Average Error: 3.7 → 1.9
Time: 42.2s
Precision: 64
Internal Precision: 128
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{(y \cdot \left(e^{(\left(\left(a + \frac{5.0}{6.0}\right) - \frac{\frac{2.0}{t}}{3.0}\right) \cdot \left(\left(c - b\right) \cdot 2.0\right) + \left(\sqrt{a + t} \cdot \frac{z \cdot 2.0}{t}\right))_*}\right) + x)_*}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 3.7

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

  2. Initial simplification1.9

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

  3. Final simplification1.9

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

Runtime

Time bar (total: 42.2s)Debug logProfile

herbie shell --seed 2018285 +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)))))))))))