Details

analyze3.0ms (0%)

Algorithm

1×

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)

sample104.0ms (1.5%)

Algorithm

1×

intervals

Results

42.0ms	108×	body	1024	valid
31.0ms	45×	body	2048	valid
14.0ms	51×	body	512	valid
3.0ms	20×	body	256	valid
3.0ms	31×	body	128	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify128.0ms (1.8%)

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

42.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.8b	(sin.f64 (+.f64 x eps))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
4×	`add-log-exp_binary64_799`
3×	`cancel-sign-sub-inv_binary64_726` `add-cube-cbrt_binary64_795`
2×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821` `sin-sum_binary64_893`
1×	`diff-log_binary64_852` `diff-sin_binary64_910` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `associate--l+_binary64_697` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 26

Calls

2 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

series90.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
28.0ms	(sin.f64 (+.f64 x eps))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5196	441

prune34.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Error

0.6b

Counts

33 → 3

Compiler

Compiled 428 to 129 computations (69.9% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_760`
8×	`add-log-exp_binary64_799`
7×	`add-sqr-sqrt_binary64_782`
5×	`add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`distribute-lft-out_binary64_711` `associate-r_binary64_700` `sum-log_binary64_851` `associate-l_binary64_701`
1×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-+r+_binary64_692` `+-commutative_binary64_690` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `sin-cos-mult_binary64_916`

Counts

3 → 41

Calls

3 calls:

11.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series115.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

58.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
30.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
27.0ms	(+.f64 x (+.f64 x eps))

simplify115.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5266	830

prune93.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Error

0.5b

Counts

53 → 8

Compiler

Compiled 1175 to 765 computations (34.9% saved)

localize16.0ms (0.2%)

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)
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_791`
24×	`add-sqr-sqrt_binary64_782`
15×	`-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `associate-r*_binary64_700`
10×	`cube-prod_binary64_788` `unpow-prod-down_binary64_839`
7×	`add-exp-log_binary64_798` `pow1_binary64_821`
6×	`add-cbrt-cube_binary64_796`
5×	`unswap-sqr_binary64_728`
4×	`add-log-exp_binary64_799` `sqr-pow_binary64_732`
3×	`cube-mult_binary64_790` `unpow3_binary64_826` `associate-l_binary64_701` `pow-unpow_binary64_837`
1×	`pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `prod-exp_binary64_809` `pow-exp_binary64_828` `rem-cube-cbrt_binary64_783` `pow-to-exp_binary64_829` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 85

Calls

4 calls:

19.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
13.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
4.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series191.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
56.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
33.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
20.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4910	1942
1	4910	1942

prune159.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	97	8	105

Error

0.5b

Counts

105 → 8

Compiler

Compiled 2419 to 1600 computations (33.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_760` `add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821` `add-sqr-sqrt_binary64_782`
1×	`pow1/3_binary64_842` `cos-mult_binary64_914` `cbrt-div_binary64_792` `cbrt-prod_binary64_791`

Counts

4 → 31

Calls

4 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

series179.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
18.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
18.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify103.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4938	762
1	4938	762

prune82.0ms (1.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	43	8	51

Error

0.5b

Counts

51 → 8

Compiler

Compiled 1664 to 953 computations (42.7% saved)

regimes493.0ms (6.9%)

Accuracy

Total 0.1b remaining (25.3%)

Threshold costs 0.1b (25.3%)

Compiler

Compiled 1887 to 1409 computations (25.3% saved)

bsearch113.0ms (1.6%)

Steps

Iters	Range		Point
7	6.080062358320328e-16	1.3712121081115658e-14	1.3585536195419535e-14
9	-9.66455689856527e-07	-4.1588302116781593e-13	-1.1151570239762008e-08

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms (0%)

sample4.8s (66.3%)

Algorithm

1×

intervals

Results

1.7s	3514×	body	1024	valid
980.0ms	1234×	body	2048	valid
375.0ms	1327×	body	512	valid
121.0ms	1324×	body	128	valid
108.0ms	596×	body	256	valid
10.0ms	5×	body	4096	valid

Compiler

Compiled 682 to 512 computations (24.9% saved)

Details

analyze3.0ms (0%)

sample104.0ms (1.5%)

simplify128.0ms (1.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite20.0ms (0.3%)

series90.0ms (1.2%)

simplify102.0ms (1.4%)

prune34.0ms (0.5%)

localize18.0ms (0.3%)

rewrite27.0ms (0.4%)

series115.0ms (1.6%)

simplify115.0ms (1.6%)

prune93.0ms (1.3%)

localize16.0ms (0.2%)

rewrite49.0ms (0.7%)

series191.0ms (2.7%)

simplify124.0ms (1.7%)

prune159.0ms (2.2%)

localize18.0ms (0.3%)

rewrite28.0ms (0.4%)

series179.0ms (2.5%)

simplify103.0ms (1.4%)

prune82.0ms (1.1%)

regimes493.0ms (6.9%)

bsearch113.0ms (1.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample4.8s (66.3%)

Profiling