Details

analyze98.0ms (1.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample83.0ms (0.9%)

Algorithm

1×

intervals

Results

29.0ms	59×	body	2048	valid
29.0ms	120×	body	1024	valid
12.0ms	50×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	13×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (0%)

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

Error

41.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.1b	(cos.f64 (+.f64 x eps))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

18.3b

Rules

5×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117`
3×	`add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
2×	`cos-sum_binary64_212` `pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
1×	`diff-cos_binary64_229` `diff-log_binary64_170` `flip3--_binary64_82` `sub-neg_binary64_71` `flip--_binary64_53` `difference-of-squares_binary64_47` `distribute-lft-out--_binary64_30` `associate--l-_binary64_16`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 382 to 101 computations (73.6% saved)

series148.0ms (1.7%)

Error

14.2b

Counts

2 → 23

Calls

2 calls:

79.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
42.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 674 to 426 computations (36.8% saved)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4917	732
1	4917	732

prune58.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Error

0.2b

Counts

50 → 8

Compiler

Compiled 740 to 279 computations (62.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
0.0b	(+.f64 x (+.f64 eps x))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite118.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

12×	`*-un-lft-identity_binary64_78`
11×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
9×	`add-log-exp_binary64_117` `add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113`
6×	`associate-l_binary64_19`
4×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-r_binary64_18`
3×	`sum-log_binary64_169` `distribute-lft-out_binary64_29`
2×	`sin-mult_binary64_233` `*-commutative_binary64_9`
1×	`unswap-sqr_binary64_46` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-+r+_binary64_10` `+-commutative_binary64_8` `associate-*r/_binary64_20`

Counts

4 → 60

Calls

4 calls:

12.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
6.0ms	(+.f64 x (+.f64 eps x))

Compiler

Compiled 1452 to 895 computations (38.4% saved)

series428.0ms (4.8%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

144.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
114.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
65.0ms	(+.f64 x (+.f64 eps x))
56.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 2082 to 1744 computations (16.2% saved)

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4912	2057
1	4912	2057

prune135.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	103	13	116

Error

0.2b

Counts

116 → 13

Compiler

Compiled 2350 to 1581 computations (32.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
3.2b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
3.2b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
3.2b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

rewrite101.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

5×	`add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`pow1_binary64_139` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`cbrt-prod_binary64_109`
1×	`pow1/3_binary64_160`

Counts

4 → 32

Calls

4 calls:

9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
8.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))

Compiler

Compiled 1431 to 808 computations (43.5% saved)

series604.0ms (6.8%)

Error

0.2b

Counts

4 → 46

Calls

4 calls:

318.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
67.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
67.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
66.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 4756 to 3360 computations (29.4% saved)

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5177	1478

prune159.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	78	13	91

Error

0.2b

Counts

91 → 13

Compiler

Compiled 3489 to 2134 computations (38.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
4.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
4.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
4.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite135.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

4×	`pow1_binary64_139` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
3×	`pow1/3_binary64_160` `sin-mult_binary64_233` `cbrt-div_binary64_110` `cbrt-prod_binary64_109`

Counts

4 → 37

Calls

4 calls:

11.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
11.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
11.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 2079 to 1284 computations (38.2% saved)

series1.4s (15.2%)

Error

0.2b

Counts

4 → 39

Calls

4 calls:

400.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
397.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
388.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
74.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 5678 to 4199 computations (26% saved)

simplify87.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4952	1873
1	4952	1873

prune176.0ms (2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	76	13	89

Error

0.2b

Counts

89 → 13

Compiler

Compiled 3923 to 2513 computations (35.9% saved)

regimes728.0ms (8.2%)

Accuracy

Total 0.3b remaining (56.9%)

Threshold costs 0.3b (56.9%)

Compiler

Compiled 4664 to 3388 computations (27.4% saved)

bsearch75.0ms (0.8%)

Steps

Iters	Range		Point
11	4.762190031467391e-05	23543123987427464.0	0.0034251863869845934
8	-0.012454799193269714	-1.3215902250932261e-06	-0.0025355825843680958

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	113	75
1	113	75

end0.0ms (0%)

sample4.1s (46.4%)

Algorithm

1×

intervals

Results

1.1s	2133×	body	2048	valid
982.0ms	3799×	body	1024	valid
213.0ms	1295×	body	512	valid
60.0ms	526×	body	256	valid
15.0ms	244×	body	128	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 1586 to 1153 computations (27.3% saved)

Details

analyze98.0ms (1.1%)

sample83.0ms (0.9%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite41.0ms (0.5%)

series148.0ms (1.7%)

simplify60.0ms (0.7%)

prune58.0ms (0.6%)

localize14.0ms (0.2%)

rewrite118.0ms (1.3%)

series428.0ms (4.8%)

simplify76.0ms (0.9%)

prune135.0ms (1.5%)

localize16.0ms (0.2%)

rewrite101.0ms (1.1%)

series604.0ms (6.8%)

simplify49.0ms (0.6%)

prune159.0ms (1.8%)

localize17.0ms (0.2%)

rewrite135.0ms (1.5%)

series1.4s (15.2%)

simplify87.0ms (1%)

prune176.0ms (2%)

regimes728.0ms (8.2%)

bsearch75.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.1s (46.4%)

Profiling