Average Error: 1.8 → 2.0
Time: 59.4s
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{1}{\frac{\frac{y}{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}}}{x}}\]

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  3. Applied associate-/l*1.9

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

  4. Taylor expanded around inf 1.9

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

  5. Simplified1.9

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

  7. Applied clear-num2.0

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

  8. Final simplification2.0

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

Runtime

Time bar (total: 59.4s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes2.02.00.11.90%
herbie shell --seed 2018297 +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))