Details

analyze1.9s (11.5%)

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

Symmetry

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample90.0ms (0.5%)

Algorithm

1×

intervals

Results

35.0ms	63×	body	1024	valid
18.0ms	143×	body	128	valid
15.0ms	38×	body	512	valid
3.0ms	12×	body	256	valid
2.0ms	15×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify134.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune9.0ms (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

15.6b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
8.8b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite215.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

12.6b

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)
3.0ms	(/.f64 F (sin.f64 B))
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 3459 to 1606 computations (53.6% saved)

series898.0ms (5.5%)

Error

0.2b

Counts

4 → 42

Calls

4 calls:

359.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
199.0ms	(/.f64 x (tan.f64 B))
191.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
95.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3294 to 2390 computations (27.4% saved)

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4917	3188
1	4917	3188

prune234.0ms (1.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	142	15	157
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	144	15	159

Error

0.0b

Counts

159 → 15

Compiler

Compiled 4658 to 2281 computations (51% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
0.4b	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
17.1b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite160.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 93

Calls

4 calls:

10.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
10.0ms	(/.f64 (.f64 F (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)
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 2798 to 1468 computations (47.5% saved)

series956.0ms (5.8%)

Error

0.0b

Counts

4 → 46

Calls

4 calls:

362.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
186.0ms	(/.f64 x (tan.f64 B))
180.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
176.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

Compiler

Compiled 3646 to 2719 computations (25.4% saved)

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4956	2980
1	4956	2980

prune186.0ms (1.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	138	16	154

Error

0.0b

Counts

154 → 16

Compiler

Compiled 4043 to 2182 computations (46% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
17.1b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite262.0ms (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))
6.0ms	(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)

series1.1s (6.6%)

Error

0.0b

Counts

4 → 50

Calls

4 calls:

336.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
327.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
180.0ms	(/.f64 x (tan.f64 B))
176.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

Compiler

Compiled 4134 to 3054 computations (26.1% saved)

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4973	4899
1	4973	4899

prune284.0ms (1.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	190	14	204

Error

0.0b

Counts

204 → 14

Compiler

Compiled 5902 to 3135 computations (46.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x))) -1/2))))
0.3b	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)))
0.3b	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2))
17.1b	(pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)

rewrite943.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

332×	`times-frac_binary64`
199×	`add-sqr-sqrt_binary64`
177×	`*-un-lft-identity_binary64`
173×	`add-cube-cbrt_binary64`
80×	`unpow-prod-down_binary64` `associate-r_binary64`
68×	`add-exp-log_binary64`
37×	`div-exp_binary64`
32×	`associate-/r*_binary64`
28×	`sqr-pow_binary64`
20×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
10×	`div-inv_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
7×	`cbrt-undiv_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `associate-/r/_binary64`
1×	`pow-pow_binary64` `inv-pow_binary64` `pow-flip_binary64` `pow-prod-down_binary64` `un-div-inv_binary64` `associate-r/_binary64` `-commutative_binary64`

Counts

4 → 311

Calls

4 calls:

34.0ms	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x))) -1/2))))
15.0ms	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)))
11.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2))
7.0ms	(pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)

Compiler

Compiled 12730 to 7442 computations (41.5% saved)

series1.1s (6.9%)

Error

0.0b

Counts

4 → 58

Calls

4 calls:

327.0ms	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)))
323.0ms	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x))) -1/2))))
256.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2))
165.0ms	(pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)

Compiler

Compiled 5061 to 3707 computations (26.8% saved)

simplify152.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

369 → 369

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4950	12289
1	4950	12289

prune727.0ms (4.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	368	1	369
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	369	14	383

Error

0.0b

Counts

383 → 14

Compiler

Compiled 12984 to 7118 computations (45.2% saved)

regimes1.2s (7.3%)

Accuracy

Total 0.2b remaining (94.6%)

Threshold costs 0.2b (94.6%)

Compiler

Compiled 12432 to 9508 computations (23.5% saved)

bsearch148.0ms (0.9%)

Steps

Iters	Range		Point
11	9.405427904795544e+64	3.912151247941615e+84	3.6203460570328665e+84
7	-2.0254186676341325e+37	-9.613106404847122e+35	-2.0068997175194047e+37

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	58	78
1	58	78

Removed

()

end0.0ms (0%)

sample5.4s (32.7%)

Algorithm

1×

intervals

Results

1.2s	2184×	body	1024	valid
534.0ms	4207×	body	128	valid
415.0ms	1102×	body	512	valid
121.0ms	498×	body	256	valid
78.0ms	627×	body	128	invalid
11.0ms	116×	body	128	nan
8.0ms	9×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 3172 to 2419 computations (23.7% saved)

Details

analyze1.9s (11.5%)

sample90.0ms (0.5%)

simplify134.0ms (0.8%)

prune9.0ms (0.1%)

localize24.0ms (0.1%)

rewrite215.0ms (1.3%)

series898.0ms (5.5%)

simplify88.0ms (0.5%)

prune234.0ms (1.4%)

localize20.0ms (0.1%)

rewrite160.0ms (1%)

series956.0ms (5.8%)

simplify90.0ms (0.5%)

prune186.0ms (1.1%)

localize16.0ms (0.1%)

rewrite262.0ms (1.6%)

series1.1s (6.6%)

simplify106.0ms (0.6%)

prune284.0ms (1.7%)

localize18.0ms (0.1%)

rewrite943.0ms (5.7%)

series1.1s (6.9%)

simplify152.0ms (0.9%)

prune727.0ms (4.4%)

regimes1.2s (7.3%)

bsearch148.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.4s (32.7%)

Profiling