Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.8

Time: 10.7s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 5.8467503159793135e+225
  2. w = -5.4870668835749775e-291
  3. h = 2.516999583642857e+20
  4. D = -8.31517320518405e-309
  5. d = -6.514768402042659e-119
  6. M = -8.17390830947066e+97

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 r133471 = c0;
        double r133472 = 2.0;
        double r133473 = w;
        double r133474 = r133472 * r133473;
        double r133475 = r133471 / r133474;
        double r133476 = d;
        double r133477 = r133476 * r133476;
        double r133478 = r133471 * r133477;
        double r133479 = h;
        double r133480 = r133473 * r133479;
        double r133481 = D;
        double r133482 = r133481 * r133481;
        double r133483 = r133480 * r133482;
        double r133484 = r133478 / r133483;
        double r133485 = r133484 * r133484;
        double r133486 = M;
        double r133487 = r133486 * r133486;
        double r133488 = r133485 - r133487;
        double r133489 = sqrt(r133488);
        double r133490 = r133484 + r133489;
        double r133491 = r133475 * r133490;
        return r133491;
}

↓

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 r133492 = c0;
        double r133493 = cbrt(r133492);
        double r133494 = r133493 * r133493;
        double r133495 = 2.0;
        double r133496 = r133494 / r133495;
        double r133497 = 0.0;
        double r133498 = r133496 * r133497;
        return r133498;
}

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 35.7

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

4. Applied add-cube-cbrt 35.7

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

5. Applied times-frac 35.7

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

6. Applied associate-*l* 34.3

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

7. Simplified 33.8

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

8. Final simplification 33.8

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

Reproduce

herbie shell --seed 2019356 
(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))))))