Average Error: 29.0 → 29.0
Time: 1.5m
Precision: 64
Internal precision: 128
\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
⬇
\[\frac{0.0001789971 \cdot \left({\left({x}^3\right)}^2 \cdot \left({x}^2 \cdot {x}^3\right)\right)}{\left(\left({\left({x}^3\right)}^2 \cdot {\left({x}^2\right)}^2\right) \cdot \left(\left(x \cdot 0.0001789971\right) \cdot \left(x + x\right) + 0.0008327945\right) + {\left({x}^3\right)}^2 \cdot \left(0.0140005442 \cdot {x}^2 + 0.0694555761\right)\right) + \left(0.7715471019 \cdot {x}^2 + \left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right)\right)} + \frac{x \cdot \left(\left({x}^2 \cdot 0.1049934947 + \left(\left(0.0424060604 \cdot x\right) \cdot {x}^3 + 1\right)\right) + {\left({x}^3\right)}^2 \cdot \left({x}^2 \cdot 0.0005064034 + 0.0072644182\right)\right)}{\left({\left({x}^3\right)}^2 \cdot {\left({x}^2\right)}^2\right) \cdot \left({x}^2 \cdot \left(0.0001789971 + 0.0001789971\right) + 0.0008327945\right) + \left(\left(0.7715471019 \cdot {x}^2 + \left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right)\right) + \left(0.0140005442 \cdot {x}^2 + 0.0694555761\right) \cdot {\left({x}^3\right)}^2\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 29.0

    \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

  2. Applied simplify 28.9

    \[\leadsto \color{blue}{\frac{x}{\left({\left({x}^2\right)}^3 \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot \left(\left(0.0001789971 + 0.0001789971\right) \cdot {x}^2 + 0.0008327945\right) + \left(\left(0.7715471019 \cdot {x}^2 + \left(\left(0.2909738639 \cdot x\right) \cdot {x}^3 + 1\right)\right) + \left(\left({x}^2 \cdot 0.0140005442\right) \cdot {\left({x}^2\right)}^3 + 0.0694555761 \cdot {\left({x}^2\right)}^3\right)\right)} \cdot \left(\left({\left({x}^2\right)}^3 \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot 0.0001789971 + \left(\left(\left(\left(0.0424060604 \cdot x\right) \cdot {x}^3 + 1\right) + {x}^2 \cdot 0.1049934947\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3 + \left({x}^2 \cdot 0.0005064034\right) \cdot {\left({x}^2\right)}^3\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in 28.9

    \[\leadsto \color{blue}{\frac{x}{\left({\left({x}^2\right)}^3 \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot \left(\left(0.0001789971 + 0.0001789971\right) \cdot {x}^2 + 0.0008327945\right) + \left(\left(0.7715471019 \cdot {x}^2 + \left(\left(0.2909738639 \cdot x\right) \cdot {x}^3 + 1\right)\right) + \left(\left({x}^2 \cdot 0.0140005442\right) \cdot {\left({x}^2\right)}^3 + 0.0694555761 \cdot {\left({x}^2\right)}^3\right)\right)} \cdot \left(\left({\left({x}^2\right)}^3 \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot 0.0001789971\right) + \frac{x}{\left({\left({x}^2\right)}^3 \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot \left(\left(0.0001789971 + 0.0001789971\right) \cdot {x}^2 + 0.0008327945\right) + \left(\left(0.7715471019 \cdot {x}^2 + \left(\left(0.2909738639 \cdot x\right) \cdot {x}^3 + 1\right)\right) + \left(\left({x}^2 \cdot 0.0140005442\right) \cdot {\left({x}^2\right)}^3 + 0.0694555761 \cdot {\left({x}^2\right)}^3\right)\right)} \cdot \left(\left(\left(\left(0.0424060604 \cdot x\right) \cdot {x}^3 + 1\right) + {x}^2 \cdot 0.1049934947\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3 + \left({x}^2 \cdot 0.0005064034\right) \cdot {\left({x}^2\right)}^3\right)\right)}\]

  5. Applied simplify 29.0

    \[\leadsto \color{blue}{\frac{0.0001789971 \cdot \left({\left({x}^3\right)}^2 \cdot \left({x}^2 \cdot {x}^3\right)\right)}{\left(\left({\left({x}^3\right)}^2 \cdot {\left({x}^2\right)}^2\right) \cdot \left(\left(x \cdot 0.0001789971\right) \cdot \left(x + x\right) + 0.0008327945\right) + {\left({x}^3\right)}^2 \cdot \left(0.0140005442 \cdot {x}^2 + 0.0694555761\right)\right) + \left(0.7715471019 \cdot {x}^2 + \left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right)\right)}} + \frac{x}{\left({\left({x}^2\right)}^3 \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot \left(\left(0.0001789971 + 0.0001789971\right) \cdot {x}^2 + 0.0008327945\right) + \left(\left(0.7715471019 \cdot {x}^2 + \left(\left(0.2909738639 \cdot x\right) \cdot {x}^3 + 1\right)\right) + \left(\left({x}^2 \cdot 0.0140005442\right) \cdot {\left({x}^2\right)}^3 + 0.0694555761 \cdot {\left({x}^2\right)}^3\right)\right)} \cdot \left(\left(\left(\left(0.0424060604 \cdot x\right) \cdot {x}^3 + 1\right) + {x}^2 \cdot 0.1049934947\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3 + \left({x}^2 \cdot 0.0005064034\right) \cdot {\left({x}^2\right)}^3\right)\right)\]

  6. Applied simplify 29.0

    \[\leadsto \frac{0.0001789971 \cdot \left({\left({x}^3\right)}^2 \cdot \left({x}^2 \cdot {x}^3\right)\right)}{\left(\left({\left({x}^3\right)}^2 \cdot {\left({x}^2\right)}^2\right) \cdot \left(\left(x \cdot 0.0001789971\right) \cdot \left(x + x\right) + 0.0008327945\right) + {\left({x}^3\right)}^2 \cdot \left(0.0140005442 \cdot {x}^2 + 0.0694555761\right)\right) + \left(0.7715471019 \cdot {x}^2 + \left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right)\right)} + \color{blue}{\frac{x \cdot \left(\left({x}^2 \cdot 0.1049934947 + \left(\left(0.0424060604 \cdot x\right) \cdot {x}^3 + 1\right)\right) + {\left({x}^3\right)}^2 \cdot \left({x}^2 \cdot 0.0005064034 + 0.0072644182\right)\right)}{\left({\left({x}^3\right)}^2 \cdot {\left({x}^2\right)}^2\right) \cdot \left({x}^2 \cdot \left(0.0001789971 + 0.0001789971\right) + 0.0008327945\right) + \left(\left(0.7715471019 \cdot {x}^2 + \left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right)\right) + \left(0.0140005442 \cdot {x}^2 + 0.0694555761\right) \cdot {\left({x}^3\right)}^2\right)}}\]
  7. Removed slow pow expressions

Runtime

Time bar (total: 1.5m) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3793905406 2290198159 3782010913 2953362661 1764418324 3288398504)'
(FPCore (x)
  :name "Jmat.Real.dawson"
  (* (/ (+ (+ (+ (+ (+ 1 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))