Henrywood and Agarwal, Equation (13)

Average Error: 58.2 → 32.7

Time: 58.6s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 3.17180604621685e+229
  2. w = -6.0148333844790955e-55
  3. h = 2.124206871236763e-145
  4. D = -3.2024855525006606e-197
  5. d = 8.652459337637894e+67
  6. M = 3.2784584263384346e+125

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 7.334396531723024 \cdot 10^{+144}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r11116554 = c0;
        double r11116555 = 2.0;
        double r11116556 = w;
        double r11116557 = r11116555 * r11116556;
        double r11116558 = r11116554 / r11116557;
        double r11116559 = d;
        double r11116560 = r11116559 * r11116559;
        double r11116561 = r11116554 * r11116560;
        double r11116562 = h;
        double r11116563 = r11116556 * r11116562;
        double r11116564 = D;
        double r11116565 = r11116564 * r11116564;
        double r11116566 = r11116563 * r11116565;
        double r11116567 = r11116561 / r11116566;
        double r11116568 = r11116567 * r11116567;
        double r11116569 = M;
        double r11116570 = r11116569 * r11116569;
        double r11116571 = r11116568 - r11116570;
        double r11116572 = sqrt(r11116571);
        double r11116573 = r11116567 + r11116572;
        double r11116574 = r11116558 * r11116573;
        return r11116574;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r11116575 = c0;
        double r11116576 = w;
        double r11116577 = 2.0;
        double r11116578 = r11116576 * r11116577;
        double r11116579 = r11116575 / r11116578;
        double r11116580 = d;
        double r11116581 = r11116580 * r11116580;
        double r11116582 = r11116575 * r11116581;
        double r11116583 = D;
        double r11116584 = r11116583 * r11116583;
        double r11116585 = h;
        double r11116586 = r11116576 * r11116585;
        double r11116587 = r11116584 * r11116586;
        double r11116588 = r11116582 / r11116587;
        double r11116589 = r11116588 * r11116588;
        double r11116590 = M;
        double r11116591 = r11116590 * r11116590;
        double r11116592 = r11116589 - r11116591;
        double r11116593 = sqrt(r11116592);
        double r11116594 = r11116593 + r11116588;
        double r11116595 = r11116579 * r11116594;
        double r11116596 = 7.334396531723024e+144;
        bool r11116597 = r11116595 <= r11116596;
        double r11116598 = 0.0;
        double r11116599 = r11116597 ? r11116595 : r11116598;
        return r11116599;
}

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. Split input into 2 regimes

2. if (* (/ 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))))) < 7.334396531723024e+144

   1. Initial program 35.0

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

   if 7.334396531723024e+144 < (* (/ 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)))))

   1. Initial program 62.5

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

   2. Simplified 55.5

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

   3. Taylor expanded around -inf 34.2

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

   5. Applied mul0 32.3

      \[\leadsto \color{blue}{0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 32.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 7.334396531723024 \cdot 10^{+144}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(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))))))