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

↓

\[\frac{x}{y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{a + t}}{t} - \left(b - c\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) - \frac{0.6666666666666666}{t}\right)\right)} + x}\]

Error

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

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In
Out

Enter valid numbers for all inputs

Derivation

Initial program 3.4
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Taylor expanded around inf 3.4
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{blue}{\frac{0.6666666666666666}{t}}\right)\right)}}\]
Final simplification3.4
\[\leadsto \frac{x}{y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{a + t}}{t} - \left(b - c\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) - \frac{0.6666666666666666}{t}\right)\right)} + x}\]

Runtime

	Baseline	Herbie	Oracle	Span	%
Regimes	3.4	3.4	0.6	2.7	0%

herbie shell --seed 2018351 
(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)))))))))))