Average Error: 33.5 → 27.0
Time: 45.8s
Precision: 64
Internal Precision: 128
\[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.2330335312361627 \cdot 10^{-71}:\\ \;\;\;\;\left|\sqrt{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{n \cdot \ell}{Om}\right) + \left(2 \cdot \ell\right))_*\right) \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(U \cdot t\right) \cdot \left(2 \cdot n\right)\right))_*}} \cdot \sqrt{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{n \cdot \ell}{Om}\right) + \left(2 \cdot \ell\right))_*\right) \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(U \cdot t\right) \cdot \left(2 \cdot n\right)\right))_*}}\right|\\ \mathbf{elif}\;t \le 8.257330990400501 \cdot 10^{-80}:\\ \;\;\;\;\sqrt{(\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_* \cdot \left(n \cdot \left(\left(-2 \cdot U\right) \cdot \frac{\ell}{Om}\right)\right) + \left(\left(U \cdot n\right) \cdot 2\right) \cdot t}\\ \mathbf{elif}\;t \le 5.914050883243675 \cdot 10^{+176}:\\ \;\;\;\;\left|\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{n \cdot \ell}{Om}\right) + \left(2 \cdot \ell\right))_*\right) \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\sqrt[3]{\left(U \cdot t\right) \cdot \left(2 \cdot n\right)} \cdot \left(\sqrt[3]{\left(U \cdot t\right) \cdot \left(2 \cdot n\right)} \cdot \sqrt[3]{\left(U \cdot t\right) \cdot \left(2 \cdot n\right)}\right)\right))_*}\right|\\ \mathbf{else}:\\ \;\;\;\;\sqrt{t - (\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(n \cdot \left(U - U*\right)\right) + \left(\left(2 \cdot \ell\right) \cdot \frac{\ell}{Om}\right))_*} \cdot \sqrt{\left(U \cdot n\right) \cdot 2}\\ \end{array}\]

Error

Bits error versus n

Bits error versus U

Bits error versus t

Bits error versus l

Bits error versus Om

Bits error versus U*

Derivation

  1. Split input into 4 regimes

  2. if t < -1.2330335312361627e-71

    1. Initial program 32.8

      \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]

    2. Initial simplification32.0

      \[\leadsto \sqrt{\left(2 \cdot \left(U \cdot n\right)\right) \cdot \left(t - (\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right)}\]
    3. Using strategy rm

    4. Applied sub-neg32.0

      \[\leadsto \sqrt{\left(2 \cdot \left(U \cdot n\right)\right) \cdot \color{blue}{\left(t + \left(-(\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right)\right)}}\]

    5. Applied distribute-rgt-in32.0

      \[\leadsto \sqrt{\color{blue}{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(-(\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right) \cdot \left(2 \cdot \left(U \cdot n\right)\right)}}\]

    6. Simplified28.8

      \[\leadsto \sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \color{blue}{\left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}}\]
    7. Using strategy rm

    8. Applied add-sqr-sqrt28.8

      \[\leadsto \sqrt{\color{blue}{\sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*} \cdot \sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}}}\]

    9. Applied rem-sqrt-square28.8

      \[\leadsto \color{blue}{\left|\sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}\right|}\]

    10. Simplified26.8

      \[\leadsto \left|\color{blue}{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right) + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*}}\right|\]
    11. Using strategy rm

    12. Applied associate-*l/25.8

      \[\leadsto \left|\sqrt{(\left((\left(U - U*\right) \cdot \color{blue}{\left(\frac{\ell \cdot n}{Om}\right)} + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*}\right|\]
    13. Using strategy rm

    14. Applied add-sqr-sqrt25.8

      \[\leadsto \left|\sqrt{\color{blue}{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{\ell \cdot n}{Om}\right) + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*} \cdot \sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{\ell \cdot n}{Om}\right) + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*}}}\right|\]

    15. Applied sqrt-prod26.0

      \[\leadsto \left|\color{blue}{\sqrt{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{\ell \cdot n}{Om}\right) + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*}} \cdot \sqrt{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{\ell \cdot n}{Om}\right) + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*}}}\right|\]

    if -1.2330335312361627e-71 < t < 8.257330990400501e-80

    1. Initial program 35.0

      \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]

    2. Initial simplification33.7

      \[\leadsto \sqrt{\left(2 \cdot \left(U \cdot n\right)\right) \cdot \left(t - (\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right)}\]
    3. Using strategy rm

    4. Applied sub-neg33.7

      \[\leadsto \sqrt{\left(2 \cdot \left(U \cdot n\right)\right) \cdot \color{blue}{\left(t + \left(-(\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right)\right)}}\]

    5. Applied distribute-rgt-in33.7

      \[\leadsto \sqrt{\color{blue}{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(-(\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right) \cdot \left(2 \cdot \left(U \cdot n\right)\right)}}\]

    6. Simplified30.6

      \[\leadsto \sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \color{blue}{\left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}}\]
    7. Using strategy rm

    8. Applied associate-*l*29.5

      \[\leadsto \sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \color{blue}{\left(n \cdot \left(\left(U \cdot -2\right) \cdot \frac{\ell}{Om}\right)\right)} \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}\]

    if 8.257330990400501e-80 < t < 5.914050883243675e+176

    1. Initial program 30.5

      \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]

    2. Initial simplification29.8

      \[\leadsto \sqrt{\left(2 \cdot \left(U \cdot n\right)\right) \cdot \left(t - (\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right)}\]
    3. Using strategy rm

    4. Applied sub-neg29.8

      \[\leadsto \sqrt{\left(2 \cdot \left(U \cdot n\right)\right) \cdot \color{blue}{\left(t + \left(-(\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right)\right)}}\]

    5. Applied distribute-rgt-in29.8

      \[\leadsto \sqrt{\color{blue}{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(-(\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right) \cdot \left(2 \cdot \left(U \cdot n\right)\right)}}\]

    6. Simplified26.9

      \[\leadsto \sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \color{blue}{\left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}}\]
    7. Using strategy rm

    8. Applied add-sqr-sqrt26.9

      \[\leadsto \sqrt{\color{blue}{\sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*} \cdot \sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}}}\]

    9. Applied rem-sqrt-square26.9

      \[\leadsto \color{blue}{\left|\sqrt{t \cdot \left(2 \cdot \left(U \cdot n\right)\right) + \left(\left(n \cdot \left(U \cdot -2\right)\right) \cdot \frac{\ell}{Om}\right) \cdot (\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_*}\right|}\]

    10. Simplified25.4

      \[\leadsto \left|\color{blue}{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right) + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*}}\right|\]
    11. Using strategy rm

    12. Applied associate-*l/24.6

      \[\leadsto \left|\sqrt{(\left((\left(U - U*\right) \cdot \color{blue}{\left(\frac{\ell \cdot n}{Om}\right)} + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(t \cdot U\right) \cdot \left(n \cdot 2\right)\right))_*}\right|\]
    13. Using strategy rm

    14. Applied add-cube-cbrt24.9

      \[\leadsto \left|\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{\ell \cdot n}{Om}\right) + \left(\ell \cdot 2\right))_*\right) \cdot \left(\frac{\left(\ell \cdot n\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \color{blue}{\left(\left(\sqrt[3]{\left(t \cdot U\right) \cdot \left(n \cdot 2\right)} \cdot \sqrt[3]{\left(t \cdot U\right) \cdot \left(n \cdot 2\right)}\right) \cdot \sqrt[3]{\left(t \cdot U\right) \cdot \left(n \cdot 2\right)}\right)})_*}\right|\]

    if 5.914050883243675e+176 < t

    1. Initial program 36.3

      \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]

    2. Initial simplification36.1

      \[\leadsto \sqrt{\left(2 \cdot \left(U \cdot n\right)\right) \cdot \left(t - (\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*\right)}\]
    3. Using strategy rm

    4. Applied sqrt-prod25.5

      \[\leadsto \color{blue}{\sqrt{2 \cdot \left(U \cdot n\right)} \cdot \sqrt{t - (\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(\left(U - U*\right) \cdot n\right) + \left(\frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right))_*}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification27.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.2330335312361627 \cdot 10^{-71}:\\ \;\;\;\;\left|\sqrt{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{n \cdot \ell}{Om}\right) + \left(2 \cdot \ell\right))_*\right) \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(U \cdot t\right) \cdot \left(2 \cdot n\right)\right))_*}} \cdot \sqrt{\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{n \cdot \ell}{Om}\right) + \left(2 \cdot \ell\right))_*\right) \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\left(U \cdot t\right) \cdot \left(2 \cdot n\right)\right))_*}}\right|\\ \mathbf{elif}\;t \le 8.257330990400501 \cdot 10^{-80}:\\ \;\;\;\;\sqrt{(\left(n \cdot \left(U - U*\right)\right) \cdot \left(\frac{\ell}{Om}\right) + \left(2 \cdot \ell\right))_* \cdot \left(n \cdot \left(\left(-2 \cdot U\right) \cdot \frac{\ell}{Om}\right)\right) + \left(\left(U \cdot n\right) \cdot 2\right) \cdot t}\\ \mathbf{elif}\;t \le 5.914050883243675 \cdot 10^{+176}:\\ \;\;\;\;\left|\sqrt{(\left((\left(U - U*\right) \cdot \left(\frac{n \cdot \ell}{Om}\right) + \left(2 \cdot \ell\right))_*\right) \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(-2 \cdot U\right)}{Om}\right) + \left(\sqrt[3]{\left(U \cdot t\right) \cdot \left(2 \cdot n\right)} \cdot \left(\sqrt[3]{\left(U \cdot t\right) \cdot \left(2 \cdot n\right)} \cdot \sqrt[3]{\left(U \cdot t\right) \cdot \left(2 \cdot n\right)}\right)\right))_*}\right|\\ \mathbf{else}:\\ \;\;\;\;\sqrt{t - (\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot \left(n \cdot \left(U - U*\right)\right) + \left(\left(2 \cdot \ell\right) \cdot \frac{\ell}{Om}\right))_*} \cdot \sqrt{\left(U \cdot n\right) \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (n U t l Om U*)
  :name "Toniolo and Linder, Equation (13)"
  (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))))

Details

Time bar (total: 31.5s)Debug log

start571.0ms

Algorithm
intervals

setup135.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize85.0ms

Local error

Found 4 expressions with local error:

18.9b
(sqrt (* (* 2 (* U n)) (- t (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l))))))
12.6b
(fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l)))
10.3b
(* (* 2 (* U n)) (- t (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l)))))
0.2b
(* (/ l Om) (/ l Om))

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

10.0ms
(* (* 2 (* U n)) (- t (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l)))))
9.0ms
(sqrt (* (* 2 (* U n)) (- t (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l))))))
6.0ms
(* (/ l Om) (/ l Om))

series2.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

1.6s
(sqrt (* (* 2 (* U n)) (- t (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l))))))
318.0ms
(* (* 2 (* U n)) (- t (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l)))))
84.0ms
(fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l)))
23.0ms
(* (/ l Om) (/ l Om))

simplify4.9s

Counts
42 → 85
Calls

42 calls. Slowest were:

874.0ms
(* (* (* (/ l Om) (/ l Om)) (/ l Om)) (* (* (/ l Om) (/ l Om)) (/ l Om)))
429.0ms
(+ (* t t) (+ (* (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l))) (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l)))) (* t (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l))))))
387.0ms
(* (- (fma (* (/ l Om) (/ l Om)) (* (- U U*) n) (* (/ l Om) (* 2 l)))) (* 2 (* U n)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.6b

localize51.0ms

Local error

Found 4 expressions with local error:

18.9b
(sqrt (+ (* t (* 2 (* U n))) (* (* (* n (* U -2)) (/ l Om)) (fma (* n (- U U*)) (/ l Om) (* 2 l)))))
10.1b
(* (* n (* U -2)) (/ l Om))
8.8b
(fma (* n (- U U*)) (/ l Om) (* 2 l))
4.4b
(* t (* 2 (* U n)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

8.0ms
(* (* n (* U -2)) (/ l Om))
5.0ms
(sqrt (+ (* t (* 2 (* U n))) (* (* (* n (* U -2)) (/ l Om)) (fma (* n (- U U*)) (/ l Om) (* 2 l)))))
4.0ms
(* t (* 2 (* U n)))

series954.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

823.0ms
(sqrt (+ (* t (* 2 (* U n))) (* (* (* n (* U -2)) (/ l Om)) (fma (* n (- U U*)) (/ l Om) (* 2 l)))))
66.0ms
(fma (* n (- U U*)) (/ l Om) (* 2 l))
37.0ms
(* (* n (* U -2)) (/ l Om))
29.0ms
(* t (* 2 (* U n)))

simplify3.1s

Counts
26 → 68
Calls

26 calls. Slowest were:

513.0ms
(- (+ (/ (* U (* n l)) Om) (* 2 l)) (/ (* n (* U* l)) Om))
387.0ms
(+ (log (* n (* U -2))) (log (/ l Om)))
260.0ms
(sqrt (+ (pow (* t (* 2 (* U n))) 3) (pow (* (* (* n (* U -2)) (/ l Om)) (fma (* n (- U U*)) (/ l Om) (* 2 l))) 3)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.0b

localize54.0ms

Local error

Found 4 expressions with local error:

18.9b
(sqrt (fma (fma (- U U*) (* (/ l Om) n) (* l 2)) (/ (* (* l n) (* -2 U)) Om) (* (* t U) (* n 2))))
6.0b
(* (/ l Om) n)
5.5b
(* (* t U) (* n 2))
5.0b
(/ (* (* l n) (* -2 U)) Om)

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

11.0ms
(/ (* (* l n) (* -2 U)) Om)
6.0ms
(* (* t U) (* n 2))
4.0ms
(* (/ l Om) n)

series2.6s

Counts
4 → 12
Calls

4 calls. Slowest were:

2.5s
(sqrt (fma (fma (- U U*) (* (/ l Om) n) (* l 2)) (/ (* (* l n) (* -2 U)) Om) (* (* t U) (* n 2))))
28.0ms
(/ (* (* l n) (* -2 U)) Om)
20.0ms
(* (* t U) (* n 2))
17.0ms
(* (/ l Om) n)

simplify2.5s

Counts
23 → 69
Calls

23 calls. Slowest were:

681.0ms
(* (* (* (* t U) (* t U)) (* t U)) (* (* (* n 2) (* n 2)) (* n 2)))
292.0ms
(* -2 (/ (* U (* n l)) Om))
265.0ms
(* -2 (/ (* U (* n l)) Om))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.0b

localize19.0ms

Local error

Found 4 expressions with local error:

18.9b
(sqrt (fma (fma (- U U*) (/ (* l n) Om) (* l 2)) (/ (* (* l n) (* -2 U)) Om) (* (* t U) (* n 2))))
5.5b
(* (* t U) (* n 2))
5.0b
(/ (* (* l n) (* -2 U)) Om)
3.8b
(* (* l n) (* -2 U))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

6.0ms
(/ (* (* l n) (* -2 U)) Om)
3.0ms
(* (* l n) (* -2 U))
3.0ms
(* (* t U) (* n 2))

series2.5s

Counts
4 → 12
Calls

4 calls. Slowest were:

2.4s
(sqrt (fma (fma (- U U*) (/ (* l n) Om) (* l 2)) (/ (* (* l n) (* -2 U)) Om) (* (* t U) (* n 2))))
52.0ms
(/ (* (* l n) (* -2 U)) Om)
20.0ms
(* (* t U) (* n 2))
17.0ms
(* (* l n) (* -2 U))

simplify3.0s

Counts
23 → 69
Calls

23 calls. Slowest were:

618.0ms
(* (* (* (* l n) (* l n)) (* l n)) (* (* (* -2 U) (* -2 U)) (* -2 U)))
564.0ms
(* (* (* (* t U) (* t U)) (* t U)) (* (* (* n 2) (* n 2)) (* n 2)))
271.0ms
(* -2 (/ (* U (* n l)) Om))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.0b

regimes1.1s

Accuracy

8.5% (8.9b remaining)

Error of 27.0b against oracle of 18.1b and baseline of 27.8b

bsearch1.5s