Details

analyze2.0s (18.3%)

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)

sample119.0ms (1.1%)

Algorithm

1×

intervals

Results

52.0ms	69×	body	1024	valid
20.0ms	132×	body	128	valid
19.0ms	39×	body	512	valid
7.0ms	17×	body	128	invalid
5.0ms	16×	body	256	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify284.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5147	32

prune15.0ms (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: 14.2b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
7.6b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
15.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite47.0ms (0.4%)

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:

16.0ms	(.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)
4.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 F (sin.f64 B))

series757.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
216.0ms	(/.f64 x (tan.f64 B))
142.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
101.0ms	(/.f64 F (sin.f64 B))

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4913	2519
1	4913	2519

prune212.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	13	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 0.0b

Counts

129 → 13

Compiler

Compiled 3863 to 1871 computations (51.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
15.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite46.0ms (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 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

series702.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
213.0ms	(/.f64 x (tan.f64 B))
115.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
110.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5034	2141

prune147.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

Compiler

Compiled 3145 to 1696 computations (46.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 F)
0.6b	(cbrt.f64 F)
2.5b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
15.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64`
18×	`add-exp-log_binary64` `cbrt-prod_binary64`
9×	`unswap-sqr_binary64` `unpow-prod-down_binary64`
8×	`add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`prod-exp_binary64`
5×	`pow1_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `div-exp_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `pow1/3_binary64`
1×	`cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

19.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)

series840.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

409.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
161.0ms	(cbrt.f64 F)
154.0ms	(cbrt.f64 F)
117.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4910	2549
1	4910	2549

prune167.0ms (1.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	106	13	119

Merged error: 0.0b

Counts

119 → 13

Compiler

Compiled 4264 to 1980 computations (53.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/4))
7.6b	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)))
15.6b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
15.6b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)

rewrite84.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
38×	`add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`pow-to-exp_binary64` `associate-l_binary64` `pow-exp_binary64`
18×	`add-cbrt-cube_binary64`
12×	`sqr-pow_binary64`
11×	`unswap-sqr_binary64`
10×	`times-frac_binary64` `div-exp_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`swap-sqr_binary64` `cbrt-unprod_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `div-inv_binary64` `pow-sqr_binary64` `pow2_binary64` `associate-*l/_binary64`

Counts

4 → 136

Calls

4 calls:

24.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)))
22.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/4))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)

series617.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

293.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)))
124.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
114.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
87.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/4))

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4915	3861
1	4915	3861

prune227.0ms (2.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	148	13	161

Merged error: 0.0b

Counts

161 → 13

Compiler

Compiled 4927 to 2614 computations (46.9% saved)

regimes121.0ms (1.1%)

Compiler: Compiled 993 to 759 computations (23.6% saved)

bsearch165.0ms (1.5%)

Steps

Iters	Range		Point
8	4895.368997526373	17268017.62964059	32635.094192521872
10	-4.7876580543533186e+33	-24781199299476136.0	-9.252926220588232e+24

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	90
1	67	90

end0.0ms (0%)

sample3.7s (34.6%)

Algorithm

1×

intervals

Results

1.6s	2242×	body	1024	valid
605.0ms	4125×	body	128	valid
521.0ms	1088×	body	512	valid
164.0ms	540×	body	256	valid
95.0ms	648×	body	128	invalid
10.0ms	102×	body	128	nan
7.0ms	5×	body	2048	valid

Compiler

Compiled 416 to 309 computations (25.7% saved)

Details

analyze2.0s (18.3%)

sample119.0ms (1.1%)

simplify284.0ms (2.7%)

prune15.0ms (0.1%)

localize22.0ms (0.2%)

rewrite47.0ms (0.4%)

series757.0ms (7.1%)

simplify95.0ms (0.9%)

prune212.0ms (2%)

localize22.0ms (0.2%)

rewrite46.0ms (0.4%)

series702.0ms (6.6%)

simplify59.0ms (0.6%)

prune147.0ms (1.4%)

localize25.0ms (0.2%)

rewrite42.0ms (0.4%)

series840.0ms (7.9%)

simplify91.0ms (0.9%)

prune167.0ms (1.6%)

localize21.0ms (0.2%)

rewrite84.0ms (0.8%)

series617.0ms (5.8%)

simplify92.0ms (0.9%)

prune227.0ms (2.1%)

regimes121.0ms (1.1%)

bsearch165.0ms (1.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.7s (34.6%)

Profiling