Henrywood and Agarwal, Equation (13)

Average Error: 58.6 → 33.9

Time: 19.8s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -3.725477247132212e+154
  2. w = -3.5314365291360164e-137
  3. h = -2.507853856030208e-140
  4. D = 1.7917392981244527e-154
  5. d = 1.3310298182834478e+275
  6. M = 2.335834279487175e+79

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 r96571 = c0;
        double r96572 = 2.0;
        double r96573 = w;
        double r96574 = r96572 * r96573;
        double r96575 = r96571 / r96574;
        double r96576 = d;
        double r96577 = r96576 * r96576;
        double r96578 = r96571 * r96577;
        double r96579 = h;
        double r96580 = r96573 * r96579;
        double r96581 = D;
        double r96582 = r96581 * r96581;
        double r96583 = r96580 * r96582;
        double r96584 = r96578 / r96583;
        double r96585 = r96584 * r96584;
        double r96586 = M;
        double r96587 = r96586 * r96586;
        double r96588 = r96585 - r96587;
        double r96589 = sqrt(r96588);
        double r96590 = r96584 + r96589;
        double r96591 = r96575 * r96590;
        return r96591;
}

↓

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 r96592 = 0.0;
        return r96592;
}

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 58.6

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

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

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

6. Simplified 33.9

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

7. Final simplification 33.9

   \[\leadsto 0\]

Reproduce

herbie shell --seed 2019308 
(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))))))