Details

sample61.0ms

Algorithm

intervals

Results

21.0ms	42×	body	2560	valid
12.0ms	43×	body	1280	valid
9.0ms	51×	body	640	valid
6.0ms	37×	body	320	valid
3.0ms	66×	body	80	valid
2.0ms	17×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize7.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
14.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
57.0ms	(/ (- 1.0 (cos x)) (* x x))

series141.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- 1.0 (cos x))
95.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.2s

Counts

64 → 64

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	116	808
1	269	678
2	747	566
3	2669	526
done	5001	517

prune191.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

8.0ms	(cbrt (- 1.0 (cos x)))
14.0ms	(- 1.0 (cos x))
15.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))

series254.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (- 1.0 (cos x)))
25.0ms	(- 1.0 (cos x))
35.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	104	1488
1	211	1135
2	504	888
3	1570	754
done	5000	720

prune420.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

8.0ms	(- 1.0 (cos x))
9.0ms	(- 1.0 (cos x))
14.0ms	(- 1.0 (cos x))
13.0ms	(- 1.0 (cos x))

series139.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- 1.0 (cos x))
36.0ms	(- 1.0 (cos x))
35.0ms	(- 1.0 (cos x))
45.0ms	(- 1.0 (cos x))

simplify4.2s

Counts

124 → 124

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	71	1684
1	148	1228
2	344	940
3	1100	784
4	4072	748
done	5000	748

prune523.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
14.1b	(/ (exp (log (- 1.0 (cos x)))) (* x x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`log-prod`
18×	`add-cube-cbrt`
15×	`exp-sum`
9×	`prod-diff` `add-cbrt-cube`
8×	`add-exp-log` `times-frac` `associate-/l*`
6×	`pow1` `log-div` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg`
2×	`cbrt-undiv` `div-exp` `log-pow` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-exp-log`

Counts

4 → 102

Calls

4 calls:

8.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
8.0ms	(- 1.0 (cos x))
24.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

series188.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(exp (log (- 1.0 (cos x))))
91.0ms	(log (- 1.0 (cos x)))
25.0ms	(- 1.0 (cos x))
46.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

simplify1.8s

Counts

114 → 114

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	170	1408
1	326	1115
2	836	970
3	2842	930
done	5001	910

prune222.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes86.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 31.1b

bsearch112.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	0.02432033747417449
9	-7465.585501010854	-0.008005822963963436	-0.032962631270408896

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	65
1	38	65
done	38	65

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	1656×	body	2560	valid
717.0ms	1503×	body	640	valid
534.0ms	1222×	body	1280	valid
197.0ms	935×	body	320	valid
162.0ms	2251×	body	80	valid
54.0ms	433×	body	160	valid