Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.8

Time: 41.6s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 2.840962048022813e+263
  2. w = -3.055499681661864e-55
  3. h = 1575.9184687212278
  4. D = 1.6665754135628296e-236
  5. d = 2.697555358207071e+192
  6. M = -2.3098971912103573e-163

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 r170127 = c0;
        double r170128 = 2.0;
        double r170129 = w;
        double r170130 = r170128 * r170129;
        double r170131 = r170127 / r170130;
        double r170132 = d;
        double r170133 = r170132 * r170132;
        double r170134 = r170127 * r170133;
        double r170135 = h;
        double r170136 = r170129 * r170135;
        double r170137 = D;
        double r170138 = r170137 * r170137;
        double r170139 = r170136 * r170138;
        double r170140 = r170134 / r170139;
        double r170141 = r170140 * r170140;
        double r170142 = M;
        double r170143 = r170142 * r170142;
        double r170144 = r170141 - r170143;
        double r170145 = sqrt(r170144);
        double r170146 = r170140 + r170145;
        double r170147 = r170131 * r170146;
        return r170147;
}

↓

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 r170148 = 0.0;
        double r170149 = log(r170148);
        double r170150 = exp(r170149);
        return r170150;
}

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 59.2

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

2. Taylor expanded around inf 35.7

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

4. Applied add-exp-log 35.7

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

5. Applied add-exp-log 49.8

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

6. Applied add-exp-log 49.8

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

7. Applied prod-exp 49.8

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

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 33.8

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

12. Final simplification 33.8

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

Reproduce

herbie shell --seed 2019235 +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))))))