Henrywood and Agarwal, Equation (13)

Average Error: 59.8 → 33.3

Time: 12.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. c0 = -1.0350484507269592e+185
  2. w = -1.7353128656778376e+18
  3. h = -5.478379097427606e-296
  4. D = 4.1008237962433196e-257
  5. d = 9.429902918018724e+96
  6. M = 1.690105319616841e-183

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 r78674 = c0;
        double r78675 = 2.0;
        double r78676 = w;
        double r78677 = r78675 * r78676;
        double r78678 = r78674 / r78677;
        double r78679 = d;
        double r78680 = r78679 * r78679;
        double r78681 = r78674 * r78680;
        double r78682 = h;
        double r78683 = r78676 * r78682;
        double r78684 = D;
        double r78685 = r78684 * r78684;
        double r78686 = r78683 * r78685;
        double r78687 = r78681 / r78686;
        double r78688 = r78687 * r78687;
        double r78689 = M;
        double r78690 = r78689 * r78689;
        double r78691 = r78688 - r78690;
        double r78692 = sqrt(r78691);
        double r78693 = r78687 + r78692;
        double r78694 = r78678 * r78693;
        return r78694;
}

↓

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 r78695 = 0.0;
        double r78696 = log(r78695);
        double r78697 = exp(r78696);
        return r78697;
}

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 59.8

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

2. Taylor expanded around inf 35.2

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

4. Applied add-exp-log 35.2

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

5. Applied add-exp-log 49.7

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

6. Applied add-exp-log 49.7

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

7. Applied prod-exp 49.7

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

8. Applied add-exp-log 57.1

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

9. Applied div-exp 57.1

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

10. Applied prod-exp 56.7

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

11. Simplified 33.3

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

12. Final simplification 33.3

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ c0 (* 2 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))))))