Henrywood and Agarwal, Equation (13)

Average Error: 59.3 → 33.5

Time: 17.4s

Precision: 64

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

• could not determine a ground truth for program body

  1. c0 = 2.6360215635901592e+175
  2. w = 3.5213725536708513e-259
  3. h = -2.9407093920776398e-288
  4. D = -9.03317912235059e-167
  5. d = 2.587516522540669e+261
  6. M = -2.5626624875900265e-287

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 r188167 = c0;
        double r188168 = 2.0;
        double r188169 = w;
        double r188170 = r188168 * r188169;
        double r188171 = r188167 / r188170;
        double r188172 = d;
        double r188173 = r188172 * r188172;
        double r188174 = r188167 * r188173;
        double r188175 = h;
        double r188176 = r188169 * r188175;
        double r188177 = D;
        double r188178 = r188177 * r188177;
        double r188179 = r188176 * r188178;
        double r188180 = r188174 / r188179;
        double r188181 = r188180 * r188180;
        double r188182 = M;
        double r188183 = r188182 * r188182;
        double r188184 = r188181 - r188183;
        double r188185 = sqrt(r188184);
        double r188186 = r188180 + r188185;
        double r188187 = r188171 * r188186;
        return r188187;
}

↓

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 r188188 = 0.0;
        double r188189 = log(r188188);
        double r188190 = exp(r188189);
        return r188190;
}

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 59.3

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

2. Taylor expanded around inf 35.3

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

4. Applied add-exp-log 35.3

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

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 56.7

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

9. Applied div-exp 56.7

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

10. Applied prod-exp 56.3

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

11. Simplified 33.5

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

12. Final simplification 33.5

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

Reproduce

herbie shell --seed 2019351 +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))))))