Average Error: 1.9 → 1.4
Time: 1.2m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{e^{(\left(\log a\right) \cdot \left(t - 1.0\right) + \left(-b\right))_*}}{\frac{y}{{z}^{y} \cdot x}} \le 4.4813484382051184 \cdot 10^{+49}:\\ \;\;\;\;\frac{e^{(\left(\log a\right) \cdot \left(t - 1.0\right) + \left(-b\right))_*}}{\frac{y}{{z}^{y} \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}\\ \end{array}\]

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

Derivation

  1. Split input into 2 regimes

  2. if (/ (exp (fma (log a) (- t 1.0) (- b))) (/ y (* x (pow z y)))) < 4.4813484382051184e+49

    1. Initial program 2.4

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

    2. Initial simplification1.6

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

    if 4.4813484382051184e+49 < (/ (exp (fma (log a) (- t 1.0) (- b))) (/ y (* x (pow z y))))

    1. Initial program 0.8

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{e^{(\left(\log a\right) \cdot \left(t - 1.0\right) + \left(-b\right))_*}}{\frac{y}{{z}^{y} \cdot x}} \le 4.4813484382051184 \cdot 10^{+49}:\\ \;\;\;\;\frac{e^{(\left(\log a\right) \cdot \left(t - 1.0\right) + \left(-b\right))_*}}{\frac{y}{{z}^{y} \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}\\ \end{array}\]

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018217 +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))