Henrywood and Agarwal, Equation (13)

Average Error: 58.8 → 33.7

Time: 8.8s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -4.392689525911108e+75
  2. w = -6.912057286316748e-234
  3. h = -2.4243362836438667e+33
  4. D = -1.2923381716909634e-229
  5. d = -3.090807666449914e+232
  6. M = 93306293809.51114

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 r140587 = c0;
        double r140588 = 2.0;
        double r140589 = w;
        double r140590 = r140588 * r140589;
        double r140591 = r140587 / r140590;
        double r140592 = d;
        double r140593 = r140592 * r140592;
        double r140594 = r140587 * r140593;
        double r140595 = h;
        double r140596 = r140589 * r140595;
        double r140597 = D;
        double r140598 = r140597 * r140597;
        double r140599 = r140596 * r140598;
        double r140600 = r140594 / r140599;
        double r140601 = r140600 * r140600;
        double r140602 = M;
        double r140603 = r140602 * r140602;
        double r140604 = r140601 - r140603;
        double r140605 = sqrt(r140604);
        double r140606 = r140600 + r140605;
        double r140607 = r140591 * r140606;
        return r140607;
}

↓

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 r140608 = 0.0;
        double r140609 = log(r140608);
        double r140610 = exp(r140609);
        return r140610;
}

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 58.8

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

2. Taylor expanded around inf 35.3

   \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{0}\]
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 49.4

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

6. Applied add-exp-log 49.4

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

7. Applied prod-exp 49.4

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

8. Applied add-exp-log 56.4

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

9. Applied div-exp 56.4

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

10. Applied prod-exp 56.0

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

11. Simplified 33.7

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

12. Final simplification 33.7

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

Reproduce

herbie shell --seed 2020056 +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))))))