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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `x`

Derivation

Initial program 3.9
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Simplified2.9
\[\leadsto \color{blue}{\frac{x}{(y \cdot \left(e^{2.0 \cdot \left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(a - \frac{2.0}{t \cdot 3.0}\right) + \frac{5.0}{6.0}\right) \cdot \left(b - c\right)\right)}\right) + x)_*}}\]
Using strategy rm
Applied associate-/r/3.3
\[\leadsto \frac{x}{(y \cdot \left(e^{2.0 \cdot \left(\color{blue}{\frac{\sqrt{a + t}}{t} \cdot z} - \left(\left(a - \frac{2.0}{t \cdot 3.0}\right) + \frac{5.0}{6.0}\right) \cdot \left(b - c\right)\right)}\right) + x)_*}\]
Applied fma-neg2.2
\[\leadsto \frac{x}{(y \cdot \left(e^{2.0 \cdot \color{blue}{(\left(\frac{\sqrt{a + t}}{t}\right) \cdot z + \left(-\left(\left(a - \frac{2.0}{t \cdot 3.0}\right) + \frac{5.0}{6.0}\right) \cdot \left(b - c\right)\right))_*}}\right) + x)_*}\]
Final simplification2.2
\[\leadsto \frac{x}{(y \cdot \left(e^{2.0 \cdot (\left(\frac{\sqrt{a + t}}{t}\right) \cdot z + \left(\left(-\left(\frac{5.0}{6.0} + \left(a - \frac{2.0}{t \cdot 3.0}\right)\right)\right) \cdot \left(b - c\right)\right))_*}\right) + x)_*}\]

Reproduce

herbie shell --seed 2019094 +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)))))))))))