Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.2

Time: 12.0s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -2.2736486955259513e-10
  2. w = 4.3811697035537754e-170
  3. h = 1.2862806256912123e-229
  4. D = 2.5855309822038082e-138
  5. d = -2.3068824554677546e+222
  6. M = 5.352451769654128e+34

Math

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

↓

\[\frac{1}{2} \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r176157 = c0;
        double r176158 = 2.0;
        double r176159 = w;
        double r176160 = r176158 * r176159;
        double r176161 = r176157 / r176160;
        double r176162 = d;
        double r176163 = r176162 * r176162;
        double r176164 = r176157 * r176163;
        double r176165 = h;
        double r176166 = r176159 * r176165;
        double r176167 = D;
        double r176168 = r176167 * r176167;
        double r176169 = r176166 * r176168;
        double r176170 = r176164 / r176169;
        double r176171 = r176170 * r176170;
        double r176172 = M;
        double r176173 = r176172 * r176172;
        double r176174 = r176171 - r176173;
        double r176175 = sqrt(r176174);
        double r176176 = r176170 + r176175;
        double r176177 = r176161 * r176176;
        return r176177;
}

↓

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 r176178 = 1.0;
        double r176179 = 2.0;
        double r176180 = r176178 / r176179;
        double r176181 = 0.0;
        double r176182 = r176180 * r176181;
        return r176182;
}

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 59.1

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

2. Taylor expanded around inf 35.1

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

4. Applied *-un-lft-identity 35.1

   \[\leadsto \frac{\color{blue}{1 \cdot c0}}{2 \cdot w} \cdot 0\]

5. Applied times-frac 35.1

   \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{c0}{w}\right)} \cdot 0\]

6. Applied associate-*l* 35.1

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{c0}{w} \cdot 0\right)}\]

7. Simplified 33.2

   \[\leadsto \frac{1}{2} \cdot \color{blue}{0}\]

8. Final simplification 33.2

   \[\leadsto \frac{1}{2} \cdot 0\]

Reproduce

herbie shell --seed 2020001 +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))))))