Henrywood and Agarwal, Equation (13)

Average Error: 59.0 → 33.8

Time: 33.1s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 1.2280580520810868e+214
  2. w = 2.1166426636481225e-72
  3. h = -2.4555874599104177e+190
  4. D = -3.692100551129768e-209
  5. d = -4.964062979692867e+221
  6. M = -4.138224280707766e+93

Math

\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

↓

\[e^{\log 0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r157599 = c0;
        double r157600 = 2.0;
        double r157601 = w;
        double r157602 = r157600 * r157601;
        double r157603 = r157599 / r157602;
        double r157604 = d;
        double r157605 = r157604 * r157604;
        double r157606 = r157599 * r157605;
        double r157607 = h;
        double r157608 = r157601 * r157607;
        double r157609 = D;
        double r157610 = r157609 * r157609;
        double r157611 = r157608 * r157610;
        double r157612 = r157606 / r157611;
        double r157613 = r157612 * r157612;
        double r157614 = M;
        double r157615 = r157614 * r157614;
        double r157616 = r157613 - r157615;
        double r157617 = sqrt(r157616);
        double r157618 = r157612 + r157617;
        double r157619 = r157603 * r157618;
        return r157619;
}

↓

double f(double __attribute__((unused)) c0, double __attribute__((unused)) w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r157620 = 0.0;
        double r157621 = log(r157620);
        double r157622 = exp(r157621);
        return r157622;
}

Error

Bits error versus c0

Bits error versus w

Bits error versus h

Bits error versus D

Bits error versus d

Bits error versus M

Derivation

1. Initial program 59.0

   \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

2. Simplified 59.8

   \[\leadsto \color{blue}{\frac{c0}{w \cdot 2} \cdot \mathsf{fma}\left(\frac{d}{\left(w \cdot h\right) \cdot D}, \frac{d \cdot c0}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot {\left(\frac{d}{D}\right)}^{3}\right), -M \cdot M\right)}\right)}\]

3. Taylor expanded around inf 35.8

   \[\leadsto \frac{c0}{w \cdot 2} \cdot \color{blue}{0}\]
4. Using strategy rm

5. Applied add-exp-log 35.8

   \[\leadsto \frac{c0}{w \cdot 2} \cdot \color{blue}{e^{\log 0}}\]

6. Applied add-exp-log 35.8

   \[\leadsto \frac{c0}{w \cdot \color{blue}{e^{\log 2}}} \cdot e^{\log 0}\]

7. Applied add-exp-log 49.8

   \[\leadsto \frac{c0}{\color{blue}{e^{\log w}} \cdot e^{\log 2}} \cdot e^{\log 0}\]

8. Applied prod-exp 49.8

   \[\leadsto \frac{c0}{\color{blue}{e^{\log w + \log 2}}} \cdot e^{\log 0}\]

9. Applied add-exp-log 57.0

   \[\leadsto \frac{\color{blue}{e^{\log c0}}}{e^{\log w + \log 2}} \cdot e^{\log 0}\]

10. Applied div-exp 57.0

    \[\leadsto \color{blue}{e^{\log c0 - \left(\log w + \log 2\right)}} \cdot e^{\log 0}\]

11. Applied prod-exp 56.5

    \[\leadsto \color{blue}{e^{\left(\log c0 - \left(\log w + \log 2\right)\right) + \log 0}}\]

12. Simplified 33.8

    \[\leadsto e^{\color{blue}{\log 0}}\]

13. Final simplification 33.8

    \[\leadsto e^{\log 0}\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2.0 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))