Details

Time bar (total: 5.9s)

sample49.0ms

Algorithm
intervals
Results
21.0ms739×body80nan
9.0ms256×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
36×times-frac
35×add-sqr-sqrt
29×add-cube-cbrt
20×sqrt-prod
13×fma-def
7×associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
4×pow1 sqrt-div div-inv distribute-lft-out
3×expm1-log1p-u associate-/r* log1p-expm1-u
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add clear-num sum-log flip-+
Counts
3 → 97
Calls
3 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
29.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series300.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(sqrt (- 1.0 (* x x)))
137.0ms
(/ (sqrt (- 1.0 (* x x))) x)
105.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify517.0ms

Counts
106 → 106
Iterations

Useful iterations: 2 (153.0ms)

IterNodesCost
01811437
14161319
214291246
done50001246

prune344.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (* (fabs (cbrt (- 1.0 (* x x)))) (/ (sqrt (cbrt (- 1.0 (* x x)))) x)))
0.0b
(* (fabs (cbrt (- 1.0 (* x x)))) (/ (sqrt (cbrt (- 1.0 (* x x)))) x))
0.0b
(cbrt (- 1.0 (* x x)))
0.0b
(cbrt (- 1.0 (* x x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
42×times-frac
34×add-cube-cbrt *-un-lft-identity associate-*r*
23×sqrt-prod
21×cbrt-prod
13×fma-def
9×add-exp-log add-cbrt-cube
6×pow1 add-log-exp
5×difference-of-squares
4×expm1-log1p-u cbrt-div log1p-expm1-u unswap-sqr
3×associate-*l*
2×flip3-- pow1/3 associate-*r/ prod-exp flip-- cbrt-unprod div-inv
1×cbrt-undiv +-commutative flip3-+ div-exp pow-prod-down frac-add sum-log *-commutative flip-+
Counts
4 → 116
Calls
4 calls:
10.0ms
(+ (/ 1.0 x) (* (fabs (cbrt (- 1.0 (* x x)))) (/ (sqrt (cbrt (- 1.0 (* x x)))) x)))
20.0ms
(* (fabs (cbrt (- 1.0 (* x x)))) (/ (sqrt (cbrt (- 1.0 (* x x)))) x))
2.0ms
(cbrt (- 1.0 (* x x)))
2.0ms
(cbrt (- 1.0 (* x x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
314.0ms
(+ (/ 1.0 x) (* (fabs (cbrt (- 1.0 (* x x)))) (/ (sqrt (cbrt (- 1.0 (* x x)))) x)))
364.0ms
(* (fabs (cbrt (- 1.0 (* x x)))) (/ (sqrt (cbrt (- 1.0 (* x x)))) x))
207.0ms
(cbrt (- 1.0 (* x x)))
233.0ms
(cbrt (- 1.0 (* x x)))

simplify1.4s

Counts
128 → 128
Iterations

Useful iterations: 2 (300.0ms)

IterNodesCost
02772862
17152662
229002450
done50012450

prune511.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11422
done1422

end0.0ms

sample1.5s

Algorithm
intervals
Results
762.0ms24242×body80nan
315.0ms8000×body80valid