Average Error: 3.9 → 1.8
Time: 2.3m
Precision: 64
Internal Precision: 384
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left((\left(c - b\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{3.0 \cdot t}\right) + \left(\frac{\sqrt{t + a}}{\frac{t}{z}}\right))_* + 0\right)}}\]

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 3.9

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

  3. Applied log1p-expm1-u10.4

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{blue}{\log_* (1 + (e^{\frac{2.0}{t \cdot 3.0}} - 1)^*)}\right)\right)}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt10.4

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\left(\sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}} \cdot \sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}\right) \cdot \sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \log_* (1 + (e^{\frac{2.0}{t \cdot 3.0}} - 1)^*)\right)\right)}}\]

  6. Applied prod-diff38.4

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left((\left(\sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}} \cdot \sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}\right) \cdot \left(\sqrt[3]{\frac{z \cdot \sqrt{t + a}}{t}}\right) + \left(-\left(\left(a + \frac{5.0}{6.0}\right) - \log_* (1 + (e^{\frac{2.0}{t \cdot 3.0}} - 1)^*)\right) \cdot \left(b - c\right)\right))_* + (\left(-\left(\left(a + \frac{5.0}{6.0}\right) - \log_* (1 + (e^{\frac{2.0}{t \cdot 3.0}} - 1)^*)\right)\right) \cdot \left(b - c\right) + \left(\left(\left(a + \frac{5.0}{6.0}\right) - \log_* (1 + (e^{\frac{2.0}{t \cdot 3.0}} - 1)^*)\right) \cdot \left(b - c\right)\right))_*\right)}}}\]

  7. Applied simplify37.7

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

  8. Applied simplify1.8

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left((\left(c - b\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{3.0 \cdot t}\right) + \left(\frac{\sqrt{t + a}}{\frac{t}{z}}\right))_* + \color{blue}{0}\right)}}\]

Runtime

Time bar (total: 2.3m)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' +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)))))))))))