Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.7

Time: 32.7s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 8.48601853573141e+214
  2. w = -3.126645723736485e-171
  3. h = 2.8080800529117657e-260
  4. D = -5.515382539318102e-291
  5. d = 3.254386793664237e+246
  6. M = -1.4209699709703747e+28

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 r6371589 = c0;
        double r6371590 = 2.0;
        double r6371591 = w;
        double r6371592 = r6371590 * r6371591;
        double r6371593 = r6371589 / r6371592;
        double r6371594 = d;
        double r6371595 = r6371594 * r6371594;
        double r6371596 = r6371589 * r6371595;
        double r6371597 = h;
        double r6371598 = r6371591 * r6371597;
        double r6371599 = D;
        double r6371600 = r6371599 * r6371599;
        double r6371601 = r6371598 * r6371600;
        double r6371602 = r6371596 / r6371601;
        double r6371603 = r6371602 * r6371602;
        double r6371604 = M;
        double r6371605 = r6371604 * r6371604;
        double r6371606 = r6371603 - r6371605;
        double r6371607 = sqrt(r6371606);
        double r6371608 = r6371602 + r6371607;
        double r6371609 = r6371593 * r6371608;
        return r6371609;
}

↓

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 r6371610 = 0.0;
        return r6371610;
}

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 59.2

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

2. Simplified 53.8

   \[\leadsto \color{blue}{\frac{\left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}\right) \cdot \left(\frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w} - M\right)} + \frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}\right) \cdot \frac{c0}{w}}{2}}\]
3. Using strategy rm

4. Applied add-log-exp 61.4

   \[\leadsto \frac{\left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}\right) \cdot \left(\frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w} - M\right)} + \color{blue}{\log \left(e^{\frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}}\right)}\right) \cdot \frac{c0}{w}}{2}\]

5. Applied add-log-exp 60.7

   \[\leadsto \frac{\left(\color{blue}{\log \left(e^{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}\right) \cdot \left(\frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w} - M\right)}}\right)} + \log \left(e^{\frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}}\right)\right) \cdot \frac{c0}{w}}{2}\]

6. Applied sum-log 60.6

   \[\leadsto \frac{\color{blue}{\log \left(e^{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}\right) \cdot \left(\frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w} - M\right)}} \cdot e^{\frac{\frac{d}{D} \cdot \frac{d}{D}}{h} \cdot \frac{c0}{w}}\right)} \cdot \frac{c0}{w}}{2}\]

7. Simplified 57.9

   \[\leadsto \frac{\log \color{blue}{\left(e^{\frac{\frac{d}{D} \cdot \left(\frac{d}{D} \cdot c0\right)}{w \cdot h} + \sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(\frac{d}{D} \cdot c0\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(\frac{d}{D} \cdot c0\right)}{w \cdot h} - M\right)}}\right)} \cdot \frac{c0}{w}}{2}\]

8. Taylor expanded around inf 35.7

   \[\leadsto \frac{\log \left(e^{\color{blue}{0}}\right) \cdot \frac{c0}{w}}{2}\]

9. Taylor expanded around 0 33.7

   \[\leadsto \frac{\color{blue}{0}}{2}\]

10. Final simplification 33.7

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019171 
(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))))))