Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.2

Time: 30.9s

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 r121593 = c0;
        double r121594 = 2.0;
        double r121595 = w;
        double r121596 = r121594 * r121595;
        double r121597 = r121593 / r121596;
        double r121598 = d;
        double r121599 = r121598 * r121598;
        double r121600 = r121593 * r121599;
        double r121601 = h;
        double r121602 = r121595 * r121601;
        double r121603 = D;
        double r121604 = r121603 * r121603;
        double r121605 = r121602 * r121604;
        double r121606 = r121600 / r121605;
        double r121607 = r121606 * r121606;
        double r121608 = M;
        double r121609 = r121608 * r121608;
        double r121610 = r121607 - r121609;
        double r121611 = sqrt(r121610);
        double r121612 = r121606 + r121611;
        double r121613 = r121597 * r121612;
        return r121613;
}

↓

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 r121614 = c0;
        double r121615 = cbrt(r121614);
        double r121616 = r121615 * r121615;
        double r121617 = 2.0;
        double r121618 = r121616 / r121617;
        double r121619 = 0.0;
        double r121620 = r121618 * r121619;
        return r121620;
}

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 +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))))))