(r59079, r59084);
        double r59086 = -121.0;
        double r59087 = -2.0;
        double r59088 = fma(r59085, r59086, r59087);
        double r59089 = r59083 - r59088;
        double r59090 = r59081 - r59089;
        double r59091 = r59075 * r59090;
        double r59092 = 333.75;
        double r59093 = 8.0;
        double r59094 = pow(r59079, r59093);
        double r59095 = 5.5;
        double r59096 = 2.0;
        double r59097 = r59096 * r59079;
        double r59098 = r59075 / r59097;
        double r59099 = fma(r59094, r59095, r59098);
        double r59100 = fma(r59092, r59083, r59099);
        double r59101 = fma(r59075, r59091, r59100);
        return r59101;
}

Error

Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]

  2. Simplified58.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)}\]

  3. Simplified58.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)}\]

  4. Final simplification58.1

    \[\leadsto \mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020014 +o rules:numerics
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096))))