Average Error: 53.7 → 42.8
Time: 58.4s
Precision: 64
Internal Precision: 128
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[0\]

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

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 53.7

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

  2. Initial simplification52.8

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

  3. Taylor expanded around 0 49.2

    \[\leadsto \frac{x}{(y \cdot \color{blue}{\left(\left(1.6666666666666667 \cdot c + \left(1.3333333333333333 \cdot \frac{b}{t} + 1\right)\right) - \left(1.3333333333333333 \cdot \frac{c}{t} + 1.6666666666666667 \cdot b\right)\right)} + x)_*}\]

  4. Simplified49.2

    \[\leadsto \frac{x}{(y \cdot \color{blue}{\left((1.3333333333333333 \cdot \left(\frac{b}{t}\right) + \left((1.6666666666666667 \cdot c + 1)_*\right))_* - (\left(\frac{c}{t}\right) \cdot 1.3333333333333333 + \left(b \cdot 1.6666666666666667\right))_*\right)} + x)_*}\]

  5. Taylor expanded around 0 42.8

    \[\leadsto \color{blue}{0}\]

  6. Final simplification42.8

    \[\leadsto 0\]

Runtime

Time bar (total: 58.4s)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(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)))))))))))