Details

analyze1.8s (13.4%)

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)

sample99.0ms (0.7%)

Algorithm

1×

intervals

Results

39.0ms	65×	body	1024	valid
17.0ms	129×	body	128	valid
15.0ms	38×	body	512	valid
11.0ms	23×	body	256	valid
2.0ms	16×	body	128	invalid
1.0ms	1×	body	2048	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify225.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune8.0ms (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: 14.9b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.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))
17.8b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite50.0ms (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:

17.0ms	(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))
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

series823.0ms (6.2%)

Counts

4 → 38

Calls

4 calls:

334.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
241.0ms	(/.f64 x (tan.f64 B))
124.0ms	(/.f64 F (sin.f64 B))
124.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

Compiler

Compiled 1865 to 1490 computations (20.1% saved)

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4928	3190
1	4928	3190

prune245.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	141	12	153
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	143	12	155

Merged error: 0.0b

Counts

155 → 12

Compiler

Compiled 4502 to 2170 computations (51.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
17.8b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite55.0ms (0.4%)

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:

19.0ms	(.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))

series960.0ms (7.2%)

Counts

4 → 46

Calls

4 calls:

320.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
306.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
225.0ms	(/.f64 x (tan.f64 B))
109.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

Compiler

Compiled 2355 to 1872 computations (20.5% saved)

simplify114.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4925	4925
1	4925	4925

prune270.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	184	12	196

Merged error: 0.0b

Counts

196 → 12

Compiler

Compiled 5822 to 3044 computations (47.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
1.0b	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))
9.7b	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
13.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`unpow-prod-down_binary64`
49×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
33×	`times-frac_binary64`
19×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
12×	`pow1_binary64`
11×	`sqr-pow_binary64` `associate-/l*_binary64`
9×	`pow-exp_binary64`
7×	`pow-unpow_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-to-exp_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 144

Calls

4 calls:

13.0ms	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))
10.0ms	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
6.0ms	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))

series1.6s (12%)

Counts

4 → 35

Calls

4 calls:

796.0ms	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
447.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))
348.0ms	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
0.0ms	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))

Compiler

Compiled 3858 to 3419 computations (11.4% saved)

simplify108.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4944	6641
1	4944	6641

prune422.0ms (3.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	179	12	191

Merged error: 0.0b

Counts

191 → 12

Compiler

Compiled 7275 to 4682 computations (35.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 B) F)
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))
17.8b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

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` `1-exp_binary64` `rec-exp_binary64` `pow-exp_binary64`
7×	`associate-r_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64`
2×	`associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `inv-pow_binary64` `pow-flip_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 219

Calls

4 calls:

23.0ms	(.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 (sin.f64 B) F)

series639.0ms (4.8%)

Counts

4 → 38

Calls

4 calls:

313.0ms	(.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
114.0ms	(/.f64 1 (/.f64 (sin.f64 B) F))
111.0ms	(/.f64 (sin.f64 B) F)
101.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

Compiler

Compiled 1885 to 1526 computations (19% saved)

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4964	5822
1	4964	5822

prune370.0ms (2.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	257	12	269

Merged error: 0.0b

Counts

269 → 12

Compiler

Compiled 7643 to 3581 computations (53.1% saved)

regimes690.0ms (5.2%)

Compiler: Compiled 6788 to 5184 computations (23.6% saved)

bsearch126.0ms (1%)

Steps

Iters	Range		Point
9	1971434.671424879	427188936776.0129	130076007.40603846
6	-6.009052523144518e+23	-1.2732757422337183e+23	-4.214528339352862e+23

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	54	72
1	54	72

end0.0ms (0%)

sample4.3s (32.5%)

Algorithm

1×

intervals

Results

1.3s	2275×	body	1024	valid
519.0ms	3980×	body	128	valid
447.0ms	1163×	body	512	valid
148.0ms	577×	body	256	valid
87.0ms	641×	body	128	invalid
14.0ms	137×	body	128	nan
5.0ms	5×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 1757 to 1336 computations (24% saved)

Details

analyze1.8s (13.4%)

sample99.0ms (0.7%)

simplify225.0ms (1.7%)

prune8.0ms (0.1%)

localize18.0ms (0.1%)

rewrite50.0ms (0.4%)

series823.0ms (6.2%)

simplify80.0ms (0.6%)

prune245.0ms (1.8%)

localize17.0ms (0.1%)

rewrite55.0ms (0.4%)

series960.0ms (7.2%)

simplify114.0ms (0.9%)

prune270.0ms (2%)

localize22.0ms (0.2%)

rewrite57.0ms (0.4%)

series1.6s (12%)

simplify108.0ms (0.8%)

prune422.0ms (3.2%)

localize20.0ms (0.2%)

rewrite66.0ms (0.5%)

series639.0ms (4.8%)

simplify110.0ms (0.8%)

prune370.0ms (2.8%)

regimes690.0ms (5.2%)

bsearch126.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.3s (32.5%)

Profiling