Henrywood and Agarwal, Equation (13)

Average Error: 58.3 → 52.1

Time: 1.1m

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 1.0546060002313458e+278
  2. w = 5.750647086431409e-94
  3. h = -7.157408665959316e-247
  4. D = -2.069612827053929e-28
  5. d = -1.0712662458827384e+280
  6. M = -1.7785649055871523e+254

Math

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

↓

\[\frac{\left(\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right) \cdot \sqrt[3]{e^{\log \left(\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}}{w} \cdot \frac{c0}{2}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r7158399 = c0;
        double r7158400 = 2.0;
        double r7158401 = w;
        double r7158402 = r7158400 * r7158401;
        double r7158403 = r7158399 / r7158402;
        double r7158404 = d;
        double r7158405 = r7158404 * r7158404;
        double r7158406 = r7158399 * r7158405;
        double r7158407 = h;
        double r7158408 = r7158401 * r7158407;
        double r7158409 = D;
        double r7158410 = r7158409 * r7158409;
        double r7158411 = r7158408 * r7158410;
        double r7158412 = r7158406 / r7158411;
        double r7158413 = r7158412 * r7158412;
        double r7158414 = M;
        double r7158415 = r7158414 * r7158414;
        double r7158416 = r7158413 - r7158415;
        double r7158417 = sqrt(r7158416);
        double r7158418 = r7158412 + r7158417;
        double r7158419 = r7158403 * r7158418;
        return r7158419;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r7158420 = c0;
        double r7158421 = d;
        double r7158422 = D;
        double r7158423 = r7158421 / r7158422;
        double r7158424 = r7158420 * r7158423;
        double r7158425 = r7158424 * r7158423;
        double r7158426 = w;
        double r7158427 = h;
        double r7158428 = r7158426 * r7158427;
        double r7158429 = r7158425 / r7158428;
        double r7158430 = M;
        double r7158431 = r7158429 - r7158430;
        double r7158432 = r7158430 + r7158429;
        double r7158433 = r7158431 * r7158432;
        double r7158434 = sqrt(r7158433);
        double r7158435 = r7158434 + r7158429;
        double r7158436 = cbrt(r7158435);
        double r7158437 = r7158436 * r7158436;
        double r7158438 = log(r7158434);
        double r7158439 = exp(r7158438);
        double r7158440 = r7158439 + r7158429;
        double r7158441 = cbrt(r7158440);
        double r7158442 = r7158437 * r7158441;
        double r7158443 = r7158442 / r7158426;
        double r7158444 = 2.0;
        double r7158445 = r7158420 / r7158444;
        double r7158446 = r7158443 * r7158445;
        return r7158446;
}

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 58.3

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

2. Simplified 51.9

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

4. Applied add-cube-cbrt 52.0

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

6. Applied add-exp-log 52.1

   \[\leadsto \frac{c0}{2} \cdot \frac{\left(\sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right) \cdot \sqrt[3]{\color{blue}{e^{\log \left(\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)}\right)}} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}}{w}\]

7. Final simplification 52.1

   \[\leadsto \frac{\left(\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right) \cdot \sqrt[3]{e^{\log \left(\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}}{w} \cdot \frac{c0}{2}\]

Reproduce

herbie shell --seed 2019138 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ 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))))))