Details

Time bar (total: 16.3s)

sample27.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
6.0ms262×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

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite19.0ms

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:
15.0ms
(/ a (- (acos a)))

series57.0ms

Counts
1 → 3
Calls
1 calls:
56.0ms
(/ a (- (acos a)))

simplify4.9s

Counts
58 → 58
Iterations

Useful iterations: 5 (1.9s)

IterNodesCost
094601
1164569
2334551
3587551
41101551
52149546
done5000546

prune145.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

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)))
8.0ms
(/ (acos a) (- a))

series65.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(/ 1 (/ (acos a) (- a)))
39.0ms
(/ (acos a) (- a))

simplify2.3s

Counts
222 → 222
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
02933186
16112657
211412356
327492260
done50002260

prune395.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1 (acos a))
0.4b
(/ (/ 1 (acos a)) (/ 1 (- a)))

rewrite115.0ms

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:
7.0ms
(/ 1 (acos a))
28.0ms
(/ (/ 1 (acos a)) (/ 1 (- a)))

series34.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(/ 1 (acos a))
27.0ms
(/ (/ 1 (acos a)) (/ 1 (- a)))

simplify2.6s

Counts
558 → 558
Iterations

Useful iterations: done (2.5s)

IterNodesCost
080512210
122738248
232567104
done50006756

prune321.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (acos a))
0.4b
(/ (cbrt (pow (/ 1 (acos a)) 3)) (/ 1 (- a)))
1.0b
(cbrt (pow (/ 1 (acos a)) 3))
1.0b
(pow (/ 1 (acos a)) 3)

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
2945×times-frac
1322×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1152×cbrt-prod
481×unpow-prod-down cube-prod
324×distribute-lft-neg-in distribute-rgt-neg-in
112×div-inv
108×neg-mul-1
38×associate-/l*
37×cube-mult unpow3 associate-/r* sqr-pow
22×add-exp-log
12×add-cbrt-cube
10×div-exp
7×pow1
5×cbrt-undiv
4×pow-exp add-log-exp
3×cube-div rec-exp pow-unpow pow-pow 1-exp
2×cbrt-div pow-flip frac-2neg clear-num inv-pow rem-cube-cbrt
1×pow-to-exp pow1/3 associate-/r/ rem-cbrt-cube associate-/l/
Counts
4 → 1400
Calls
4 calls:
11.0ms
(/ 1 (acos a))
81.0ms
(/ (cbrt (pow (/ 1 (acos a)) 3)) (/ 1 (- a)))
11.0ms
(cbrt (pow (/ 1 (acos a)) 3))
21.0ms
(pow (/ 1 (acos a)) 3)

series119.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1 (acos a))
31.0ms
(/ (cbrt (pow (/ 1 (acos a)) 3)) (/ 1 (- a)))
12.0ms
(cbrt (pow (/ 1 (acos a)) 3))
69.0ms
(pow (/ 1 (acos a)) 3)

simplify2.9s

Counts
1412 → 1412
Iterations

Useful iterations: 2 (2.0s)

IterNodesCost
0126439073
1190621658
2344819297
done500019297

prune596.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample1.2s

Algorithm
intervals
Results
717.0ms8000×body80valid
259.0ms7984×body80nan