Details

Time bar (total: 22.3s)

sample32.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
8.0ms288×body80nan

simplify1.0ms

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: 0.3b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

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)))

series52.0ms

Counts
1 → 3
Calls
1 calls:
52.0ms
(/ a (- (acos a)))

simplify5.0s

Counts
58 → 58
Iterations

Useful iterations: 5 (1.9s)

IterNodesCost
094601
1164569
2334551
3587551
41101551
52149546
done5000546

prune183.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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:
15.0ms
(/ 1 (/ (acos a) (- a)))
9.0ms
(/ (acos a) (- a))

series77.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(/ 1 (/ (acos a) (- a)))
39.0ms
(/ (acos a) (- a))

simplify2.4s

Counts
222 → 222
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
02933186
16112657
211412356
327492260
done50002260

prune431.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

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)))
0.6b
(* (cbrt (/ (acos a) (- a))) (cbrt (/ (acos a) (- a))))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
262×cbrt-prod
228×times-frac
176×add-sqr-sqrt
164×*-un-lft-identity
152×add-cube-cbrt
69×distribute-rgt-neg-in
63×distribute-lft-neg-in
43×swap-sqr
37×associate-*r* associate-*l*
21×neg-mul-1
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×add-cbrt-cube add-log-exp
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 → 276
Calls
4 calls:
8.0ms
(cbrt (/ (acos a) (- a)))
8.0ms
(cbrt (/ (acos a) (- a)))
8.0ms
(cbrt (/ (acos a) (- a)))
89.0ms
(* (cbrt (/ (acos a) (- a))) (cbrt (/ (acos a) (- a))))

series997.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(cbrt (/ (acos a) (- a)))
230.0ms
(cbrt (/ (acos a) (- a)))
255.0ms
(cbrt (/ (acos a) (- a)))
284.0ms
(* (cbrt (/ (acos a) (- a))) (cbrt (/ (acos a) (- a))))

simplify4.5s

Counts
288 → 288
Iterations

Useful iterations: done (4.5s)

IterNodesCost
02974926
14594666
212054571
320404429
448394176
done50004060

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (/ 1 (- a))) (cbrt (/ 1 (- a))))
0.5b
(cbrt (/ 1 (- a)))
0.5b
(cbrt (/ 1 (- a)))
0.5b
(cbrt (/ (acos a) (- a)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
278×cbrt-prod
238×times-frac
192×add-sqr-sqrt
174×*-un-lft-identity
152×add-cube-cbrt
69×distribute-rgt-neg-in
63×distribute-lft-neg-in
45×swap-sqr
37×associate-*r* associate-*l*
21×neg-mul-1
16×unswap-sqr
11×pow1
9×pow1/3 div-inv
7×cbrt-div
6×add-exp-log
4×add-cbrt-cube add-log-exp
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 → 285
Calls
4 calls:
125.0ms
(* (cbrt (/ 1 (- a))) (cbrt (/ 1 (- a))))
10.0ms
(cbrt (/ 1 (- a)))
8.0ms
(cbrt (/ 1 (- a)))
9.0ms
(cbrt (/ (acos a) (- a)))

series1.6s

Counts
4 → 12
Calls
4 calls:
349.0ms
(* (cbrt (/ 1 (- a))) (cbrt (/ 1 (- a))))
674.0ms
(cbrt (/ 1 (- a)))
289.0ms
(cbrt (/ 1 (- a)))
242.0ms
(cbrt (/ (acos a) (- a)))

simplify3.4s

Counts
297 → 297
Iterations

Useful iterations: done (3.4s)

IterNodesCost
03704545
15373771
29483689
316713532
437373480
done50003308

prune954.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes92.0ms

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

sample892.0ms

Algorithm
intervals
Results
328.0ms8000×body80valid
271.0ms8037×body80nan