Error

Derivation

1. Initial program 3.6

   \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
2. Using strategy rm

3. Applied add-cube-cbrt3.6

   \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\left(\sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}} \cdot \sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}\right) \cdot \sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

4. Applied prod-diff22.7

   \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left((\left(\sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}} \cdot \sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}\right) \cdot \left(\sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}\right) + \left(-\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right))_* + (\left(-\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right) \cdot \left(b - c\right) + \left(\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right))_*\right)}}}\]

5. Simplified21.0

   \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{(\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{t + a}\right))_*} + (\left(-\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right) \cdot \left(b - c\right) + \left(\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right))_*\right)}}\]

6. Simplified1.8

   \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left((\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{t + a}\right))_* + \color{blue}{0}\right)}}\]
7. Using strategy rm

8. Applied add-sqr-sqrt1.8

   \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(\sqrt{e^{2.0 \cdot \left((\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{t + a}\right))_* + 0\right)}} \cdot \sqrt{e^{2.0 \cdot \left((\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{t + a}\right))_* + 0\right)}}\right)}}\]

9. Applied associate-*r*1.8

   \[\leadsto \frac{x}{x + \color{blue}{\left(y \cdot \sqrt{e^{2.0 \cdot \left((\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{t + a}\right))_* + 0\right)}}\right) \cdot \sqrt{e^{2.0 \cdot \left((\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{t + a}\right))_* + 0\right)}}}}\]

10. Final simplification1.8

    \[\leadsto \frac{x}{x + \left(\sqrt{e^{(\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{a + t}\right))_* \cdot 2.0}} \cdot y\right) \cdot \sqrt{e^{(\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right) + \left(\frac{z}{t} \cdot \sqrt{a + t}\right))_* \cdot 2.0}}}\]

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

Details

Time bar (total: 54.7s)Debug log