Average Error: 3.6 → 2.7
Time: 4.6m
Precision: 64
Internal Precision: 128
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{y \cdot e^{2.0 \cdot \left(\sqrt{a + t} \cdot \frac{z}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)} + x}\]

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

Bits error versus c

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.6

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

  3. Applied associate-/l*2.9

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

  5. Applied associate-/r/2.7

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

  6. Final simplification2.7

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

Runtime

Time bar (total: 4.6m)Debug logProfile

herbie shell --seed 2018349 
(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)))))))))))