Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.7

Time: 8.3s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -6.434147471184152e+182
  2. w = 1.7179588205773664e+35
  3. h = 1.4319626602174737e-185
  4. D = 7.515129888206609e-110
  5. d = -4.746233778049425e+266
  6. M = 4.9553047113067274e+225

Math

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

↓

\[0 \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r117627 = c0;
        double r117628 = 2.0;
        double r117629 = w;
        double r117630 = r117628 * r117629;
        double r117631 = r117627 / r117630;
        double r117632 = d;
        double r117633 = r117632 * r117632;
        double r117634 = r117627 * r117633;
        double r117635 = h;
        double r117636 = r117629 * r117635;
        double r117637 = D;
        double r117638 = r117637 * r117637;
        double r117639 = r117636 * r117638;
        double r117640 = r117634 / r117639;
        double r117641 = r117640 * r117640;
        double r117642 = M;
        double r117643 = r117642 * r117642;
        double r117644 = r117641 - r117643;
        double r117645 = sqrt(r117644);
        double r117646 = r117640 + r117645;
        double r117647 = r117631 * r117646;
        return r117647;
}

↓

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 r117648 = 0.0;
        double r117649 = r117648 * r117648;
        return r117649;
}

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. Taylor expanded around inf 35.5

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

4. Applied add-cube-cbrt 35.5

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

5. Simplified 35.5

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

6. Simplified 33.7

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

7. Final simplification 33.7

   \[\leadsto 0 \cdot 0\]

Reproduce

herbie shell --seed 2020057 
(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))))))