Details

analyze1.6s (9.1%)

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)

sample103.0ms (0.6%)

Algorithm

1×

intervals

Results

48.0ms	83×	body	1024	valid
16.0ms	38×	body	512	valid
15.0ms	117×	body	128	valid
5.0ms	18×	body	256	valid
2.0ms	14×	body	128	invalid
0.0ms	3×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify242.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune11.0ms (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

12.3b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

7.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
0.2b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
0.0b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 F (sin.f64 B))
7.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.6b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite52.0ms (0.3%)

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

8 calls:

16.0ms	(.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))
0.0ms	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2)) (/.f64 x (tan.f64 B)))

series973.0ms (5.7%)

Counts

4 → 52

Calls

4 calls:

420.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
252.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
201.0ms	(/.f64 x (tan.f64 B))
100.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 2763 to 2207 computations (20.1% saved)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4936	4015
1	4936	4015

prune353.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	11	167
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	11	169

Error

0.0b

Counts

169 → 11

Compiler

Compiled 5164 to 2523 computations (51.1% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.2b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
0.0b	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
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))
17.6b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite43.0ms (0.3%)

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

8 calls:

12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
11.0ms	(/.f64 (.f64 F (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)
3.0ms	(/.f64 x (tan.f64 B))
0.0ms	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))

series1.0s (6%)

Counts

4 → 57

Calls

4 calls:

405.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
231.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
194.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
191.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 3077 to 2482 computations (19.3% saved)

simplify102.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4935	4086
1	4935	4086

prune230.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	150	11	161

Error

0.0b

Counts

161 → 11

Compiler

Compiled 4734 to 2515 computations (46.9% saved)

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
0.3b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.1b	(/.f64 x (tan.f64 B))
0.0b	(-.f64 (.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
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))
17.6b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite54.0ms (0.3%)

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

8 calls:

16.0ms	(.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))
0.0ms	(-.f64 (.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))

series1.2s (7.1%)

Counts

4 → 63

Calls

4 calls:

404.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
380.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
231.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
197.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 3535 to 2803 computations (20.7% saved)

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4935	6286
1	4935	6286

prune338.0ms (2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	202	10	212

Error

0.0b

Counts

212 → 10

Compiler

Compiled 6794 to 3584 computations (47.2% saved)

localize25.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(/.f64 (.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)) (sin.f64 B))
0.3b	(.f64 F (/.f64 (.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)) (sin.f64 B)))
0.1b	(/.f64 x (tan.f64 B))
0.0b	(-.f64 (.f64 F (/.f64 (.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)) (sin.f64 B))) (/.f64 x (tan.f64 B)))
0.4b	(/.f64 (.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)) (sin.f64 B))
0.6b	(.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))
18.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
18.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)

rewrite72.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-exp-log_binary64`
30×	`add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
14×	`pow-to-exp_binary64` `pow-exp_binary64`
12×	`sqr-pow_binary64`
11×	`add-cbrt-cube_binary64`
10×	`div-exp_binary64`
9×	`unswap-sqr_binary64`
7×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
6×	`pow-unpow_binary64` `pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-pow_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `pow-sqr_binary64` `pow2_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

8 calls:

21.0ms	(.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))
20.0ms	(/.f64 (.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)) (sin.f64 B))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
0.0ms	(-.f64 (.f64 F (/.f64 (.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)) (sin.f64 B))) (/.f64 x (tan.f64 B)))

series1.0s (5.9%)

Counts

4 → 64

Calls

4 calls:

376.0ms	(/.f64 (.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)) (sin.f64 B))
242.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
240.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
150.0ms	(.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))

Compiler

Compiled 4158 to 3404 computations (18.1% saved)

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4946	5957
1	4946	5957

prune349.0ms (2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	179	10	189

Error

0.0b

Counts

189 → 10

Compiler

Compiled 6903 to 4061 computations (41.2% saved)

simplify38.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	727	2686
1	727	2686

regimes494.0ms (2.9%)

Accuracy

Total 0.2b remaining (89.1%)

Threshold costs 0.2b (89.1%)

Compiler

Compiled 5139 to 3939 computations (23.4% saved)

bsearch170.0ms (1%)

Steps

Iters	Range		Point
9	5979.98041323502	17249463807528.086	97778852.442119
11	-3.35751375917937e+47	-3.580538644051995e+17	-2.957723683841436e+47

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	55	75
1	55	75

end0.0ms (0%)

sample8.3s (48.5%)

Algorithm

1×

intervals

Results

1.3s	2236×	body	1024	valid
520.0ms	4090×	body	128	valid
413.0ms	1098×	body	512	valid
142.0ms	567×	body	256	valid
78.0ms	626×	body	128	invalid
11.0ms	113×	body	128	nan
9.0ms	9×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 5259 to 4010 computations (23.7% saved)

Pareto

0.07083104719448642

Details

analyze1.6s (9.1%)

sample103.0ms (0.6%)

simplify242.0ms (1.4%)

prune11.0ms (0.1%)

localize20.0ms (0.1%)

rewrite52.0ms (0.3%)

series973.0ms (5.7%)

simplify89.0ms (0.5%)

prune353.0ms (2.1%)

localize20.0ms (0.1%)

rewrite43.0ms (0.3%)

series1.0s (6%)

simplify102.0ms (0.6%)

prune230.0ms (1.3%)

localize21.0ms (0.1%)

rewrite54.0ms (0.3%)

series1.2s (7.1%)

simplify106.0ms (0.6%)

prune338.0ms (2%)

localize25.0ms (0.1%)

rewrite72.0ms (0.4%)

series1.0s (5.9%)

simplify104.0ms (0.6%)

prune349.0ms (2%)

simplify38.0ms (0.2%)

regimes494.0ms (2.9%)

bsearch170.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.3s (48.5%)

Profiling