Details

analyze1.8s (19.1%)

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
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)

sample133.0ms (1.4%)

Algorithm

1×

intervals

Results

54.0ms	53×	body	1280	valid
27.0ms	43×	body	640	valid
16.0ms	116×	body	80	valid
15.0ms	35×	body	320	valid
3.0ms	23×	body	80	invalid
3.0ms	9×	body	160	valid
0.0ms	2×	body	80	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify613.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4687	32
1	4687	32

prune12.0ms (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: 13.1b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
4.8b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_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×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

25.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
15.0ms	(.f64 (/.f64 F (sin.f64 B)) (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))

series99.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
29.0ms	(/.f64 x (tan.f64 B))
24.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
10.0ms	(/.f64 F (sin.f64 B))

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5055	2525

prune177.0ms (1.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	111	16	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	16	129

Merged error: 0.0b

Counts

129 → 16

Compiler

Compiled 3945 to 1933 computations (51% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
17.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
6.0ms	(/.f64 x (tan.f64 B))

series79.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
22.0ms	(/.f64 x (tan.f64 B))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify101.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4982	2141
1	4982	2141

prune123.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	106	15	121

Merged error: 0.0b

Counts

121 → 15

Compiler

Compiled 3215 to 1755 computations (45.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.7b	(.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)) (/.f64 1 (sin.f64 B)))
17.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

16.0ms	(.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)) (/.f64 1 (sin.f64 B)))
11.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

series83.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)) (/.f64 1 (sin.f64 B)))
22.0ms	(/.f64 x (tan.f64 B))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
13.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4944	2695
1	4944	2695

prune137.0ms (1.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	127	15	142

Merged error: 0.0b

Counts

142 → 15

Compiler

Compiled 3927 to 2215 computations (43.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
17.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_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` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

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

series98.0ms (1%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
29.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
22.0ms	(/.f64 x (tan.f64 B))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify132.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4933	3927
1	4933	3927

prune142.0ms (1.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	149	16	165

Merged error: 0.0b

Counts

165 → 16

Compiler

Compiled 4646 to 2408 computations (48.2% saved)

regimes244.0ms (2.6%)

Compiler: Compiled 1191 to 942 computations (20.9% saved)

bsearch107.0ms (1.1%)

Steps

Iters	Range		Point
8	0.12221191436371898	7506.824194327046	7379.805553361057
3	-536694.9226236013	-412625.1496383991	-508391.5278730379

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	128	98
1	128	98

end0.0ms (0%)

sample4.8s (51.6%)

Algorithm

1×

intervals

Results

1.6s	1729×	body	1280	valid
841.0ms	1413×	body	640	valid
526.0ms	3807×	body	80	valid
300.0ms	728×	body	320	valid
95.0ms	684×	body	80	invalid
89.0ms	323×	body	160	valid
11.0ms	114×	body	80	nan
1.0ms	1×	body	640	invalid
0.0ms	1×	body	320	invalid

Compiler

Compiled 487 to 375 computations (23% saved)

Details

analyze1.8s (19.1%)

sample133.0ms (1.4%)

simplify613.0ms (6.6%)

prune12.0ms (0.1%)

localize21.0ms (0.2%)

rewrite53.0ms (0.6%)

series99.0ms (1.1%)

simplify79.0ms (0.8%)

prune177.0ms (1.9%)

localize19.0ms (0.2%)

rewrite40.0ms (0.4%)

series79.0ms (0.8%)

simplify101.0ms (1.1%)

prune123.0ms (1.3%)

localize23.0ms (0.2%)

rewrite44.0ms (0.5%)

series83.0ms (0.9%)

simplify115.0ms (1.2%)

prune137.0ms (1.5%)

localize22.0ms (0.2%)

rewrite44.0ms (0.5%)

series98.0ms (1%)

simplify132.0ms (1.4%)

prune142.0ms (1.5%)

regimes244.0ms (2.6%)

bsearch107.0ms (1.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample4.8s (51.6%)

Profiling