Details

Time bar (total: 22.5s)

sample35.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
7.0ms270×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

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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:
9.0ms
(/ a (- (acos a)))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(/ a (- (acos a)))

simplify4.6s

Counts
58 → 58
Iterations

Useful iterations: 5 (1.9s)

IterNodesCost
094601
1164569
2334551
3587551
41101551
52149546
done5000546

prune181.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (acos a) (- a)))
0.3b
(/ (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:
17.0ms
(/ 1 (/ (acos a) (- a)))
16.0ms
(/ (acos a) (- a))

series83.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(/ 1 (/ (acos a) (- a)))
50.0ms
(/ (acos a) (- a))

simplify2.5s

Counts
222 → 222
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
02933186
16112657
211412356
327492260
done50002260

prune400.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite71.0ms

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:
34.0ms
(/ 1 (* (acos a) (/ -1 a)))
35.0ms
(* (acos a) (/ -1 a))

series76.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ 1 (* (acos a) (/ -1 a)))
44.0ms
(* (acos a) (/ -1 a))

simplify5.0s

Counts
71 → 71
Iterations

Useful iterations: 3 (3.2s)

IterNodesCost
0111695
1259569
2859446
34033444
done5000444

prune152.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a))
0.6b
(cbrt (- a))
1.0b
(sqrt (acos a))
1.0b
(sqrt (acos a))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
20×cbrt-prod
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 62
Calls
4 calls:
4.0ms
(cbrt (- a))
3.0ms
(cbrt (- a))
2.0ms
(sqrt (acos a))
2.0ms
(sqrt (acos a))

series636.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(cbrt (- a))
329.0ms
(cbrt (- a))
19.0ms
(sqrt (acos a))
20.0ms
(sqrt (acos a))

simplify7.4s

Counts
74 → 74
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
053414
170380
2104358
3178352
4397352
51249352
64910352
done5001352

prune179.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample909.0ms

Algorithm
intervals
Results
270.0ms8000×body80valid
175.0ms7844×body80nan