Details

analyze1.1s (1.6%)

Algorithm

1×

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)

sample133.0ms (0.2%)

Algorithm

1×

intervals

Results

48.0ms	36×	body	2048	valid
31.0ms	4×	body	4096	valid
22.0ms	58×	body	1024	valid
10.0ms	126×	body	128	valid
7.0ms	25×	body	512	valid
1.0ms	7×	body	256	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify151.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	299	20
1	299	20

prune14.0ms (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: 18.8b

Counts

2 → 2

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
5.1b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
30.6b	(tan.f64 (*.f64 PI.f64 l))

rewrite42.0ms (0.1%)

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:

13.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
8.0ms	(*.f64 PI.f64 l)
7.0ms	(*.f64 PI.f64 l)
4.0ms	(tan.f64 (*.f64 PI.f64 l))

series246.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
70.0ms	(tan.f64 (*.f64 PI.f64 l))
15.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5225	914

prune326.0ms (0.5%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	44	34	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	36	80

Merged error: 13.5b

Counts

80 → 36

Compiler

Compiled 1945 to 656 computations (66.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.2b	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
30.6b	(tan.f64 (*.f64 PI.f64 l))

rewrite34.0ms (0.1%)

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:

8.0ms	(*.f64 PI.f64 l)
8.0ms	(*.f64 PI.f64 l)
5.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series200.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(tan.f64 (*.f64 PI.f64 l))
83.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
17.0ms	(*.f64 PI.f64 l)
15.0ms	(*.f64 PI.f64 l)

simplify159.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	5145	1019

prune388.0ms (0.6%)

Pruning

62 alts after pruning (60 fresh and 2 done)

	Pruned	Kept	Total
New	49	35	84
Fresh	9	25	34
Picked	0	1	1
Done	0	1	1
Total	58	62	120

Merged error: 13.5b

Counts

120 → 62

Compiler

Compiled 2621 to 1037 computations (60.4% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.3b	(/.f64 (sin.f64 (.f64 PI.f64 l)) (.f64 (cos.f64 (*.f64 PI.f64 l)) F))
30.7b	(cos.f64 (*.f64 PI.f64 l))
30.7b	(sin.f64 (*.f64 PI.f64 l))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

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

series129.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (sin.f64 (.f64 PI.f64 l)) (.f64 (cos.f64 (*.f64 PI.f64 l)) F))
16.0ms	(*.f64 PI.f64 l)
14.0ms	(cos.f64 (*.f64 PI.f64 l))
14.0ms	(sin.f64 (*.f64 PI.f64 l))

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5012	953

prune420.0ms (0.6%)

Pruning

87 alts after pruning (84 fresh and 3 done)

	Pruned	Kept	Total
New	37	28	65
Fresh	3	56	59
Picked	0	1	1
Done	0	2	2
Total	40	87	127

Merged error: 7.6b

Counts

127 → 87

Compiler

Compiled 3217 to 1378 computations (57.2% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
30.4b	(cos.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
30.7b	(sin.f64 (*.f64 PI.f64 l))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 40

Calls

4 calls:

3.0ms	(cos.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
2.0ms	(sin.f64 (*.f64 PI.f64 l))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series32.0ms (0%)

Counts

4 → 8

Calls

4 calls:

16.0ms	(sin.f64 (*.f64 PI.f64 l))
15.0ms	(cos.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5083	458

prune413.0ms (0.6%)

Pruning

96 alts after pruning (92 fresh and 4 done)

	Pruned	Kept	Total
New	36	12	48
Fresh	3	80	83
Picked	0	1	1
Done	0	3	3
Total	39	96	135

Merged error: 7.6b

Counts

135 → 96

Compiler

Compiled 1140 to 328 computations (71.2% saved)

regimes4.7s (6.8%)

Compiler: Compiled 26230 to 15878 computations (39.5% saved)

bsearch51.4s (75%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify32.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	165	176
1	165	176

end0.0ms (0%)

sample8.3s (12.1%)

Algorithm

1×

intervals

Results

1.3s	1074×	body	2048	valid
653.0ms	1772×	body	1024	valid
314.0ms	4085×	body	128	valid
228.0ms	51×	body	4096	valid
167.0ms	671×	body	512	valid
58.0ms	347×	body	256	valid
15.0ms	182×	body	128	invalid
8.0ms	13×	body	2048	invalid
2.0ms	4×	body	8192	exit

Compiler

Compiled 4842 to 2832 computations (41.5% saved)

Pareto

0.42892300462681665

Details

analyze1.1s (1.6%)

sample133.0ms (0.2%)

simplify151.0ms (0.2%)

prune14.0ms (0%)

localize19.0ms (0%)

rewrite42.0ms (0.1%)

series246.0ms (0.4%)

simplify87.0ms (0.1%)

prune326.0ms (0.5%)

localize9.0ms (0%)

rewrite34.0ms (0.1%)

series200.0ms (0.3%)

simplify159.0ms (0.2%)

prune388.0ms (0.6%)

localize11.0ms (0%)

rewrite17.0ms (0%)

series129.0ms (0.2%)

simplify68.0ms (0.1%)

prune420.0ms (0.6%)

localize17.0ms (0%)

rewrite12.0ms (0%)

series32.0ms (0%)

simplify76.0ms (0.1%)

prune413.0ms (0.6%)

regimes4.7s (6.8%)

bsearch51.4s (75%)

simplify32.0ms (0%)

end0.0ms (0%)

sample8.3s (12.1%)

Profiling