Average Error: 1.9 → 2.3
Time: 1.6m
Precision: 64
Internal Precision: 384
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - 1.0\right) \cdot \log a \le -591.6896912817447:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(\sqrt[3]{\left(t - 1.0\right) \cdot \log a} \cdot \sqrt[3]{\left(t - 1.0\right) \cdot \log a}\right) \cdot \sqrt[3]{\left(t - 1.0\right) \cdot \log a}\right) - b}}{y}\\ \mathbf{if}\;\left(t - 1.0\right) \cdot \log a \le -167.9720135823427:\\ \;\;\;\;x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(\sqrt[3]{\left(t - 1.0\right) \cdot \log a} \cdot \sqrt[3]{\left(t - 1.0\right) \cdot \log a}\right) \cdot \sqrt[3]{\left(t - 1.0\right) \cdot \log a}\right) - b}}{y}\\ \end{array}\]

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 (* (- t 1.0) (log a)) < -591.6896912817447 or -167.9720135823427 < (* (- t 1.0) (log a))

    1. Initial program 1.0

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

    3. Applied add-cube-cbrt1.3

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(\sqrt[3]{\left(t - 1.0\right) \cdot \log a} \cdot \sqrt[3]{\left(t - 1.0\right) \cdot \log a}\right) \cdot \sqrt[3]{\left(t - 1.0\right) \cdot \log a}}\right) - b}}{y}\]

    if -591.6896912817447 < (* (- t 1.0) (log a)) < -167.9720135823427

    1. Initial program 5.9

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

    3. Applied associate-/l*2.3

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

    4. Applied simplify6.7

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{z}^{y}}{e^{b}} \cdot {a}^{\left(t - 1.0\right)}}}}\]
    5. Using strategy rm

    6. Applied div-inv6.7

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{y}{\frac{{z}^{y}}{e^{b}} \cdot {a}^{\left(t - 1.0\right)}}}}\]

    7. Applied simplify6.7

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed '#(1064397287 3527694221 3797617954 1138343853 2854031332 1153838279)' 
(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))