Henrywood and Agarwal, Equation (13)

Average Error: 59.3 → 33.9

Time: 27.9s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -1.9223366757178428e+272
  2. w = -4.229672497930909e-233
  3. h = -4.821880340259577e+242
  4. D = -3.0781381641647126e-166
  5. d = -9.035983238058826e+172
  6. M = 3.778636398349861e+119

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 r105397 = c0;
        double r105398 = 2.0;
        double r105399 = w;
        double r105400 = r105398 * r105399;
        double r105401 = r105397 / r105400;
        double r105402 = d;
        double r105403 = r105402 * r105402;
        double r105404 = r105397 * r105403;
        double r105405 = h;
        double r105406 = r105399 * r105405;
        double r105407 = D;
        double r105408 = r105407 * r105407;
        double r105409 = r105406 * r105408;
        double r105410 = r105404 / r105409;
        double r105411 = r105410 * r105410;
        double r105412 = M;
        double r105413 = r105412 * r105412;
        double r105414 = r105411 - r105413;
        double r105415 = sqrt(r105414);
        double r105416 = r105410 + r105415;
        double r105417 = r105401 * r105416;
        return r105417;
}

↓

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 r105418 = c0;
        double r105419 = cbrt(r105418);
        double r105420 = r105419 * r105419;
        double r105421 = 2.0;
        double r105422 = r105420 / r105421;
        double r105423 = 0.0;
        double r105424 = r105422 * r105423;
        return r105424;
}

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 59.3

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

2. Taylor expanded around inf 35.8

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

4. Applied add-cube-cbrt 35.8

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

5. Applied times-frac 35.8

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

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 33.9

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

8. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019305 
(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))))))