Henrywood and Agarwal, Equation (13)

Average Error: 59.5 → 33.5

Time: 9.7s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 3.786311799510893e+256
  2. w = -3.242436378278166e+41
  3. h = 1.7708104344166085e-304
  4. D = -3.730111778772213e-46
  5. d = -3.8310843269031653e+295
  6. M = 8.27187383621877e+89

Math

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

↓

\[0 \cdot \sqrt[3]{0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r160141 = c0;
        double r160142 = 2.0;
        double r160143 = w;
        double r160144 = r160142 * r160143;
        double r160145 = r160141 / r160144;
        double r160146 = d;
        double r160147 = r160146 * r160146;
        double r160148 = r160141 * r160147;
        double r160149 = h;
        double r160150 = r160143 * r160149;
        double r160151 = D;
        double r160152 = r160151 * r160151;
        double r160153 = r160150 * r160152;
        double r160154 = r160148 / r160153;
        double r160155 = r160154 * r160154;
        double r160156 = M;
        double r160157 = r160156 * r160156;
        double r160158 = r160155 - r160157;
        double r160159 = sqrt(r160158);
        double r160160 = r160154 + r160159;
        double r160161 = r160145 * r160160;
        return r160161;
}

↓

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 r160162 = 0.0;
        double r160163 = cbrt(r160162);
        double r160164 = r160162 * r160163;
        return r160164;
}

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 59.5

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

2. Taylor expanded around inf 35.7

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

4. Applied add-cube-cbrt 35.7

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

5. Applied associate-*r* 35.7

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

6. Simplified 33.5

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

7. Final simplification 33.5

   \[\leadsto 0 \cdot \sqrt[3]{0}\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(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))))))