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

↓

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

Error

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

Derivation

Initial program 3.8
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Using strategy rm
Applied div-inv3.8
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\left(z \cdot \sqrt{t + a}\right) \cdot \frac{1}{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Applied fma-neg2.7
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{(\left(z \cdot \sqrt{t + a}\right) \cdot \left(\frac{1}{t}\right) + \left(-\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right))_*}}}\]
Applied simplify2.7
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot (\left(z \cdot \sqrt{t + a}\right) \cdot \left(\frac{1}{t}\right) + \color{blue}{\left(\left(\left(\frac{5.0}{6.0} + a\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(c - b\right)\right)})_*}}\]

Runtime

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' +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)))))))))))