Details

analyze2.0s (12.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4785	128
1	4785	128
0	3	3
1	3	3

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
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample104.0ms (0.6%)

Algorithm

1×

intervals

Results

47.0ms	79×	body	1024	valid
17.0ms	128×	body	128	valid
14.0ms	35×	body	512	valid
4.0ms	14×	body	256	valid
3.0ms	23×	body	128	invalid
0.0ms	3×	body	128	nan
0.0ms	1×	body	256	invalid

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune14.0ms (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

12.9b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
5.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite213.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

10.6b

Rules

44×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`prod-exp_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `associate-/r_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 115

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3459 to 1606 computations (53.6% saved)

series1.0s (6.2%)

Error

0.1b

Counts

4 → 47

Calls

4 calls:

386.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
237.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
211.0ms	(/.f64 x (tan.f64 B))
96.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4019 to 2916 computations (27.4% saved)

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4930	3752
1	4930	3752

prune242.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	150	12	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	12	164

Error

0.0b

Counts

164 → 12

Compiler

Compiled 4987 to 2478 computations (50.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
16.4b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite261.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
25×	`unpow-prod-down_binary64` `associate-r_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-l_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `cbrt-unprod_binary64`
1×	`pow-pow_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 138

Calls

4 calls:

15.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
10.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
7.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 4662 to 2467 computations (47.1% saved)

series1.2s (7.6%)

Error

0.0b

Counts

4 → 57

Calls

4 calls:

375.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
341.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
221.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
192.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 5141 to 3763 computations (26.8% saved)

simplify116.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4928	5824
1	4928	5824

prune321.0ms (2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	194	13	207

Error

0.0b

Counts

207 → 13

Compiler

Compiled 6558 to 3540 computations (46% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 1 (/.f64 (sin.f64 B) F))
5.3b	(.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite438.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

168×	`times-frac_binary64`
130×	`add-sqr-sqrt_binary64`
99×	`*-un-lft-identity_binary64`
93×	`add-cube-cbrt_binary64`
68×	`add-exp-log_binary64`
44×	`associate-l_binary64`
29×	`div-exp_binary64`
21×	`prod-exp_binary64`
20×	`add-cbrt-cube_binary64`
16×	`associate-/r*_binary64`
15×	`unswap-sqr_binary64`
11×	`unpow-prod-down_binary64`
10×	`div-inv_binary64`
8×	`pow-to-exp_binary64` `pow-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
7×	`sqr-pow_binary64` `cbrt-undiv_binary64` `associate-r_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64`
1×	`pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64` `inv-pow_binary64` `pow-flip_binary64` `tan-quot_binary64`

Counts

4 → 220

Calls

4 calls:

26.0ms	(.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
6.0ms	(/.f64 1 (/.f64 (sin.f64 B) F))
4.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 7428 to 3743 computations (49.6% saved)

series958.0ms (5.9%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

379.0ms	(.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
226.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
182.0ms	(/.f64 x (tan.f64 B))
97.0ms	(/.f64 1 (/.f64 (sin.f64 B) F))

Compiler

Compiled 4129 to 3027 computations (26.7% saved)

simplify127.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4925	6469
1	4925	6469

prune416.0ms (2.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	266	14	280

Error

0.0b

Counts

280 → 14

Compiler

Compiled 8483 to 4170 computations (50.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (tan.f64 B))
0.2b	(*.f64 x (/.f64 1 (tan.f64 B)))
5.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite234.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

51×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64` `times-frac_binary64`
31×	`add-cube-cbrt_binary64` `add-exp-log_binary64`
21×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64` `associate-l_binary64`
10×	`prod-exp_binary64`
9×	`unswap-sqr_binary64`
8×	`unpow-prod-down_binary64` `pow1_binary64`
7×	`div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `cbrt-unprod_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`*-commutative_binary64` `1-exp_binary64` `rec-exp_binary64` `tan-quot_binary64` `associate-/r/_binary64`
1×	`pow-pow_binary64` `associate-l/_binary64` `pow-prod-down_binary64` `un-div-inv_binary64` `associate-r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 129

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
8.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
4.0ms	(/.f64 1 (tan.f64 B))

Compiler

Compiled 4093 to 2244 computations (45.2% saved)

series916.0ms (5.7%)

Error

0.0b

Counts

4 → 46

Calls

4 calls:

354.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
218.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
199.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
68.0ms	(/.f64 1 (tan.f64 B))

Compiler

Compiled 4104 to 3054 computations (25.6% saved)

simplify118.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4884	3803
1	4884	3803

prune243.0ms (1.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	2	9	11
Picked	1	0	1
Done	0	2	2
Total	176	13	189

Error

0.0b

Counts

189 → 13

Compiler

Compiled 5293 to 2870 computations (45.8% saved)

regimes1.1s (6.6%)

Accuracy

Total 0.2b remaining (92.4%)

Threshold costs 0.2b (92.4%)

Compiler

Compiled 11140 to 8484 computations (23.8% saved)

bsearch147.0ms (0.9%)

Steps

Iters	Range		Point
8	22972.897208697406	7379942.130199348	7311478.62933065
8	-1.0737811248148504e+29	-4.1033572478357464e+24	-4.172578609705223e+24

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	103
1	89	103

end0.0ms (0%)

sample5.7s (35.3%)

Algorithm

1×

intervals

Results

1.3s	2279×	body	1024	valid
557.0ms	4085×	body	128	valid
427.0ms	1074×	body	512	valid
146.0ms	560×	body	256	valid
98.0ms	709×	body	128	invalid
12.0ms	114×	body	128	nan
2.0ms	2×	body	2048	valid
1.0ms	2×	body	256	invalid

Compiler

Compiled 2865 to 2174 computations (24.1% saved)

Details

analyze2.0s (12.3%)

sample104.0ms (0.6%)

simplify133.0ms (0.8%)

prune14.0ms (0.1%)

localize19.0ms (0.1%)

rewrite213.0ms (1.3%)

series1.0s (6.2%)

simplify83.0ms (0.5%)

prune242.0ms (1.5%)

localize20.0ms (0.1%)

rewrite261.0ms (1.6%)

series1.2s (7.6%)

simplify116.0ms (0.7%)

prune321.0ms (2%)

localize19.0ms (0.1%)

rewrite438.0ms (2.7%)

series958.0ms (5.9%)

simplify127.0ms (0.8%)

prune416.0ms (2.6%)

localize19.0ms (0.1%)

rewrite234.0ms (1.4%)

series916.0ms (5.7%)

simplify118.0ms (0.7%)

prune243.0ms (1.5%)

regimes1.1s (6.6%)

bsearch147.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.7s (35.3%)

Profiling