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)

sample102.0ms (1.8%)

Algorithm

1×

intervals

Results

47.0ms	68×	body	2048	valid
39.0ms	131×	body	1024	valid
7.0ms	39×	body	512	valid
1.0ms	12×	body	256	valid
0.0ms	6×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify172.0ms (3.1%)

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: 40.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.9b	(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))
4.0ms	(cos.f64 (+.f64 x eps))

series104.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

77.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
27.0ms	(cos.f64 (+.f64 x eps))

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4863	429
1	4863	429

prune33.0ms (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: 0.5b

Counts

30 → 6

Compiler

Compiled 438 to 162 computations (63% 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))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.9b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite46.0ms (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))

series281.0ms (5%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
88.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
43.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(+.f64 x (+.f64 x eps))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4969	1369
1	4969	1369

prune95.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	65	13	78

Merged error: 0.4b

Counts

78 → 13

Compiler

Compiled 1666 to 1103 computations (33.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.9b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.9b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.9b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite35.0ms (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:

8.0ms	(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)))

series285.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
40.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
37.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
37.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4814	675
1	4814	675

prune94.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	45	12	57

Merged error: 0.4b

Counts

57 → 12

Compiler

Compiled 1989 to 1217 computations (38.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.6b	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.9b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.1b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_105`
24×	`add-sqr-sqrt_binary64_98`
15×	`add-cube-cbrt_binary64_109` `-un-lft-identity_binary64_77` `associate-r*_binary64_19`
10×	`unpow-prod-down_binary64_153` `cube-prod_binary64_102`
7×	`add-exp-log_binary64_112` `pow1_binary64_135`
6×	`add-cbrt-cube_binary64_110`
5×	`unswap-sqr_binary64_45`
4×	`add-log-exp_binary64_113` `sqr-pow_binary64_49`
3×	`associate-l_binary64_20` `cube-mult_binary64_104` `pow-unpow_binary64_151` `unpow3_binary64_140`
1×	`pow-to-exp_binary64_143` `rem-cbrt-cube_binary64_100` `rem-cube-cbrt_binary64_99` `pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `pow-exp_binary64_142` `prod-exp_binary64_123` `*-commutative_binary64_10` `pow1/3_binary64_156` `pow-pow_binary64_146`

Counts

4 → 85

Calls

4 calls:

16.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
8.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
8.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series289.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
89.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
37.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
35.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4843	1960
1	4843	1960

prune119.0ms (2.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	97	12	109

Merged error: 0.4b

Counts

109 → 12

Compiler

Compiled 2285 to 1504 computations (34.2% saved)

regimes141.0ms (2.5%)

Compiler: Compiled 723 to 578 computations (20.1% saved)

bsearch69.0ms (1.2%)

Steps

Iters	Range		Point
8	1.8398143021311394e-11	9.412924937912301e-08	9.269560447117668e-08
8	-0.005641666064101144	-2.355165639800751e-07	-2.9840549938089332e-05

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%)

sample3.3s (59.4%)

Algorithm

1×

intervals

Results

1.4s	2111×	body	2048	valid
1.2s	3844×	body	1024	valid
247.0ms	1300×	body	512	valid
64.0ms	499×	body	256	valid
16.0ms	244×	body	128	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 294 to 224 computations (23.8% saved)

Details

analyze2.0ms (0%)

sample102.0ms (1.8%)

simplify172.0ms (3.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series104.0ms (1.8%)

simplify95.0ms (1.7%)

prune33.0ms (0.6%)

localize13.0ms (0.2%)

rewrite46.0ms (0.8%)

series281.0ms (5%)

simplify57.0ms (1%)

prune95.0ms (1.7%)

localize17.0ms (0.3%)

rewrite35.0ms (0.6%)

series285.0ms (5.1%)

simplify61.0ms (1.1%)

prune94.0ms (1.7%)

localize16.0ms (0.3%)

rewrite51.0ms (0.9%)

series289.0ms (5.1%)

simplify83.0ms (1.5%)

prune119.0ms (2.1%)

regimes141.0ms (2.5%)

bsearch69.0ms (1.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.3s (59.4%)

Profiling