Average Error: 53.7 → 49.9
Time: 2.2m
Precision: 64
Internal Precision: 320
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.028065649190901 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{e^{2.0 \cdot \left(\frac{{\left(\left(\sqrt{a + t} \cdot z\right) \cdot \left(\left(\sqrt{a + t} \cdot z\right) \cdot \left(\sqrt{a + t} \cdot z\right)\right)\right)}^{\frac{1}{3}}}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)} \cdot y + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\sqrt{a + t} \cdot z}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \log \left(e^{\frac{2.0}{3.0 \cdot t}}\right)\right) \cdot \left(b - c\right)\right)}}\\ \end{array}\]

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

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if z < -3.028065649190901e+78

    1. Initial program 57.7

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

    3. Applied add-cbrt-cube60.2

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\color{blue}{\sqrt[3]{\left(\left(z \cdot \sqrt{t + a}\right) \cdot \left(z \cdot \sqrt{t + a}\right)\right) \cdot \left(z \cdot \sqrt{t + a}\right)}}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    4. Using strategy rm

    5. Applied pow1/345.6

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

    if -3.028065649190901e+78 < z

    1. Initial program 52.4

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

    3. Applied add-log-exp51.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{blue}{\log \left(e^{\frac{2.0}{t \cdot 3.0}}\right)}\right)\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification49.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.028065649190901 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{e^{2.0 \cdot \left(\frac{{\left(\left(\sqrt{a + t} \cdot z\right) \cdot \left(\left(\sqrt{a + t} \cdot z\right) \cdot \left(\sqrt{a + t} \cdot z\right)\right)\right)}^{\frac{1}{3}}}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)} \cdot y + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\sqrt{a + t} \cdot z}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \log \left(e^{\frac{2.0}{3.0 \cdot t}}\right)\right) \cdot \left(b - c\right)\right)}}\\ \end{array}\]

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed 2018255 
(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)))))))))))