Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.2

Time: 30.0s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -6.2207241140174846e-117
  2. w = 4.3776406734974095e-271
  3. h = 3.5532294286425617e-187
  4. D = 3.087063154587703e-293
  5. d = 1.0656776998337841e+73
  6. M = -1.3242498669743827e+73

Math

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

↓

\[\frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r102498 = c0;
        double r102499 = 2.0;
        double r102500 = w;
        double r102501 = r102499 * r102500;
        double r102502 = r102498 / r102501;
        double r102503 = d;
        double r102504 = r102503 * r102503;
        double r102505 = r102498 * r102504;
        double r102506 = h;
        double r102507 = r102500 * r102506;
        double r102508 = D;
        double r102509 = r102508 * r102508;
        double r102510 = r102507 * r102509;
        double r102511 = r102505 / r102510;
        double r102512 = r102511 * r102511;
        double r102513 = M;
        double r102514 = r102513 * r102513;
        double r102515 = r102512 - r102514;
        double r102516 = sqrt(r102515);
        double r102517 = r102511 + r102516;
        double r102518 = r102502 * r102517;
        return r102518;
}

↓

double f(double c0, double __attribute__((unused)) w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r102519 = c0;
        double r102520 = cbrt(r102519);
        double r102521 = r102520 * r102520;
        double r102522 = 2.0;
        double r102523 = r102521 / r102522;
        double r102524 = 0.0;
        double r102525 = r102523 * r102524;
        return r102525;
}

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 59.1

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

2. Taylor expanded around inf 35.1

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

4. Applied add-cube-cbrt 35.1

   \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{c0} \cdot \sqrt[3]{c0}\right) \cdot \sqrt[3]{c0}}}{2 \cdot w} \cdot 0\]

5. Applied times-frac 35.1

   \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot \frac{\sqrt[3]{c0}}{w}\right)} \cdot 0\]

6. Applied associate-*l* 33.6

   \[\leadsto \color{blue}{\frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot \left(\frac{\sqrt[3]{c0}}{w} \cdot 0\right)}\]

7. Simplified 33.2

   \[\leadsto \frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot \color{blue}{0}\]

8. Final simplification 33.2

   \[\leadsto \frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot 0\]

Reproduce

herbie shell --seed 2019347 
(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))))))