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)

sample104.0ms (1.6%)

Algorithm

1×

intervals

Results

51.0ms	71×	body	2048	valid
36.0ms	123×	body	1024	valid
7.0ms	38×	body	512	valid
2.0ms	16×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify178.0ms (2.7%)

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

Merged error: 42.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0b	(cos.f64 (+.f64 x eps))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
4×	`add-log-exp_binary64_118`
3×	`add-cube-cbrt_binary64_114` `cancel-sign-sub-inv_binary64_45`
2×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `cos-sum_binary64_213` `pow1_binary64_140`
1×	`associate--l-_binary64_17` `distribute-lft-out--_binary64_31` `diff-cos_binary64_230` `flip--_binary64_54` `difference-of-squares_binary64_48` `diff-log_binary64_171` `flip3--_binary64_83` `sub-neg_binary64_72`

Counts

2 → 26

Calls

2 calls:

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

series104.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

76.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
28.0ms	(cos.f64 (+.f64 x eps))

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5098	444

prune100.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	24	8	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	8	33

Merged error: 0.4b

Counts

33 → 8

Compiler

Compiled 1436 to 837 computations (41.7% 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)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_79`
11×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
9×	`add-sqr-sqrt_binary64_101` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114`
6×	`associate-l_binary64_20`
4×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150` `associate-r_binary64_19`
3×	`sum-log_binary64_170` `distribute-lft-out_binary64_30`
2×	`sin-mult_binary64_234` `*-commutative_binary64_10`
1×	`flip-+_binary64_53` `+-commutative_binary64_9` `associate-*r/_binary64_21` `unswap-sqr_binary64_47` `associate-+r+_binary64_11` `flip3-+_binary64_82`

Counts

4 → 60

Calls

4 calls:

15.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
14.0ms	(.f64 -2 (.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))

series285.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
95.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
40.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
32.0ms	(+.f64 x (+.f64 x eps))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4950	1369
1	4950	1369

prune281.0ms (4.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	10	72
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	68	12	80

Merged error: 0.4b

Counts

80 → 12

Compiler

Compiled 4763 to 3491 computations (26.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
3.5b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
8×	`add-sqr-sqrt_binary64_101`
7×	`sin-sum_binary64_212`
6×	`associate-l_binary64_20` `add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
5×	`distribute-lft-in_binary64_28` `distribute-rgt-in_binary64_29`
4×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150` `associate-r_binary64_19`
3×	`add-log-exp_binary64_118`
2×	`sin-mult_binary64_234` `*-commutative_binary64_10`
1×	`associate-*r/_binary64_21` `unswap-sqr_binary64_47`

Counts

3 → 52

Calls

3 calls:

10.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
9.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
4.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

series254.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

125.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
89.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
40.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4857	1328
1	4857	1328

prune295.0ms (4.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Merged error: 0.1b

Counts

73 → 13

Compiler

Compiled 4857 to 3903 computations (19.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
0.1b	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_101`
10×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-cube-cbrt_binary64_114` `pow1_binary64_140` `*-un-lft-identity_binary64_79`
9×	`associate-l_binary64_20` `associate-r_binary64_19`
6×	`add-log-exp_binary64_118`
3×	`unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150`
2×	`flip-+_binary64_53` `associate-*r/_binary64_21` `flip3-+_binary64_82`
1×	`sum-log_binary64_170` `sin-cos-mult_binary64_235` `distribute-lft-in_binary64_28` `+-commutative_binary64_9` `distribute-rgt-in_binary64_29`

Counts

4 → 70

Calls

4 calls:

12.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))
8.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
8.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
6.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))

series542.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

236.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))
165.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
71.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
70.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4978	1986
1	4978	1986

prune480.0ms (7.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	8	4	12
Picked	0	1	1
Done	0	0	0
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

Compiler

Compiled 8752 to 6755 computations (22.8% saved)

regimes81.0ms (1.2%)

Compiler: Compiled 894 to 710 computations (20.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	24	35

end0.0ms (0%)

sample3.5s (52.5%)

Algorithm

1×

intervals

Results

1.3s	2047×	body	2048	valid
1.2s	3905×	body	1024	valid
251.0ms	1283×	body	512	valid
64.0ms	509×	body	256	valid
17.0ms	254×	body	128	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 475 to 379 computations (20.2% saved)

Details

analyze2.0ms (0%)

sample104.0ms (1.6%)

simplify178.0ms (2.7%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite14.0ms (0.2%)

series104.0ms (1.6%)

simplify57.0ms (0.8%)

prune100.0ms (1.5%)

localize13.0ms (0.2%)

rewrite48.0ms (0.7%)

series285.0ms (4.2%)

simplify60.0ms (0.9%)

prune281.0ms (4.2%)

localize12.0ms (0.2%)

rewrite31.0ms (0.5%)

series254.0ms (3.8%)

simplify99.0ms (1.5%)

prune295.0ms (4.4%)

localize19.0ms (0.3%)

rewrite40.0ms (0.6%)

series542.0ms (8.1%)

simplify80.0ms (1.2%)

prune480.0ms (7.1%)

regimes81.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (52.5%)

Profiling