Henrywood and Agarwal, Equation (13)

Average Error: 59.5 → 34.3

Time: 17.1s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 7.207411752533894e+263
  2. w = -2.583916300593085e+78
  3. h = 1.9447514843596075e-296
  4. D = 4.094557822017715e-256
  5. d = -2.171862009418387e+239
  6. M = 5.402450236825196e+48

Math

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

↓

\[0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r187600 = c0;
        double r187601 = 2.0;
        double r187602 = w;
        double r187603 = r187601 * r187602;
        double r187604 = r187600 / r187603;
        double r187605 = d;
        double r187606 = r187605 * r187605;
        double r187607 = r187600 * r187606;
        double r187608 = h;
        double r187609 = r187602 * r187608;
        double r187610 = D;
        double r187611 = r187610 * r187610;
        double r187612 = r187609 * r187611;
        double r187613 = r187607 / r187612;
        double r187614 = r187613 * r187613;
        double r187615 = M;
        double r187616 = r187615 * r187615;
        double r187617 = r187614 - r187616;
        double r187618 = sqrt(r187617);
        double r187619 = r187613 + r187618;
        double r187620 = r187604 * r187619;
        return r187620;
}

↓

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 r187621 = 0.0;
        return r187621;
}

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 59.5

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

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

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

5. Simplified 35.7

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

6. Simplified 34.3

   \[\leadsto 0 \cdot \color{blue}{0}\]

7. Final simplification 34.3

   \[\leadsto 0\]

Reproduce

herbie shell --seed 2019318 
(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))))))