Henrywood and Agarwal, Equation (13)

Average Error: 59.0 → 33.6

Time: 28.8s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -4.794616215934883e+260
  2. w = 7.363782728748913e-172
  3. h = 1.500650409784679e+171
  4. D = 3.4182388245606946e-306
  5. d = 9.058335141669097e+275
  6. M = -2.2119225060225628e+116

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 r136086 = c0;
        double r136087 = 2.0;
        double r136088 = w;
        double r136089 = r136087 * r136088;
        double r136090 = r136086 / r136089;
        double r136091 = d;
        double r136092 = r136091 * r136091;
        double r136093 = r136086 * r136092;
        double r136094 = h;
        double r136095 = r136088 * r136094;
        double r136096 = D;
        double r136097 = r136096 * r136096;
        double r136098 = r136095 * r136097;
        double r136099 = r136093 / r136098;
        double r136100 = r136099 * r136099;
        double r136101 = M;
        double r136102 = r136101 * r136101;
        double r136103 = r136100 - r136102;
        double r136104 = sqrt(r136103);
        double r136105 = r136099 + r136104;
        double r136106 = r136090 * r136105;
        return r136106;
}

↓

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 r136107 = 0.0;
        return r136107;
}

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 59.0

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

2. Taylor expanded around inf 35.6

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

4. Applied add-cbrt-cube 35.6

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

5. Applied add-cbrt-cube 42.1

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

6. Applied add-cbrt-cube 42.1

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

7. Applied cbrt-unprod 42.1

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

8. Applied add-cbrt-cube 48.2

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

9. Applied cbrt-undiv 48.7

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

10. Applied cbrt-unprod 48.7

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

11. Simplified 33.6

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

12. Final simplification 33.6

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019179 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2.0 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))))))