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)

sample98.0ms (1.7%)

Algorithm

1×

intervals

Results

43.0ms	130×	body	1024	valid
39.0ms	62×	body	2048	valid
7.0ms	40×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	10×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify161.0ms (2.7%)

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: 39.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.2b	(cos.f64 (+.f64 x eps))

rewrite14.0ms (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:

8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms	(cos.f64 (+.f64 x eps))

series111.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

79.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
32.0ms	(cos.f64 (+.f64 x eps))

simplify96.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4863	429
1	4863	429

prune34.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	23	6	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	6	30

Merged error: 0.3b

Counts

30 → 6

Compiler

Compiled 455 to 166 computations (63.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_77`
11×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135`
9×	`add-log-exp_binary64_113` `add-sqr-sqrt_binary64_98`
7×	`add-cube-cbrt_binary64_109`
6×	`associate-l_binary64_20`
4×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `associate-r_binary64_19`
3×	`distribute-lft-out_binary64_30` `sum-log_binary64_165`
2×	`sin-mult_binary64_229` `*-commutative_binary64_10`
1×	`flip-+_binary64_51` `flip3-+_binary64_80` `+-commutative_binary64_9` `associate-*r/_binary64_21` `unswap-sqr_binary64_45` `associate-+r+_binary64_11`

Counts

4 → 60

Calls

4 calls:

13.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.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))

series288.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
91.0ms	(*.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))
33.0ms	(+.f64 x (+.f64 x eps))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4969	1369
1	4969	1369

prune98.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	66	12	78

Merged error: 0.2b

Counts

78 → 12

Compiler

Compiled 1724 to 1138 computations (34% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(.f64 (.f64 (sin.f64 (/.f64 eps 2)) -2) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_77`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135`
4×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
3×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `distribute-lft-out_binary64_30` `sum-log_binary64_165` `associate-r_binary64_19`
1×	`associate-l_binary64_20` `flip-+_binary64_51` `flip3-+_binary64_80` `+-commutative_binary64_9` `*-commutative_binary64_10` `associate-+r+_binary64_11`

Counts

3 → 40

Calls

3 calls:

15.0ms	(.f64 (.f64 (sin.f64 (/.f64 eps 2)) -2) (sin.f64 (/.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))

series188.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

117.0ms	(.f64 (.f64 (sin.f64 (/.f64 eps 2)) -2) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
40.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(+.f64 x (+.f64 x eps))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5054	822

prune65.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	49	12	61

Merged error: 0.2b

Counts

61 → 12

Compiler

Compiled 1221 to 803 computations (34.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite36.0ms (0.6%)

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`
1×	`pow1/3_binary64_156`

Counts

4 → 32

Calls

4 calls:

9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series282.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
41.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
35.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
34.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4814	675
1	4814	675

prune79.0ms (1.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	43	13	56

Merged error: 0.2b

Counts

56 → 13

Compiler

Compiled 1769 to 1044 computations (41% saved)

regimes264.0ms (4.5%)

Compiler: Compiled 1870 to 1408 computations (24.7% saved)

bsearch87.0ms (1.5%)

Steps

Iters	Range		Point
10	4.766648698077205e-19	0.0003693174546992489	0.00011573277381876863
10	-0.7690085446444335	-8.177773180557729e-15	-6.346909542350063e-06

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	81
1	83	81

end0.0ms (0%)

sample3.7s (62.5%)

Algorithm

1×

intervals

Results

1.4s	2079×	body	2048	valid
1.2s	3810×	body	1024	valid
247.0ms	1295×	body	512	valid
68.0ms	559×	body	256	valid
16.0ms	253×	body	128	valid
8.0ms	4×	body	4096	valid

Compiler

Compiled 663 to 489 computations (26.2% saved)

Details

analyze2.0ms (0%)

sample98.0ms (1.7%)

simplify161.0ms (2.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite14.0ms (0.2%)

series111.0ms (1.9%)

simplify96.0ms (1.6%)

prune34.0ms (0.6%)

localize13.0ms (0.2%)

rewrite44.0ms (0.8%)

series288.0ms (4.9%)

simplify59.0ms (1%)

prune98.0ms (1.7%)

localize12.0ms (0.2%)

rewrite33.0ms (0.6%)

series188.0ms (3.2%)

simplify59.0ms (1%)

prune65.0ms (1.1%)

localize17.0ms (0.3%)

rewrite36.0ms (0.6%)

series282.0ms (4.8%)

simplify65.0ms (1.1%)

prune79.0ms (1.3%)

regimes264.0ms (4.5%)

bsearch87.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.7s (62.5%)

Profiling