Henrywood and Agarwal, Equation (13)

Average Error: 59.6 → 34.4

Time: 9.9s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 7.82674757927098e+191
  2. w = -1.0691369593176215e-177
  3. h = 5.574278911088489e-22
  4. D = -2.7097114655346684e+19
  5. d = -4.2647586952588136e+288
  6. M = -2.4932486355435744e-112

Math

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

↓

\[\sqrt[3]{0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r201053 = c0;
        double r201054 = 2.0;
        double r201055 = w;
        double r201056 = r201054 * r201055;
        double r201057 = r201053 / r201056;
        double r201058 = d;
        double r201059 = r201058 * r201058;
        double r201060 = r201053 * r201059;
        double r201061 = h;
        double r201062 = r201055 * r201061;
        double r201063 = D;
        double r201064 = r201063 * r201063;
        double r201065 = r201062 * r201064;
        double r201066 = r201060 / r201065;
        double r201067 = r201066 * r201066;
        double r201068 = M;
        double r201069 = r201068 * r201068;
        double r201070 = r201067 - r201069;
        double r201071 = sqrt(r201070);
        double r201072 = r201066 + r201071;
        double r201073 = r201057 * r201072;
        return r201073;
}

↓

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 r201074 = 0.0;
        double r201075 = cbrt(r201074);
        return r201075;
}

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 59.6

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

2. Taylor expanded around inf 36.3

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

4. Applied add-cbrt-cube 36.3

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

5. Applied add-cbrt-cube 42.7

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

6. Applied add-cbrt-cube 42.7

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

7. Applied cbrt-unprod 42.7

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

8. Applied add-cbrt-cube 49.3

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

9. Applied cbrt-undiv 49.7

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

10. Applied cbrt-unprod 49.7

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

11. Simplified 34.4

    \[\leadsto \sqrt[3]{\color{blue}{0}}\]

12. Final simplification 34.4

    \[\leadsto \sqrt[3]{0}\]

Reproduce

herbie shell --seed 2020024 +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))))))