Henrywood and Agarwal, Equation (13)

Average Error: 59.3 → 33.4

Time: 31.3s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -2.295024957636829e+132
  2. w = -1.0459561824906476e-187
  3. h = -6.187928141723591e-216
  4. D = -2.661563675686751e-249
  5. d = 5.049148371172753e+293
  6. M = 2.2438624246711994e+121

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 r90536 = c0;
        double r90537 = 2.0;
        double r90538 = w;
        double r90539 = r90537 * r90538;
        double r90540 = r90536 / r90539;
        double r90541 = d;
        double r90542 = r90541 * r90541;
        double r90543 = r90536 * r90542;
        double r90544 = h;
        double r90545 = r90538 * r90544;
        double r90546 = D;
        double r90547 = r90546 * r90546;
        double r90548 = r90545 * r90547;
        double r90549 = r90543 / r90548;
        double r90550 = r90549 * r90549;
        double r90551 = M;
        double r90552 = r90551 * r90551;
        double r90553 = r90550 - r90552;
        double r90554 = sqrt(r90553);
        double r90555 = r90549 + r90554;
        double r90556 = r90540 * r90555;
        return r90556;
}

↓

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 r90557 = 0.0;
        return r90557;
}

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 35.4

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

4. Applied add-cube-cbrt 35.4

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

5. Simplified 35.4

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

6. Simplified 33.4

   \[\leadsto 0 \cdot \color{blue}{0}\]

7. Final simplification 33.4

   \[\leadsto 0\]

Reproduce

herbie shell --seed 2019303 
(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))))))