Details

analyze2.0ms (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)

sample92.0ms (1.6%)

Algorithm

1×

intervals

Results

39.0ms	64×	body	2048	valid
36.0ms	129×	body	1024	valid
7.0ms	41×	body	512	valid
2.0ms	14×	body	256	valid
0.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify171.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

Merged error: 39.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.7b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.8b	(cos.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_113` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
2×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `cos-sum_binary64_208` `add-cube-cbrt_binary64_109`
1×	`associate--l-_binary64_17` `distribute-lft-out--_binary64_31` `sub-neg_binary64_70` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `diff-log_binary64_166` `diff-cos_binary64_225`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms	(cos.f64 (+.f64 x eps))

series106.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

79.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
27.0ms	(cos.f64 (+.f64 x eps))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4863	429
1	4863	429

prune33.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	22	7	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	7	30

Merged error: 0.3b

Counts

30 → 7

Compiler

Compiled 468 to 177 computations (62.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(/.f64 (+.f64 x (+.f64 x eps)) 2)
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_77`
18×	`add-sqr-sqrt_binary64_98`
16×	`add-cube-cbrt_binary64_109`
15×	`times-frac_binary64_83` `distribute-lft-out_binary64_30`
9×	`add-log-exp_binary64_113`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`pow1_binary64_135`
5×	`associate-/l*_binary64_24`
3×	`associate-/r_binary64_23` `associate-l_binary64_20` `sum-log_binary64_165` `associate-r*_binary64_19`
2×	`flip-+_binary64_51` `flip3-+_binary64_80` `associate-/l/_binary64_26`
1×	`pow-prod-down_binary64_145` `sin-mult_binary64_229` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `+-commutative_binary64_9` `div-exp_binary64_125` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10` `associate-+r+_binary64_11` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 78

Calls

4 calls:

12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
11.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series218.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
44.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
42.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
37.0ms	(+.f64 x (+.f64 x eps))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4961	1327
1	4961	1327

prune116.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	86	11	97

Merged error: 0.2b

Counts

97 → 11

Compiler

Compiled 1978 to 1352 computations (31.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (+.f64 x (*.f64 eps 1/2))))
4.8b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))
4.8b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))
4.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135`
3×	`cbrt-prod_binary64_105`
2×	`sin-sum_binary64_207`
1×	`pow1/3_binary64_156`

Counts

4 → 34

Calls

4 calls:

9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
5.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))
5.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))
3.0ms	(cbrt.f64 (sin.f64 (+.f64 x (*.f64 eps 1/2))))

series276.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt.f64 (sin.f64 (+.f64 x (*.f64 eps 1/2))))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
37.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))
32.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4891	645
1	4891	645

prune106.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	44	13	57

Merged error: 0.2b

Counts

57 → 13

Compiler

Compiled 2006 to 1446 computations (27.9% saved)

localize38.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (+.f64 x (*.f64 eps 1/2))))
0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.8b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))
4.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-prod_binary64_105` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135`
2×	`pow1/3_binary64_156`
1×	`sin-sum_binary64_207`

Counts

4 → 37

Calls

4 calls:

8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
5.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))
3.0ms	(cbrt.f64 (sin.f64 (+.f64 x (*.f64 eps 1/2))))

series412.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
169.0ms	(cbrt.f64 (sin.f64 (+.f64 x (*.f64 eps 1/2))))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4866	790
1	4866	790

prune110.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	49	13	62

Merged error: 0.2b

Counts

62 → 13

Compiler

Compiled 2264 to 1530 computations (32.4% saved)

regimes168.0ms (2.9%)

Compiler: Compiled 1068 to 848 computations (20.6% saved)

bsearch74.0ms (1.3%)

Steps

Iters	Range		Point
9	158084.04547040968	140318637868774.84	161896.90463515825
10	-29782.00160110871	-1.0347582234434808e-06	-0.00021991234504609484

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	60
1	71	60

end0.0ms (0%)

sample3.3s (58.2%)

Algorithm

1×

intervals

Results

1.3s	2079×	body	2048	valid
1.1s	3824×	body	1024	valid
248.0ms	1323×	body	512	valid
62.0ms	535×	body	256	valid
15.0ms	236×	body	128	valid
6.0ms	3×	body	4096	valid

Compiler

Compiled 396 to 313 computations (21% saved)

Details

analyze2.0ms (0%)

sample92.0ms (1.6%)

simplify171.0ms (3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series106.0ms (1.9%)

simplify100.0ms (1.7%)

prune33.0ms (0.6%)

localize13.0ms (0.2%)

rewrite45.0ms (0.8%)

series218.0ms (3.8%)

simplify72.0ms (1.2%)

prune116.0ms (2%)

localize24.0ms (0.4%)

rewrite25.0ms (0.4%)

series276.0ms (4.8%)

simplify74.0ms (1.3%)

prune106.0ms (1.8%)

localize38.0ms (0.7%)

rewrite28.0ms (0.5%)

series412.0ms (7.2%)

simplify72.0ms (1.3%)

prune110.0ms (1.9%)

regimes168.0ms (2.9%)

bsearch74.0ms (1.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (58.2%)

Profiling