Details

Time bar (total: 14.7s)

sample27.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
6.0ms310×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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:
7.0ms
(/ a (- (acos a)))

series38.0ms

Counts
1 → 3
Calls
1 calls:
38.0ms
(/ a (- (acos a)))

simplify5.4s

Counts
58 → 58
Iterations

Useful iterations: 5 (2.0s)

IterNodesCost
094601
1164569
2334551
3587551
41101551
52149546
done5000546

prune139.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (acos a) (- a))
0.3b
(/ 1 (/ (acos a) (- a)))

rewrite75.0ms

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:
21.0ms
(/ (acos a) (- a))
29.0ms
(/ 1 (/ (acos a) (- a)))

series80.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (acos a) (- a))
31.0ms
(/ 1 (/ (acos a) (- a)))

simplify2.6s

Counts
222 → 222
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
02933186
16112657
211352356
327522260
done50002260

prune399.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
17×add-sqr-sqrt
16×add-cbrt-cube
13×times-frac associate-*r*
12×add-cube-cbrt *-un-lft-identity
10×div-exp
8×prod-exp
7×pow1
5×cbrt-undiv
4×cbrt-unprod
3×rec-exp 1-exp associate-*l* associate-/l*
2×pow-flip associate-*r/ pow-prod-down div-inv add-log-exp unswap-sqr
1×frac-2neg clear-num associate-/r* associate-/r/ *-commutative inv-pow
Counts
2 → 65
Calls
2 calls:
39.0ms
(/ 1 (* (acos a) (/ -1 a)))
25.0ms
(* (acos a) (/ -1 a))

series81.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ 1 (* (acos a) (/ -1 a)))
41.0ms
(* (acos a) (/ -1 a))

simplify5.4s

Counts
71 → 71
Iterations

Useful iterations: 3 (3.3s)

IterNodesCost
0111695
1259569
2859446
34033444
done5000444

prune152.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- (/ (acos a) a)))
0.5b
(cbrt (- (/ (acos a) a)))
0.5b
(cbrt (- (/ (acos a) a)))
0.5b
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
218×cbrt-prod
126×times-frac
121×add-sqr-sqrt
117×*-un-lft-identity
113×add-cube-cbrt
93×distribute-rgt-neg-in
91×distribute-lft-neg-in
35×swap-sqr
33×associate-*r* associate-*l*
14×div-inv
11×pow1
9×pow1/3
7×neg-mul-1 cbrt-div distribute-neg-frac
6×add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 243
Calls
4 calls:
5.0ms
(cbrt (- (/ (acos a) a)))
6.0ms
(cbrt (- (/ (acos a) a)))
5.0ms
(cbrt (- (/ (acos a) a)))
112.0ms
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))

series1.0ms