Error

Derivation

1. Initial program 3.7

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

3. Applied div-inv3.7

   \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\left(z \cdot \sqrt{t + a}\right) \cdot \frac{1}{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

4. Applied prod-diff21.9

   \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left((\left(z \cdot \sqrt{t + a}\right) \cdot \left(\frac{1}{t}\right) + \left(-\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right))_* + (\left(-\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right) \cdot \left(b - c\right) + \left(\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right))_*\right)}}}\]

5. Simplified20.1

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

6. Simplified1.7

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

7. Final simplification1.7

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

Reproduce

herbie shell --seed 2019005 +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: 33.8s)Debug log