Error

Derivation

1. Initial program 3.8

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

2. Initial simplification1.8

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

4. Applied add-sqr-sqrt1.8

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

5. Applied associate-*r*1.8

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

7. Applied div-inv1.8

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

8. Applied associate-*l*2.0

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

9. Final simplification2.0

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

Runtime

Time bar (total: 52.8s)Debug logProfile

herbie shell --seed 2018354 +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)))))))))))