\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]

↓

\[\frac{e^{(y \cdot \left(\log z\right) + \left((\left(t - 1.0\right) \cdot \left(\log a\right) + \left(-b\right))_*\right))_*} \cdot x}{y}\]

Error

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

Derivation

Initial program 1.9
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
Using strategy rm
Applied add-log-exp1.9
\[\leadsto \frac{x \cdot e^{\color{blue}{\log \left(e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right)}}}{y}\]
Applied rem-exp-log1.9
\[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{y}\]
Simplified1.9
\[\leadsto \frac{x \cdot e^{\color{blue}{(y \cdot \left(\log z\right) + \left((\left(t - 1.0\right) \cdot \left(\log a\right) + \left(-b\right))_*\right))_*}}}{y}\]
Final simplification1.9
\[\leadsto \frac{e^{(y \cdot \left(\log z\right) + \left((\left(t - 1.0\right) \cdot \left(\log a\right) + \left(-b\right))_*\right))_*} \cdot x}{y}\]

Runtime

	Baseline	Herbie	Oracle	Span	%
Regimes	1.9	1.9	0.0	1.9	0%

herbie shell --seed 2018353 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))