Details

analyze2.0ms

Algorithm

Search

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

sample101.0ms

Algorithm

intervals

Results

53.0ms	119×	body	1280	valid
22.0ms	18×	body	2560	valid
9.0ms	32×	body	640	valid
6.0ms	35×	body	320	valid
2.0ms	39×	body	80	valid
1.0ms	13×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune1.0ms

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: 35.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.3b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.5b	(sin.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` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 25

Calls

2 calls:

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

series579.0ms

Counts

2 → 6

Calls

2 calls:

391.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
188.0ms	(sin.f64 (+.f64 x eps))

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	223	153
1	223	153
0	27	45
1	27	45
0	223	153
1	223	153
0	27	45
1	27	45
0	16	3
1	16	3
0	309	246
1	309	246
0	34	63
1	34	63
0	309	246
1	309	246
0	34	63
1	34	63
0	9	3
1	9	3

simplify170.0ms

Counts

31 → 31

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4887	390
1	4887	390

prune26.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	4	32

Merged error: 0.5b

Counts

32 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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-cos-mult_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

7.0ms	(+.f64 x (+.f64 x eps))
10.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
7.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

245.0ms	(+.f64 x (+.f64 x eps))
229.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
431.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
433.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (207.0ms)

Iter	Nodes	Cost
0	376	351
1	376	351
0	66	77
1	66	77
0	376	351
1	376	351
0	66	77
1	66	77
0	3769	3
1	3769	3
0	562	678
1	562	678
0	68	69
1	68	69
0	562	678
1	562	678
0	68	69
1	68	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

simplify139.0ms

Counts

94 → 94

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4928	1440
1	4928	1440

prune95.0ms

Filtered

68 candidates to 94 candidates (-38.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	87	11	98

Merged error: 0.5b

Counts

98 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite29.0ms

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:

11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

208.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
420.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
476.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
435.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (208.0ms)

Iter	Nodes	Cost
0	376	351
1	376	351
0	66	77
1	66	77
0	376	351
1	376	351
0	66	77
1	66	77
0	3769	3
1	3769	3
0	517	732
1	517	732
0	125	159
1	125	159
0	517	732
1	517	732
0	125	159
1	125	159
0	4035	3
1	4035	3
0	143	1763
1	143	1763
0	60	9
1	60	9
0	143	1763
1	143	1763
0	60	9
1	60	9
0	5095	36
0	363	1851
1	363	1851
0	122	336
1	122	336
0	363	1851
1	363	1851
0	122	336
1	122	336
0	1	3
1	1	3

simplify115.0ms

Counts

101 → 101

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5348	1899

prune96.0ms

Filtered

59 candidates to 101 candidates (-71.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	100	12	112

Merged error: 0.5b

Counts

112 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (pow.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) 3))
0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.5b	(pow.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) 3)
2.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

20×	`log-pow_binary64` `cbrt-prod_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`exp-prod_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`pow1_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `log-prod_binary64`
2×	`sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 86

Calls

4 calls:

5.0ms	(cbrt.f64 (pow.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) 3))
11.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
11.0ms	(pow.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) 3)
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.7s

Counts

4 → 12

Calls

4 calls:

467.0ms	(cbrt.f64 (pow.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) 3))
379.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
448.0ms	(pow.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) 3)
431.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	376	351
1	376	351
0	66	77
1	66	77
0	376	351
1	376	351
0	66	77
1	66	77
0	3769	3
1	3769	3
0	614	1044
1	614	1044
0	144	215
1	144	215
0	614	1044
1	614	1044
0	144	215
1	144	215
0	4686	3
1	4686	3
0	473	591
1	473	591
0	86	133
1	86	133
0	473	591
1	473	591
0	86	133
1	86	133
0	4946	3
1	4946	3
0	171	1799
1	171	1799
0	41	9
1	41	9
0	171	1799
1	171	1799
0	41	9
1	41	9
0	5095	36

simplify137.0ms

Counts

98 → 98

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4896	1610
1	4896	1610

prune73.0ms

Filtered

60 candidates to 98 candidates (-63.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	97	13	110

Merged error: 0.5b

Counts

110 → 13

regimes104.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.8b

bsearch91.0ms

Steps

Iters	Range		Point
10	3.888997768081172e-11	709712647.4179375	1.3434189137285421e-08
9	-0.27474757022010354	-1.422123626850807e-10	-6.930299090527721e-09

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	3311×	body	1280	valid
572.0ms	622×	body	2560	valid
470.0ms	1748×	body	640	valid
133.0ms	758×	body	320	valid
66.0ms	1157×	body	80	valid
52.0ms	404×	body	160	valid

Iter	Nodes	Cost
0	223	153
1	223	153
0	27	45
1	27	45
0	223	153
1	223	153
0	27	45
1	27	45
0	16	3
1	16	3
0	309	246
1	309	246
0	34	63
1	34	63
0	309	246
1	309	246
0	34	63
1	34	63
0	9	3
1	9	3

Iter	Nodes	Cost
0	223	153
1	223	153
0	27	45
1	27	45
0	223	153
1	223	153
0	27	45
1	27	45
0	16	3
1	16	3
0	309	246
1	309	246
0	34	63
1	34	63
0	309	246
1	309	246
0	34	63
1	34	63
0	9	3
1	9	3

Details

analyze2.0ms

sample101.0ms

simplify25.0ms

prune1.0ms

localize8.0ms

rewrite14.0ms

series579.0ms

simplify170.0ms

prune26.0ms

localize15.0ms

rewrite37.0ms

series1.3s

simplify139.0ms

prune95.0ms

localize16.0ms

rewrite29.0ms

series1.5s

simplify115.0ms

prune96.0ms

localize19.0ms

rewrite39.0ms

series1.7s

simplify137.0ms

prune73.0ms

regimes104.0ms

bsearch91.0ms

simplify7.0ms

end0.0ms

sample2.9s

Profiling

Iter	Nodes	Cost
0	223	153
1	223	153
0	27	45
1	27	45
0	223	153
1	223	153
0	27	45
1	27	45
0	16	3
1	16	3
0	309	246
1	309	246
0	34	63
1	34	63
0	309	246
1	309	246
0	34	63
1	34	63
0	9	3
1	9	3