Details

analyze114.0ms (1.2%)

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)

sample103.0ms (1%)

Algorithm

1×

intervals

Results

41.0ms	132×	body	1024	valid
38.0ms	57×	body	2048	valid
8.0ms	42×	body	512	valid
2.0ms	17×	body	256	valid
1.0ms	8×	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

40.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.8b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.2b	(cos.f64 (+.f64 x eps))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

18.5b

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)

series193.0ms (2%)

Error

14.9b

Counts

2 → 23

Calls

2 calls:

116.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
46.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 674 to 426 computations (36.8% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4917	732
1	4917	732

prune78.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Error

0.2b

Counts

50 → 7

Compiler

Compiled 714 to 270 computations (62.2% saved)

localize27.0ms (0.3%)

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)))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite133.0ms (1.4%)

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:

14.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
11.0ms	(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)))
6.0ms	(+.f64 x (+.f64 eps x))

Compiler

Compiled 1452 to 895 computations (38.4% saved)

series528.0ms (5.4%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

169.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
140.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
84.0ms	(+.f64 x (+.f64 eps x))
68.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 2082 to 1744 computations (16.2% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4912	2057
1	4912	2057

prune143.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	105	10	115

Error

0.2b

Counts

115 → 10

Compiler

Compiled 2230 to 1495 computations (33% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)))
0.6b	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)
3.0b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
7.5b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3))

rewrite241.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`cbrt-prod_binary64_109`
24×	`add-sqr-sqrt_binary64_100`
15×	`add-cube-cbrt_binary64_113` `-un-lft-identity_binary64_78` `associate-r*_binary64_18`
10×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
7×	`pow1_binary64_139` `add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114`
5×	`unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117` `sqr-pow_binary64_50`
3×	`unpow3_binary64_144` `cube-mult_binary64_108` `pow-unpow_binary64_155` `associate-l_binary64_19`
1×	`pow1/3_binary64_160` `rem-cbrt-cube_binary64_102` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `rem-cube-cbrt_binary64_101` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

4 → 85

Calls

4 calls:

16.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
16.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)))
12.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)
12.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3))

Compiler

Compiled 2536 to 1670 computations (34.1% saved)

series589.0ms (6%)

Error

0.2b

Counts

4 → 47

Calls

4 calls:

201.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)
144.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)))
85.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
72.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3))

Compiler

Compiled 2625 to 2172 computations (17.3% saved)

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5009	2916

prune206.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	132	10	142

Error

0.2b

Counts

142 → 10

Compiler

Compiled 3307 to 2252 computations (31.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 x) (cos.f64 eps))
0.1b	(+.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x)))
0.2b	(*.f64 (sin.f64 eps) (sin.f64 x))
2.8b	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 eps) (sin.f64 x))))

rewrite100.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`add-log-exp_binary64_117`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
3×	`cos-mult_binary64_232` `cancel-sign-sub-inv_binary64_44`
2×	`sum-log_binary64_169` `diff-log_binary64_170` `flip3-+_binary64_81` `frac-sub_binary64_87` `flip-+_binary64_52` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `*-commutative_binary64_9`
1×	`flip3--_binary64_82` `sub-neg_binary64_71` `flip--_binary64_53` `associate--r+_binary64_14` `sin-mult_binary64_233` `+-commutative_binary64_8`

Counts

4 → 67

Calls

4 calls:

12.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 eps) (sin.f64 x))))
8.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))
4.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
4.0ms	(+.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x)))

Compiler

Compiled 1583 to 289 computations (81.7% saved)

series537.0ms (5.5%)

Error

0.2b

Counts

4 → 40

Calls

4 calls:

190.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 eps) (sin.f64 x))))
139.0ms	(+.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x)))
91.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
90.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 1665 to 931 computations (44.1% saved)

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5324	1848

prune110.0ms (1.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	100	7	107
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	101	16	117

Error

0.1b

Counts

117 → 16

Compiler

Compiled 1996 to 468 computations (76.6% saved)

regimes858.0ms (8.7%)

Accuracy

Total 0.4b remaining (83.9%)

Threshold costs 0.4b (83.9%)

Compiler

Compiled 5790 to 3925 computations (32.2% saved)

bsearch73.0ms (0.7%)

Steps

Iters	Range		Point
9	2.13199055564998e-08	16.724583358149186	0.0029740925941223197
8	-1.0000069373194402	-2.5070953418002607e-05	-0.00271818890310635

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	157	106
1	157	106

end0.0ms (0%)

sample5.3s (54.3%)

Algorithm

1×

intervals

Results

1.3s	2027×	body	2048	valid
1.2s	3872×	body	1024	valid
272.0ms	1347×	body	512	valid
75.0ms	512×	body	256	valid
26.0ms	240×	body	128	valid
3.0ms	2×	body	4096	valid

Compiler

Compiled 1981 to 1336 computations (32.6% saved)

Details

analyze114.0ms (1.2%)

sample103.0ms (1%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite50.0ms (0.5%)

series193.0ms (2%)

simplify67.0ms (0.7%)

prune78.0ms (0.8%)

localize27.0ms (0.3%)

rewrite133.0ms (1.4%)

series528.0ms (5.4%)

simplify91.0ms (0.9%)

prune143.0ms (1.4%)

localize16.0ms (0.2%)

rewrite241.0ms (2.4%)

series589.0ms (6%)

simplify104.0ms (1.1%)

prune206.0ms (2.1%)

localize11.0ms (0.1%)

rewrite100.0ms (1%)

series537.0ms (5.5%)

simplify100.0ms (1%)

prune110.0ms (1.1%)

regimes858.0ms (8.7%)

bsearch73.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.3s (54.3%)

Profiling