Details

analyze107.0ms (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)

sample77.0ms (0.8%)

Algorithm

1×

intervals

Results

31.0ms	135×	body	1024	valid
27.0ms	60×	body	2048	valid
5.0ms	32×	body	512	valid
2.0ms	21×	body	256	valid
0.0ms	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

prune7.0ms (0.1%)

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

39.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.5b	(cos.f64 (+.f64 x eps))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

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

Compiler

Compiled 382 to 101 computations (73.6% saved)

series152.0ms (1.5%)

Error

16.4b

Counts

2 → 23

Calls

2 calls:

80.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
45.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 674 to 426 computations (36.8% saved)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4917	732
1	4917	732

prune54.0ms (0.6%)

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

0.4b

Counts

50 → 7

Compiler

Compiled 686 to 257 computations (62.5% saved)

localize12.0ms (0.1%)

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)))
5.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite118.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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))))
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)

series441.0ms (4.5%)

Error

0.3b

Counts

4 → 48

Calls

4 calls:

147.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
123.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
66.0ms	(+.f64 x (+.f64 eps x))
57.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 2082 to 1744 computations (16.2% saved)

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4912	2057
1	4912	2057

prune134.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	102	13	115

Error

0.3b

Counts

115 → 13

Compiler

Compiled 2361 to 1587 computations (32.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.3b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
5.5b	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
5.5b	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
5.5b	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))

rewrite152.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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` `associate-*r/_binary64_20` `cbrt-div_binary64_110` `cbrt-prod_binary64_109`

Counts

4 → 37

Calls

4 calls:

14.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
12.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
12.0ms	(cbrt.f64 (.f64 -2 (.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 2257 to 1462 computations (35.2% saved)

series1.9s (18.9%)

Error

0.3b

Counts

4 → 42

Calls

4 calls:

575.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
546.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
540.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
78.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 7236 to 5493 computations (24.1% saved)

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4958	2488
1	4958	2488

prune241.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	79	13	92

Error

0.3b

Counts

92 → 13

Compiler

Compiled 4873 to 3318 computations (31.9% 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)))
0.5b	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)
5.3b	(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))

rewrite181.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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:

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

Compiler

Compiled 2536 to 1670 computations (34.1% saved)

series476.0ms (4.8%)

Error

0.3b

Counts

4 → 48

Calls

4 calls:

174.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)
123.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)))
57.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
57.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3))

Compiler

Compiled 2668 to 2207 computations (17.3% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5009	2959

prune170.0ms (1.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	132	14	146

Error

0.3b

Counts

146 → 14

Compiler

Compiled 3173 to 2144 computations (32.4% saved)

regimes843.0ms (8.5%)

Accuracy

Total 0.3b remaining (59.4%)

Threshold costs 0.3b (59.4%)

Compiler

Compiled 5778 to 4345 computations (24.8% saved)

bsearch75.0ms (0.8%)

Steps

Iters	Range		Point
10	4.184407777433746e-07	10489.444113331905	0.0022378297832547816
9	-4009.4676246315566	-3.754910456363706e-06	-0.0033612638349102826

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	125	96
1	125	96

end0.0ms (0%)

sample4.3s (44%)

Algorithm

1×

intervals

Results

1.0s	2079×	body	2048	valid
924.0ms	3821×	body	1024	valid
213.0ms	1329×	body	512	valid
69.0ms	519×	body	256	valid
15.0ms	252×	body	128	valid

Compiler

Compiled 1971 to 1473 computations (25.3% saved)

Details

analyze107.0ms (1.1%)

sample77.0ms (0.8%)

simplify10.0ms (0.1%)

prune7.0ms (0.1%)

localize6.0ms (0.1%)

rewrite38.0ms (0.4%)

series152.0ms (1.5%)

simplify60.0ms (0.6%)

prune54.0ms (0.6%)

localize12.0ms (0.1%)

rewrite118.0ms (1.2%)

series441.0ms (4.5%)

simplify79.0ms (0.8%)

prune134.0ms (1.4%)

localize17.0ms (0.2%)

rewrite152.0ms (1.5%)

series1.9s (18.9%)

simplify102.0ms (1%)

prune241.0ms (2.4%)

localize16.0ms (0.2%)

rewrite181.0ms (1.8%)

series476.0ms (4.8%)

simplify91.0ms (0.9%)

prune170.0ms (1.7%)

regimes843.0ms (8.5%)

bsearch75.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.3s (44%)

Profiling