Average Error: 3.6 → 11.2
Time: 56.7s
Precision: 64
Internal Precision: 576
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.457178538926173 \cdot 10^{-81} \lor \neg \left(a \le -6.074263936852065 \cdot 10^{-172}\right) \land \left(a \le -2.2172521833931558 \cdot 10^{-214} \lor \neg \left(a \le 1.3360974902915475 \cdot 10^{+140}\right)\right):\\ \;\;\;\;\frac{x}{e^{\left(c \cdot 0.8333333333333334 - a \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{2.0 \cdot \left(\frac{\sqrt{a + t} \cdot z}{t} - \left(b \cdot 0.8333333333333334 + \frac{0.6666666666666666}{t} \cdot \left(c - b\right)\right)\right)} + x}\\ \end{array}\]

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 a < -4.457178538926173e-81 or -6.074263936852065e-172 < a < -2.2172521833931558e-214 or 1.3360974902915475e+140 < a

    1. Initial program 4.8

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

    2. Taylor expanded around -inf 15.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}}\]

    3. Simplified12.4

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left(0.8333333333333334 \cdot c - \left(b - c\right) \cdot a\right)}}}\]

    if -4.457178538926173e-81 < a < -6.074263936852065e-172 or -2.2172521833931558e-214 < a < 1.3360974902915475e+140

    1. Initial program 2.9

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

    2. Taylor expanded around 0 2.9

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{blue}{\frac{0.6666666666666666}{t}}\right)\right)}}\]

    3. Taylor expanded around 0 11.9

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{c}{t} + 0.8333333333333334 \cdot b\right) - 0.6666666666666666 \cdot \frac{b}{t}\right)}\right)}}\]

    4. Simplified10.5

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\left(0.8333333333333334 \cdot b + \left(c - b\right) \cdot \frac{0.6666666666666666}{t}\right)}\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.457178538926173 \cdot 10^{-81} \lor \neg \left(a \le -6.074263936852065 \cdot 10^{-172}\right) \land \left(a \le -2.2172521833931558 \cdot 10^{-214} \lor \neg \left(a \le 1.3360974902915475 \cdot 10^{+140}\right)\right):\\ \;\;\;\;\frac{x}{e^{\left(c \cdot 0.8333333333333334 - a \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{2.0 \cdot \left(\frac{\sqrt{a + t} \cdot z}{t} - \left(b \cdot 0.8333333333333334 + \frac{0.6666666666666666}{t} \cdot \left(c - b\right)\right)\right)} + x}\\ \end{array}\]

Runtime

Time bar (total: 56.7s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes14.811.20.314.524.5%
herbie shell --seed 2018296 
(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)))))))))))