Average Error: 0.3 → 0.3
Time: 1.2m
Precision: 64
Internal Precision: 576
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\frac{a}{-{\left(\cos^{-1} a\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)} \cdot \sqrt[3]{\cos^{-1} a}}\]

Error

Bits error versus a

Derivation

  1. Initial program 0.3

    \[\frac{a}{-\cos^{-1} a}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.7

    \[\leadsto \frac{a}{-\color{blue}{\left(\sqrt[3]{\cos^{-1} a} \cdot \sqrt[3]{\cos^{-1} a}\right) \cdot \sqrt[3]{\cos^{-1} a}}}\]
  4. Using strategy rm

  5. Applied pow1/30.7

    \[\leadsto \frac{a}{-\left(\sqrt[3]{\cos^{-1} a} \cdot \color{blue}{{\left(\cos^{-1} a\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos^{-1} a}}\]

  6. Applied pow1/30.7

    \[\leadsto \frac{a}{-\left(\color{blue}{{\left(\cos^{-1} a\right)}^{\frac{1}{3}}} \cdot {\left(\cos^{-1} a\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos^{-1} a}}\]

  7. Applied pow-prod-up0.3

    \[\leadsto \frac{a}{-\color{blue}{{\left(\cos^{-1} a\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)}} \cdot \sqrt[3]{\cos^{-1} a}}\]

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed '#(376638549 3830080768 3905278455 3542335916 3807831211 3252027093)' 
(FPCore (a)
  :name "Random Jason Timeout Test 010"
  (/ a (- (acos a))))