Details

analyze1.1s (18.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1027	40
1	1027	40
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.2%	0.1%	7
18.7%	81.2%	0.1%	8
29.7%	69.5%	0.9%	9
30.4%	67.9%	1.7%	10
36.3%	61.1%	2.6%	11
36.9%	59.5%	3.6%	12
39.9%	55.9%	4.2%	13
40.2%	54.9%	4.9%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample78.0ms (1.3%)

Algorithm

1×

intervals

Results

27.0ms	32×	body	2048	valid
18.0ms	58×	body	1024	valid
10.0ms	3×	body	4096	valid
7.0ms	132×	body	128	valid
3.0ms	21×	body	512	valid
1.0ms	10×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	299	20
1	299	20

prune6.0ms (0.1%)

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

15.9b

Counts

2 → 2

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
2.7b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
29.8b	(tan.f64 (*.f64 PI.f64 l))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `tan-quot_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 66

Calls

4 calls:

6.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
4.0ms	(*.f64 PI.f64 l)
4.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series162.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
51.0ms	(tan.f64 (*.f64 PI.f64 l))
14.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5225	914

prune96.0ms (1.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	59	19	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	19	80

Error

13.3b

Counts

80 → 19

Compiler

Compiled 1627 to 464 computations (71.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
29.8b	(tan.f64 (*.f64 PI.f64 l))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `tan-quot_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 72

Calls

4 calls:

4.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series131.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
39.0ms	(tan.f64 (*.f64 PI.f64 l))
13.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify112.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5145	1019

prune88.0ms (1.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	82	21	103

Error

13.3b

Counts

103 → 21

Compiler

Compiled 1820 to 569 computations (68.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.5b	(/.f64 1 (/.f64 F (tan.f64 (*.f64 PI.f64 l))))
29.8b	(tan.f64 (*.f64 PI.f64 l))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64`
14×	`associate-/r*_binary64`
13×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`div-exp_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`associate-/r/_binary64` `div-inv_binary64` `tan-quot_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `rec-exp_binary64` `*-commutative_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 124

Calls

4 calls:

7.0ms	(/.f64 1 (/.f64 F (tan.f64 (*.f64 PI.f64 l))))
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series149.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(/.f64 1 (/.f64 F (tan.f64 (*.f64 PI.f64 l))))
35.0ms	(tan.f64 (*.f64 PI.f64 l))
13.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4931	2260
1	4931	2260

prune124.0ms (2.1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	19	20
Picked	0	1	1
Done	0	0	0
Total	135	22	157

Error

13.3b

Counts

157 → 22

Compiler

Compiled 3134 to 1039 computations (66.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
29.8b	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-r_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 55

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))
3.0ms	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series52.0ms (0.9%)

Counts

4 → 8

Calls

4 calls:

38.0ms	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
14.0ms	(.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4976	538
1	4976	538

prune52.0ms (0.9%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	2	18	20
Picked	0	1	1
Done	0	1	1
Total	63	22	85

Error

13.2b

Counts

85 → 22

Compiler

Compiled 1113 to 367 computations (67% saved)

regimes491.0ms (8.4%)

Accuracy

Total 0.3b remaining (2.1%)

Threshold costs 0.3b (2.1%)

Compiler

Compiled 5895 to 3510 computations (40.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms (0%)

sample2.8s (48.4%)

Algorithm

1×

intervals

Results

902.0ms	1071×	body	2048	valid
437.0ms	1755×	body	1024	valid
209.0ms	4021×	body	128	valid
206.0ms	62×	body	4096	valid
125.0ms	766×	body	512	valid
39.0ms	325×	body	256	valid
12.0ms	210×	body	128	invalid
2.0ms	5×	body	2048	invalid
2.0ms	4×	body	8192	exit

Compiler

Compiled 922 to 550 computations (40.3% saved)

Details

analyze1.1s (18.5%)

sample78.0ms (1.3%)

simplify21.0ms (0.4%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite21.0ms (0.4%)

series162.0ms (2.8%)

simplify77.0ms (1.3%)

prune96.0ms (1.6%)

localize8.0ms (0.1%)

rewrite17.0ms (0.3%)

series131.0ms (2.2%)

simplify112.0ms (1.9%)

prune88.0ms (1.5%)

localize10.0ms (0.2%)

rewrite26.0ms (0.4%)

series149.0ms (2.5%)

simplify102.0ms (1.7%)

prune124.0ms (2.1%)

localize15.0ms (0.3%)

rewrite16.0ms (0.3%)

series52.0ms (0.9%)

simplify80.0ms (1.4%)

prune52.0ms (0.9%)

regimes491.0ms (8.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.8s (48.4%)

Profiling