Details

Time bar (total: 10.4s)

sample25.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
4.0ms248×body80nan

simplify1.0ms

Counts
1 → 1
Iterations
IterNodes
done4
04

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-cbrt-cube add-exp-log associate-/l*
1×pow1 cbrt-undiv clear-num frac-2neg div-exp div-inv add-log-exp
Counts
1 → 55
Calls
1 calls:
8.0ms
(/ a (- (acos a)))

series32.0ms

Counts
1 → 3
Calls
1 calls:
32.0ms
(/ a (- (acos a)))

simplify945.0ms

Counts
58 → 58
Iterations
IterNodes
done5001
32040
2462
1171
094

prune232.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- (acos a)) a)
0.5b
(/ 1 (/ (- (acos a)) a))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in
37×associate-/r*
16×neg-mul-1
15×add-exp-log
13×associate-/l*
9×add-cbrt-cube
8×div-exp
6×div-inv
4×cbrt-undiv
3×pow1
2×rec-exp clear-num frac-2neg 1-exp add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 217
Calls
2 calls:
13.0ms
(/ (- (acos a)) a)
25.0ms
(/ 1 (/ (- (acos a)) a))

series101.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(/ (- (acos a)) a)
55.0ms
(/ 1 (/ (- (acos a)) a))

simplify1.6s

Counts
223 → 223
Iterations
IterNodes
done5000
23876
1785
0288

prune654.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
0.6b
(cbrt a)
0.9b
(sqrt (acos a))
0.9b
(sqrt (acos a))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×add-cbrt-cube add-exp-log add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(cbrt a)
8.0ms
(sqrt (acos a))
2.0ms
(sqrt (acos a))

series638.0ms

Counts
4 → 12
Calls
4 calls:
311.0ms
(cbrt a)
285.0ms
(cbrt a)
20.0ms
(sqrt (acos a))
21.0ms
(sqrt (acos a))

simplify2.0s

Counts
60 → 60
Iterations
IterNodes
done5001
53389
4982
3372
2136
162
040

prune257.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt a) (cbrt a))
0.6b
(cbrt a)
0.6b
(cbrt a)
0.6b
(cbrt a)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
17.0ms
(* (cbrt a) (cbrt a))
1.0ms
(cbrt a)
1.0ms
(cbrt a)
1.0ms
(cbrt a)

series1.2s

Counts
4 → 12
Calls
4 calls:
322.0ms
(* (cbrt a) (cbrt a))
300.0ms
(cbrt a)
302.0ms
(cbrt a)
260.0ms
(cbrt a)

simplify1.1s

Counts
85 → 85
Iterations
IterNodes
done5000
2727
1138
061

prune311.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 0b

regimes153.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify0.0ms

Iterations
IterNodes
done4
04

end0.0ms

sample1.0s

Algorithm
intervals
Results
356.0ms8000×body80valid
275.0ms7876×body80nan