Random Jason Timeout Test 006

Average Error: 34.1 → 34.1

Time: 46.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 7.843670218358717e+76

Math

\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

↓

\[\left|\left(\left(\tan^{-1}_* \frac{\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \left(\left(\sqrt[3]{\sqrt{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}} \cdot \sqrt{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}} \cdot \sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}\right) \cdot \sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

C

double f(double a) {
        double r724086 = a;
        double r724087 = expm1(r724086);
        double r724088 = sin(r724087);
        double r724089 = expm1(r724088);
        double r724090 = atan(r724086);
        double r724091 = atan2(r724089, r724090);
        double r724092 = fmod(r724091, r724086);
        double r724093 = fabs(r724092);
        return r724093;
}

↓

double f(double a) {
        double r724094 = a;
        double r724095 = expm1(r724094);
        double r724096 = sin(r724095);
        double r724097 = expm1(r724096);
        double r724098 = cbrt(r724097);
        double r724099 = r724098 * r724098;
        double r724100 = log(r724099);
        double r724101 = exp(r724100);
        double r724102 = sqrt(r724101);
        double r724103 = r724102 * r724102;
        double r724104 = cbrt(r724103);
        double r724105 = cbrt(r724101);
        double r724106 = r724104 * r724105;
        double r724107 = r724106 * r724105;
        double r724108 = r724098 * r724107;
        double r724109 = atan(r724094);
        double r724110 = atan2(r724108, r724109);
        double r724111 = fmod(r724110, r724094);
        double r724112 = fabs(r724111);
        return r724112;
}

Error

Bits error versus a

Derivation

1. Initial program 34.1

   \[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
2. Using strategy rm

3. Applied add-cube-cbrt 34.1

   \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\color{blue}{\left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}}}{\tan^{-1} a}\right) \bmod a\right)\right|\]
4. Using strategy rm

5. Applied add-exp-log 34.1

   \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\color{blue}{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}}{\tan^{-1} a}\right) \bmod a\right)\right|\]
6. Using strategy rm

7. Applied add-cube-cbrt 34.1

   \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\color{blue}{\left(\left(\sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}} \cdot \sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}\right) \cdot \sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}}{\tan^{-1} a}\right) \bmod a\right)\right|\]
8. Using strategy rm

9. Applied add-sqr-sqrt 34.1

   \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\left(\left(\sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}} \cdot \sqrt[3]{\color{blue}{\sqrt{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}} \cdot \sqrt{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}}}\right) \cdot \sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}\right) \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}}{\tan^{-1} a}\right) \bmod a\right)\right|\]

10. Final simplification 34.1

    \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \left(\left(\sqrt[3]{\sqrt{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}} \cdot \sqrt{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}} \cdot \sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}\right) \cdot \sqrt[3]{e^{\log \left(\sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}\right)}}\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))