Details

analyze103.0ms (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)

sample80.0ms (0.9%)

Algorithm

1×

intervals

Results

30.0ms	64×	body	2048	valid
29.0ms	122×	body	1024	valid
8.0ms	49×	body	512	valid
2.0ms	15×	body	256	valid
0.0ms	6×	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

41.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.7b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.5b	(cos.f64 (+.f64 x eps))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

21.3b

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)

series141.0ms (1.5%)

Error

12.3b

Counts

2 → 23

Calls

2 calls:

73.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
41.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 674 to 426 computations (36.8% saved)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4917	732
1	4917	732

prune56.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Error

0.2b

Counts

50 → 6

Compiler

Compiled 720 to 262 computations (63.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite116.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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` `associate-*r/_binary64_20` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-+r+_binary64_10` `+-commutative_binary64_8`

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))))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
7.0ms	(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)

series436.0ms (4.8%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

151.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
122.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
56.0ms	(+.f64 x (+.f64 eps x))
55.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 2082 to 1744 computations (16.2% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4912	2057
1	4912	2057

prune134.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	102	12	114

Error

0.1b

Counts

114 → 12

Compiler

Compiled 2352 to 1561 computations (33.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.3b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
5.6b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
5.6b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
5.6b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite134.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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:

13.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
10.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
10.0ms	(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)

series1.5s (16%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

425.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
425.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
419.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
83.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 6500 to 4751 computations (26.9% saved)

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5468	2188

prune209.0ms (2.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	77	14	91

Error

0.1b

Counts

91 → 14

Compiler

Compiled 4565 to 2935 computations (35.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
3.3b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
3.3b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

rewrite92.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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))
8.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 1431 to 810 computations (43.4% saved)

series572.0ms (6.3%)

Error

0.1b

Counts

4 → 46

Calls

4 calls:

297.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
66.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
64.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
63.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 4756 to 3426 computations (28% saved)

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5177	1478

prune140.0ms (1.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	78	14	92

Error

0.1b

Counts

92 → 14

Compiler

Compiled 3227 to 1928 computations (40.3% saved)

regimes697.0ms (7.6%)

Accuracy

Total 0.3b remaining (58.6%)

Threshold costs 0.3b (58.6%)

Compiler

Compiled 5510 to 3965 computations (28% saved)

bsearch79.0ms (0.9%)

Steps

Iters	Range		Point
10	9.2588245299409e-07	27593.54723754286	0.002587152165659276
9	-0.1226564069781698	-1.076192542297029e-06	-0.0024570334936235773

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	145	85
1	145	85

end0.0ms (0%)

sample4.3s (47.3%)

Algorithm

1×

intervals

Results

1.1s	2069×	body	2048	valid
951.0ms	3803×	body	1024	valid
230.0ms	1341×	body	512	valid
61.0ms	548×	body	256	valid
20.0ms	237×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 1877 to 1351 computations (28% saved)

Details

analyze103.0ms (1.1%)

sample80.0ms (0.9%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite42.0ms (0.5%)

series141.0ms (1.5%)

simplify64.0ms (0.7%)

prune56.0ms (0.6%)

localize11.0ms (0.1%)

rewrite116.0ms (1.3%)

series436.0ms (4.8%)

simplify82.0ms (0.9%)

prune134.0ms (1.5%)

localize16.0ms (0.2%)

rewrite134.0ms (1.5%)

series1.5s (16%)

simplify61.0ms (0.7%)

prune209.0ms (2.3%)

localize22.0ms (0.2%)

rewrite92.0ms (1%)

series572.0ms (6.3%)

simplify52.0ms (0.6%)

prune140.0ms (1.5%)

regimes697.0ms (7.6%)

bsearch79.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.3s (47.3%)

Profiling