Details

analyze900.0ms (17.4%)

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)

sample48.0ms (0.9%)

Algorithm

1×

intervals

Results

16.0ms	58×	body	1024	valid
10.0ms	138×	body	128	valid
7.0ms	37×	body	512	valid
3.0ms	22×	body	256	valid
1.0ms	11×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify113.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune7.0ms (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)

localize10.0ms (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))

rewrite33.0ms (0.6%)

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:

16.0ms	(-.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))

series370.0ms (7.1%)

Counts

3 → 15

Calls

3 calls:

242.0ms	(/.f64 x (tan.f64 B))
110.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
18.0ms	(/.f64 1 (sin.f64 B))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5692	1500

prune101.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	10	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

Compiler

Compiled 1676 to 694 computations (58.6% saved)

localize9.0ms (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 x (sin.f64 B))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite29.0ms (0.6%)

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:

8.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 x (sin.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

series378.0ms (7.3%)

Counts

4 → 21

Calls

4 calls:

182.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
91.0ms	(/.f64 x (sin.f64 B))
89.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
16.0ms	(/.f64 1 (sin.f64 B))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4988	1677
1	4988	1677

prune105.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Merged error: 0.0b

Counts

135 → 8

Compiler

Compiled 2215 to 815 computations (63.2% saved)

localize8.0ms (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))

rewrite15.0ms (0.3%)

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:

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

series138.0ms (2.7%)

Counts

2 → 12

Calls

2 calls:

69.0ms	(*.f64 x (cos.f64 B))
69.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5385	960

prune51.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	60	8	68

Merged error: 0.0b

Counts

68 → 8

Compiler

Compiled 994 to 449 computations (54.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.6%)

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×	`associate-r_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64`
4×	`div-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-r/_binary64` `associate-l*_binary64` `div-inv_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:

7.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
7.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
6.0ms	(/.f64 (cos.f64 B) (sin.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))

series322.0ms (6.2%)

Counts

4 → 18

Calls

4 calls:

195.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
86.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
25.0ms	(/.f64 (cos.f64 B) (sin.f64 B))
16.0ms	(/.f64 1 (sin.f64 B))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5053	1742

prune89.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Merged error: 0.0b

Counts

130 → 8

Compiler

Compiled 2071 to 702 computations (66.1% saved)

regimes170.0ms (3.3%)

Compiler: Compiled 1483 to 1098 computations (26% 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%)

sample2.0s (38%)

Algorithm

1×

intervals

Results

616.0ms	2279×	body	1024	valid
294.0ms	3950×	body	128	valid
220.0ms	1171×	body	512	valid
88.0ms	595×	body	256	valid
12.0ms	183×	body	128	invalid
3.0ms	5×	body	2048	valid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 507 to 378 computations (25.4% saved)

Details

analyze900.0ms (17.4%)

sample48.0ms (0.9%)

simplify113.0ms (2.2%)

prune7.0ms (0.1%)

localize10.0ms (0.2%)

rewrite33.0ms (0.6%)

series370.0ms (7.1%)

simplify74.0ms (1.4%)

prune101.0ms (1.9%)

localize9.0ms (0.2%)

rewrite29.0ms (0.6%)

series378.0ms (7.3%)

simplify75.0ms (1.4%)

prune105.0ms (2%)

localize8.0ms (0.1%)

rewrite15.0ms (0.3%)

series138.0ms (2.7%)

simplify56.0ms (1.1%)

prune51.0ms (1%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series322.0ms (6.2%)

simplify71.0ms (1.4%)

prune89.0ms (1.7%)

regimes170.0ms (3.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (38%)

Profiling