Details

analyze917.0ms (15%)

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample57.0ms (0.9%)

Algorithm

1×

intervals

Results

26.0ms	74×	body	1024	valid
9.0ms	127×	body	128	valid
7.0ms	30×	body	512	valid
4.0ms	25×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify186.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	130	14
1	130	14

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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `difference-of-squares_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`distribute-lft-out--_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`

Counts

3 → 94

Calls

3 calls:

18.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))

series518.0ms (8.5%)

Counts

3 → 9

Calls

3 calls:

242.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
230.0ms	(/.f64 x (tan.f64 B))
46.0ms	(/.f64 1 (sin.f64 B))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5791	1419

prune99.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 0.0b

Counts

105 → 11

Compiler

Compiled 1619 to 682 computations (57.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 x (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64`
4×	`div-exp_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-*l/_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cancel-sign-sub-inv_binary64` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

9.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
8.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
4.0ms	(/.f64 x (sin.f64 B))

series525.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
170.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
99.0ms	(/.f64 x (sin.f64 B))
37.0ms	(/.f64 1 (sin.f64 B))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	1611
1	4939	1611

prune102.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	7	3	10
Picked	0	1	1
Done	0	0	0
Total	119	8	127

Merged error: 0b

Counts

127 → 8

Compiler

Compiled 2163 to 755 computations (65.1% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 x (cos.f64 B))
0.1b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
4.0ms	(*.f64 x (cos.f64 B))

series196.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

144.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
51.0ms	(*.f64 x (cos.f64 B))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4946	882
1	4946	882

prune49.0ms (0.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	54	8	62

Merged error: 0b

Counts

62 → 8

Compiler

Compiled 962 to 426 computations (55.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 (sin.f64 B) x)
0.2b	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
0.3b	(/.f64 1 (/.f64 (sin.f64 B) x))

rewrite55.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
112×	`add-sqr-sqrt_binary64`
100×	`*-un-lft-identity_binary64`
98×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`
40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
19×	`associate-/r*_binary64`
17×	`div-exp_binary64`
11×	`div-inv_binary64`
9×	`associate-/l*_binary64`
8×	`pow1_binary64` `cbrt-undiv_binary64`
7×	`prod-exp_binary64`
5×	`1-exp_binary64` `unswap-sqr_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64`
1×	`pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 206

Calls

4 calls:

18.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
7.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
4.0ms	(/.f64 (sin.f64 B) x)
4.0ms	(/.f64 1 (sin.f64 B))

series339.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
95.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
47.0ms	(/.f64 (sin.f64 B) x)
37.0ms	(/.f64 1 (sin.f64 B))

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5018	3064

prune195.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	218	8	226

Merged error: 0b

Counts

226 → 8

Compiler

Compiled 4380 to 1709 computations (61% saved)

regimes187.0ms (3.1%)

Compiler: Compiled 1699 to 1182 computations (30.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	14
1	26	14

end0.0ms (0%)

sample2.2s (36.6%)

Algorithm

1×

intervals

Results

812.0ms	2276×	body	1024	valid
311.0ms	4065×	body	128	valid
237.0ms	1080×	body	512	valid
85.0ms	574×	body	256	valid
15.0ms	207×	body	128	invalid
4.0ms	5×	body	2048	valid
0.0ms	2×	body	512	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 579 to 406 computations (29.9% saved)

Details

analyze917.0ms (15%)

sample57.0ms (0.9%)

simplify186.0ms (3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite43.0ms (0.7%)

series518.0ms (8.5%)

simplify70.0ms (1.1%)

prune99.0ms (1.6%)

localize10.0ms (0.2%)

rewrite33.0ms (0.5%)

series525.0ms (8.6%)

simplify72.0ms (1.2%)

prune102.0ms (1.7%)

localize9.0ms (0.1%)

rewrite14.0ms (0.2%)

series196.0ms (3.2%)

simplify65.0ms (1.1%)

prune49.0ms (0.8%)

localize11.0ms (0.2%)

rewrite55.0ms (0.9%)

series339.0ms (5.5%)

simplify107.0ms (1.7%)

prune195.0ms (3.2%)

regimes187.0ms (3.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (36.6%)

Profiling