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

↓

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

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 2.0
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
Using strategy rm
Applied add-sqr-sqrt2.0
\[\leadsto \frac{x \cdot \color{blue}{\left(\sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}}{y}\]
Final simplification2.0
\[\leadsto \frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)}{y}\]

Runtime

	Baseline	Herbie	Oracle	Span	%
Regimes	2.0	2.0	0.0	1.9	0%

herbie shell --seed 2018340 +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))