Average Error: 1.8 → 1.0
Time: 1.9m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\sqrt[3]{\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}}} \le -9.939663084627983 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{\frac{e^{b} \cdot y}{{z}^{y} \cdot \left({a}^{t} \cdot {a}^{\left(-1.0\right)}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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 (cbrt (/ (* (exp b) y) (* (pow z y) (pow a (- t 1.0))))) < -9.939663084627983e-102

    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. Using strategy rm

    3. Applied associate-/l*1.2

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

    4. Applied simplify0.2

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

    6. Applied sub-neg0.2

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

    7. Applied unpow-prod-up0.1

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

    if -9.939663084627983e-102 < (cbrt (/ (* (exp b) y) (* (pow z y) (pow a (- t 1.0)))))

    1. Initial program 1.5

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' 
(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))