Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample95.0ms

Algorithm

intervals

Results

57.0ms	161×	body	1280	valid
16.0ms	18×	body	2560	valid
9.0ms	39×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 39.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.5b	(cos.f64 (+.f64 x eps))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64` `insert-posit16`
1×	`sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-cos_binary64`

Counts

2 → 25

Calls

2 calls:

8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms	(cos.f64 (+.f64 x eps))

series680.0ms

Counts

2 → 6

Calls

2 calls:

312.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
367.0ms	(cos.f64 (+.f64 x eps))

Iterations

Useful iterations: 0 (200.0ms)

Iter	Nodes	Cost
0	237	165
1	237	165
0	34	53
1	34	53
0	237	165
1	237	165
0	34	53
1	34	53
0	4583	3
1	4583	3
0	332	270
1	332	270
0	23	59
1	23	59
0	332	270
1	332	270
0	23	59
1	23	59
0	5092	59

simplify128.0ms

Counts

31 → 31

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4943	446
1	4943	446

prune37.0ms

Filtered

28 candidates to 31 candidates (-10.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 0.6b

Counts

32 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(/.f64 (+.f64 x (+.f64 x eps)) 2)
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out_binary64` `times-frac_binary64`
9×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`associate-/l*_binary64`
4×	`insert-posit16`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

9.0ms	(+.f64 x (+.f64 x eps))
10.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

234.0ms	(+.f64 x (+.f64 x eps))
221.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
410.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
388.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (173.0ms)

Iter	Nodes	Cost
0	362	339
1	362	339
0	59	69
1	59	69
0	362	339
1	362	339
0	59	69
1	59	69
0	10	3
1	10	3
0	546	666
1	546	666
0	66	69
1	66	69
0	546	666
1	546	666
0	66	69
1	66	69
0	4427	3
1	4427	3
0	300	225
1	300	225
0	40	45
1	40	45
0	300	225
1	300	225
0	40	45
1	40	45
0	10	18
1	10	18
0	199	111
1	199	111
0	17	27
1	17	27
0	199	111
1	199	111
0	17	27
1	17	27
0	9	30
1	9	30

simplify136.0ms

Counts

94 → 94

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4943	1440
1	4943	1440

prune95.0ms

Filtered

67 candidates to 94 candidates (-40.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	88	13	101

Merged error: 0.6b

Counts

101 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow1/3_binary64`

Counts

4 → 44

Calls

4 calls:

3.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.8s

Counts

4 → 12

Calls

4 calls:

452.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
458.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
460.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
382.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	362	339
1	362	339
0	59	69
1	59	69
0	362	339
1	362	339
0	59	69
1	59	69
0	10	3
1	10	3
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	4891	54
1	4891	54
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	4891	54
1	4891	54
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	4891	54
1	4891	54

simplify153.0ms

Counts

56 → 56

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	5088	735

prune114.0ms

Filtered

51 candidates to 56 candidates (-9.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	54	15	69

Merged error: 0.6b

Counts

69 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.5b	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.4b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
15×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `associate-l_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 89

Calls

4 calls:

17.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
9.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

202.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
417.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
383.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
203.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	143	1763
1	143	1763
0	53	9
1	53	9
0	143	1763
1	143	1763
0	53	9
1	53	9
0	1	3
1	1	3
0	362	339
1	362	339
0	59	69
1	59	69
0	362	339
1	362	339
0	59	69
1	59	69
0	10	3
1	10	3
0	503	720
1	503	720
0	137	151
1	137	151
0	503	720
1	503	720
0	137	151
1	137	151
0	4875	3
1	4875	3
0	363	1851
1	363	1851
0	94	336
1	94	336
0	363	1851
1	363	1851
0	94	336
1	94	336
0	1	3
1	1	3

simplify111.0ms

Counts

101 → 101

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5320	1866

prune73.0ms

Filtered

56 candidates to 101 candidates (-80.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	2	10	12
Picked	0	1	1
Done	0	2	2
Total	101	15	116

Merged error: 0.6b

Counts

116 → 15

regimes114.0ms

Accuracy

90.3% (1.4b remaining)

Error of 1.8b against oracle of 0.4b and baseline of 14.9b

bsearch72.0ms

Steps

Iters	Range		Point
9	9.236627242841603e+44	2.2621706952140806e+51	9.384489792595554e+44
6	-1.5860327770667884	-0.27474757022010354	-0.27960507509546756

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	60
1	71	60

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.8s	4478×	body	1280	valid
567.0ms	622×	body	2560	valid
440.0ms	1813×	body	640	valid
120.0ms	696×	body	320	valid
33.0ms	298×	body	160	valid
5.0ms	93×	body	80	valid

Details

analyze2.0ms

sample95.0ms

simplify31.0ms

prune2.0ms

localize8.0ms

rewrite14.0ms

series680.0ms

simplify128.0ms

prune37.0ms

localize14.0ms

rewrite45.0ms

series1.3s

simplify136.0ms

prune95.0ms

localize19.0ms

rewrite18.0ms

series1.8s

simplify153.0ms

prune114.0ms

localize16.0ms

rewrite48.0ms

series1.2s

simplify111.0ms

prune73.0ms

regimes114.0ms

bsearch72.0ms

simplify7.0ms

end0.0ms

sample3.1s

Profiling