Details

analyze905.0ms (15.9%)

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)

sample62.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	85×	body	1024	valid
9.0ms	110×	body	128	valid
8.0ms	38×	body	512	valid
3.0ms	23×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify186.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	130	14
1	130	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)

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))
0.2b	(/.f64 x (tan.f64 B))

rewrite37.0ms (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:

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))

series537.0ms (9.4%)

Counts

3 → 9

Calls

3 calls:

252.0ms	(/.f64 x (tan.f64 B))
243.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
41.0ms	(/.f64 1 (sin.f64 B))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5791	1419

prune101.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

Compiler

Compiled 1587 to 659 computations (58.5% saved)

localize11.0ms (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))

rewrite34.0ms (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:

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))

series514.0ms (9%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
165.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
100.0ms	(/.f64 x (sin.f64 B))
38.0ms	(/.f64 1 (sin.f64 B))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4939	1611
1	4939	1611

prune103.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Merged error: 0b

Counts

125 → 7

Compiler

Compiled 2118 to 735 computations (65.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
0.2b	(*.f64 x (cos.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))
5.0ms	(*.f64 x (cos.f64 B))

series195.0ms (3.4%)

Counts

2 → 6

Calls

2 calls:

137.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
58.0ms	(*.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

prune48.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Merged error: 0b

Counts

61 → 7

Compiler

Compiled 917 to 406 computations (55.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 1 (tan.f64 B))
0.3b	(*.f64 x (/.f64 1 (tan.f64 B)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64` `times-frac_binary64`
28×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`
14×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64` `div-exp_binary64`
4×	`prod-exp_binary64`
3×	`1-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `frac-sub_binary64` `tan-quot_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 114

Calls

4 calls:

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

series621.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
230.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
103.0ms	(/.f64 1 (tan.f64 B))
36.0ms	(/.f64 1 (sin.f64 B))

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4841	1438
1	4841	1438

prune96.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	126	7	133

Merged error: 0b

Counts

133 → 7

Compiler

Compiled 1903 to 953 computations (49.9% saved)

regimes36.0ms (0.6%)

Compiler: Compiled 220 to 152 computations (30.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	14
1	36	14

end0.0ms (0%)

sample1.8s (32.2%)

Algorithm

1×

intervals

Results

821.0ms	2324×	body	1024	valid
302.0ms	3939×	body	128	valid
255.0ms	1148×	body	512	valid
86.0ms	586×	body	256	valid
11.0ms	163×	body	128	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

Details

analyze905.0ms (15.9%)

sample62.0ms (1.1%)

simplify186.0ms (3.3%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series537.0ms (9.4%)

simplify73.0ms (1.3%)

prune101.0ms (1.8%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series514.0ms (9%)

simplify70.0ms (1.2%)

prune103.0ms (1.8%)

localize9.0ms (0.2%)

rewrite14.0ms (0.2%)

series195.0ms (3.4%)

simplify65.0ms (1.1%)

prune48.0ms (0.8%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series621.0ms (10.9%)

simplify77.0ms (1.4%)

prune96.0ms (1.7%)

regimes36.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (32.2%)

Profiling