Details

Time bar (total: 19.4s)

sample38.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
9.0ms276×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ a (- (acos a)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 55
Calls
1 calls:
14.0ms
(/ a (- (acos a)))

series44.0ms

Counts
1 → 3
Calls
1 calls:
44.0ms
(/ a (- (acos a)))

simplify4.7s

Counts
58 → 58
Iterations

Useful iterations: 5 (1.8s)

IterNodesCost
094601
1164569
2334551
3587551
41101551
52149546
done5000546

prune124.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ -1 (acos a))
0.3b
(* a (/ -1 (acos a)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×associate-*r*
9×add-exp-log add-cbrt-cube
4×pow1
3×associate-*l* associate-/r* associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv add-log-exp unswap-sqr
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 59
Calls
2 calls:
10.0ms
(/ -1 (acos a))
17.0ms
(* a (/ -1 (acos a)))

series55.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(/ -1 (acos a))
43.0ms
(* a (/ -1 (acos a)))

simplify8.2s

Counts
65 → 65
Iterations

Useful iterations: 3 (551.0ms)

IterNodesCost
086558
1180510
2502460
31348458
43468458
done5001458

prune228.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (acos a) (- a))
0.4b
(/ 1 (/ (acos a) (- a)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×distribute-lft-neg-in distribute-rgt-neg-in
44×associate-/r*
16×neg-mul-1
15×add-exp-log
9×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
4×cbrt-undiv
3×pow1
2×rec-exp frac-2neg 1-exp clear-num add-log-exp
1×acos-asin pow-flip div-sub associate-/r/ inv-pow
Counts
2 → 216
Calls
2 calls:
14.0ms
(/ (acos a) (- a))
17.0ms
(/ 1 (/ (acos a) (- a)))

series74.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(/ (acos a) (- a))
27.0ms
(/ 1 (/ (acos a) (- a)))

simplify2.6s

Counts
222 → 222
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
02933186
16112657
211352356
327522260
done50002260

prune456.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1 (acos a))
0.6b
(/ (/ 1 (acos a)) (/ 1 (- a)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
1186×times-frac
535×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
126×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×add-exp-log
42×neg-mul-1
37×associate-/r*
34×div-exp
16×add-cbrt-cube associate-/l*
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×frac-2neg clear-num add-log-exp
1×pow-flip associate-/r/ associate-/l/ inv-pow
Counts
2 → 552
Calls
2 calls:
6.0ms
(/ 1 (acos a))
56.0ms
(/ (/ 1 (acos a)) (/ 1 (- a)))

series56.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(/ 1 (acos a))
43.0ms
(/ (/ 1 (acos a)) (/ 1 (- a)))

simplify2.2s

Counts
558 → 558
Iterations

Useful iterations: done (2.2s)

IterNodesCost
080512210
122738248
232567104
done50006756

prune325.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes1.0ms