Details

analyze1.9s (17.7%)

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)

sample118.0ms (1.1%)

Algorithm

1×

intervals

Results

57.0ms	69×	body	1024	valid
21.0ms	140×	body	128	valid
19.0ms	38×	body	512	valid
4.0ms	9×	body	256	valid
3.0ms	23×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify285.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (113.0ms)

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: 14.8b

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 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
9.5b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite46.0ms (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:

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))

series757.0ms (7%)

Counts

4 → 12

Calls

4 calls:

292.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
220.0ms	(/.f64 x (tan.f64 B))
145.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
99.0ms	(/.f64 F (sin.f64 B))

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4913	2519
1	4913	2519

prune204.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 0.0b

Counts

129 → 10

Compiler

Compiled 3776 to 1806 computations (52.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.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))
18.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite48.0ms (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:

14.0ms	(/.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))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

series695.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
206.0ms	(/.f64 x (tan.f64 B))
114.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
112.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5034	2141

prune137.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 0.0b

Counts

115 → 10

Compiler

Compiled 3048 to 1627 computations (46.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
0.4b	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
18.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite68.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

189×	`times-frac_binary64`
112×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
51×	`unpow-prod-down_binary64`
35×	`associate-/r*_binary64`
22×	`add-exp-log_binary64`
17×	`sqr-pow_binary64`
13×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
5×	`pow1_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`
2×	`associate-/r/_binary64`
1×	`pow-pow_binary64` `tan-quot_binary64`

Counts

4 → 210

Calls

4 calls:

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

series792.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

287.0ms	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
207.0ms	(/.f64 x (tan.f64 B))
189.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
109.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify120.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4962	7920
1	4962	7920

prune382.0ms (3.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	221	11	232

Merged error: 0.0b

Counts

232 → 11

Compiler

Compiled 7840 to 3986 computations (49.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 B))
0.7b	(cbrt.f64 (sin.f64 B))
3.7b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 F (cbrt.f64 (sin.f64 B))))
18.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite43.0ms (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:

18.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 F (cbrt.f64 (sin.f64 B))))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
2.0ms	(cbrt.f64 (sin.f64 B))
2.0ms	(cbrt.f64 (sin.f64 B))

series776.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

416.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 F (cbrt.f64 (sin.f64 B))))
131.0ms	(cbrt.f64 (sin.f64 B))
119.0ms	(cbrt.f64 (sin.f64 B))
110.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4936	2604
1	4936	2604

prune163.0ms (1.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	105	12	117

Merged error: 0.0b

Counts

117 → 12

Compiler

Compiled 4205 to 1771 computations (57.9% saved)

regimes106.0ms (1%)

Compiler: Compiled 855 to 663 computations (22.5% saved)

bsearch152.0ms (1.4%)

Steps

Iters	Range		Point
8	2014.5860550080608	4307813.888336371	57055.06105628091
9	-17861.081965927067	-0.0035721181480970177	-17504.90229493893

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	70	95
1	70	95

end0.0ms (0%)

sample3.6s (33.6%)

Algorithm

1×

intervals

Results

1.6s	2223×	body	1024	valid
602.0ms	4108×	body	128	valid
514.0ms	1091×	body	512	valid
170.0ms	572×	body	256	valid
93.0ms	645×	body	128	invalid
11.0ms	112×	body	128	nan
9.0ms	6×	body	2048	valid
1.0ms	1×	body	1024	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 373 to 278 computations (25.5% saved)

Details

analyze1.9s (17.7%)

sample118.0ms (1.1%)

simplify285.0ms (2.6%)

prune15.0ms (0.1%)

localize22.0ms (0.2%)

rewrite46.0ms (0.4%)

series757.0ms (7%)

simplify94.0ms (0.9%)

prune204.0ms (1.9%)

localize20.0ms (0.2%)

rewrite48.0ms (0.4%)

series695.0ms (6.5%)

simplify60.0ms (0.6%)

prune137.0ms (1.3%)

localize20.0ms (0.2%)

rewrite68.0ms (0.6%)

series792.0ms (7.4%)

simplify120.0ms (1.1%)

prune382.0ms (3.6%)

localize25.0ms (0.2%)

rewrite43.0ms (0.4%)

series776.0ms (7.2%)

simplify91.0ms (0.8%)

prune163.0ms (1.5%)

regimes106.0ms (1%)

bsearch152.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.6s (33.6%)

Profiling