Details

Time bar (total: 15.0s)

sample28.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
6.0ms267×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)))

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

series61.0ms

Counts
1 → 3
Calls
1 calls:
61.0ms
(/ a (- (acos a)))

simplify1.5s

Counts
58 → 58
Iterations

Useful iterations: 3 (273.0ms)

IterNodesCost
094601
1171569
2459553
31923551
done5000551

prune141.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite48.0ms

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
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 frac-2neg 1-exp clear-num add-log-exp
1×neg-sub0 pow-flip div-sub distribute-frac-neg associate-/r/ inv-pow
Counts
2 → 217
Calls
2 calls:
15.0ms
(/ 1 (/ (- (acos a)) a))
16.0ms
(/ (- (acos a)) a)

series76.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ 1 (/ (- (acos a)) a))
42.0ms
(/ (- (acos a)) a)

simplify2.1s

Counts
223 → 223
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02883166
17852622
243592554
done50002550

prune392.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×add-exp-log neg-mul-1
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
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 → 580
Calls
2 calls:
15.0ms
(/ 1 (- (acos a)))
38.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series40.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
32.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.4s

Counts
586 → 586
Iterations

Useful iterations: done (2.3s)

IterNodesCost
080712511
129399204
done50008268

prune486.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt (acos a)))
1.0b
(/ 1 (- (sqrt (acos a))))
1.0b
(sqrt (acos a))
1.0b
(sqrt (acos a))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
60×add-sqr-sqrt
58×add-cube-cbrt *-un-lft-identity
42×sqrt-prod
24×distribute-lft-neg-in distribute-rgt-neg-in
22×associate-/r*
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×associate-/l*
4×neg-mul-1 pow-flip div-exp add-log-exp
3×sqrt-pow1 pow1/2
2×cbrt-undiv rem-sqrt-square rec-exp frac-2neg 1-exp clear-num div-inv inv-pow
Counts
4 → 154
Calls
4 calls:
14.0ms
(/ 1 (sqrt (acos a)))
26.0ms
(/ 1 (- (sqrt (acos a))))
2.0ms
(sqrt (acos a))
2.0ms
(sqrt (acos a))

series111.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1 (sqrt (acos a)))
49.0ms
(/ 1 (- (sqrt (acos a))))
12.0ms
(sqrt (acos a))
12.0ms
(sqrt (acos a))

simplify5.8s

Counts
166 → 166
Iterations

Useful iterations: 2 (133.0ms)

IterNodesCost
01371639
12331272
27271242
347721242
done50001242

prune346.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes90.0ms

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
322.0ms8000×body80valid
202.0ms8113×body80nan