Random Jason Timeout Test 004

Average Error: 34.1 → 33.7

Time: 14.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = -2.147009436181225e-259
  2. c = 1.0551194375545526e+290

Math

\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

↓

\[\sqrt{\left(\left(\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

C

double f(double a, double c) {
        double r15546 = c;
        double r15547 = cosh(r15546);
        double r15548 = a;
        double r15549 = log1p(r15548);
        double r15550 = fmod(r15547, r15549);
        return r15550;
}

↓

double f(double a, double c) {
        double r15551 = -1.0;
        double r15552 = c;
        double r15553 = r15551 * r15552;
        double r15554 = exp(r15553);
        double r15555 = exp(r15552);
        double r15556 = r15554 + r15555;
        double r15557 = sqrt(r15556);
        double r15558 = 0.5;
        double r15559 = sqrt(r15558);
        double r15560 = r15557 * r15559;
        double r15561 = cosh(r15552);
        double r15562 = sqrt(r15561);
        double r15563 = r15560 * r15562;
        double r15564 = a;
        double r15565 = log1p(r15564);
        double r15566 = fmod(r15563, r15565);
        double r15567 = sqrt(r15566);
        double r15568 = r15567 * r15567;
        return r15568;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.1

   \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
2. Using strategy rm

3. Applied add-sqr-sqrt 34.1

   \[\leadsto \left(\color{blue}{\left(\sqrt{\cosh c} \cdot \sqrt{\cosh c}\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

4. Taylor expanded around inf 34.0

   \[\leadsto \left(\left(\color{blue}{\left(\sqrt{e^{c} + e^{-c}} \cdot \sqrt{\frac{1}{2}}\right)} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

5. Simplified 34.0

   \[\leadsto \left(\left(\color{blue}{\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
6. Using strategy rm

7. Applied add-sqr-sqrt 33.7

   \[\leadsto \color{blue}{\sqrt{\left(\left(\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

8. Final simplification 33.7

   \[\leadsto \sqrt{\left(\left(\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))