Details

analyze2.0s (7.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4785	128
1	4785	128
0	3	3
1	3	3

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)

sample102.0ms (0.4%)

Algorithm

1×

intervals

Results

44.0ms	75×	body	1024	valid
16.0ms	43×	body	512	valid
15.0ms	117×	body	128	valid
5.0ms	21×	body	256	valid
2.0ms	19×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify136.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune11.0ms (0%)

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

12.8b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
5.1b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite311.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

10.7b

Rules

44×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64` `*-un-lft-identity_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×	`prod-exp_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `associate-/r_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_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)
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3318 to 1540 computations (53.6% saved)

series1.6s (5.9%)

Error

0.2b

Counts

4 → 51

Calls

4 calls:

629.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
352.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
318.0ms	(/.f64 x (tan.f64 B))
153.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4114 to 3060 computations (25.6% saved)

simplify103.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4923	3898
1	4923	3898

prune347.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	154	12	166
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	12	168

Error

0.0b

Counts

168 → 12

Compiler

Compiled 4336 to 2201 computations (49.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
17.5b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite416.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 138

Calls

4 calls:

16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
10.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
7.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 4498 to 2383 computations (47% saved)

series2.0s (7.5%)

Error

0.0b

Counts

4 → 61

Calls

4 calls:

614.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
570.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
335.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
308.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 5383 to 4024 computations (25.2% saved)

simplify105.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4964	6120
1	4964	6120

prune504.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	191	8	199
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	199	12	211

Error

0.0b

Counts

211 → 12

Compiler

Compiled 5859 to 3226 computations (44.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
0.4b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
17.5b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite578.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

120×	`times-frac_binary64`
89×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
31×	`add-exp-log_binary64`
25×	`unpow-prod-down_binary64` `associate-r_binary64`
16×	`add-cbrt-cube_binary64` `associate-/r*_binary64`
13×	`div-exp_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
8×	`pow1_binary64`
7×	`div-inv_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `associate-l_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-unprod_binary64`
1×	`pow-pow_binary64` `inv-pow_binary64` `pow-flip_binary64` `associate-/r/_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64`

Counts

4 → 186

Calls

4 calls:

16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
10.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
6.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
6.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))

Compiler

Compiled 6388 to 3494 computations (45.3% saved)

series2.0s (7.5%)

Error

0.0b

Counts

4 → 61

Calls

4 calls:

610.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
587.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
323.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
304.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))

Compiler

Compiled 5611 to 4252 computations (24.2% saved)

simplify116.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4954	7039
1	4954	7039

prune572.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	247	12	259

Error

0.0b

Counts

259 → 12

Compiler

Compiled 6927 to 3909 computations (43.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
17.5b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite440.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

60×	`add-sqr-sqrt_binary64`
55×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
28×	`associate-r_binary64`
25×	`unpow-prod-down_binary64` `add-exp-log_binary64`
16×	`add-cbrt-cube_binary64` `associate-l_binary64`
9×	`pow1_binary64` `sqr-pow_binary64`
7×	`div-exp_binary64` `associate-/l*_binary64`
6×	`prod-exp_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-/r*_binary64`
2×	`pow-prod-down_binary64` `*-commutative_binary64`
1×	`pow-pow_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-r/_binary64` `associate-l/_binary64`

Counts

4 → 142

Calls

4 calls:

15.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
10.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
7.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

Compiler

Compiled 5033 to 2434 computations (51.6% saved)

series1.9s (7.1%)

Error

0.0b

Counts

4 → 61

Calls

4 calls:

610.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
555.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
314.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
230.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

Compiler

Compiled 5725 to 4099 computations (28.4% saved)

simplify87.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5111	6236

prune472.0ms (1.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	203	12	215

Error

0.0b

Counts

215 → 12

Compiler

Compiled 6193 to 3084 computations (50.2% saved)

regimes9.3s (35.1%)

Accuracy

Total 0.2b remaining (80.1%)

Threshold costs 0.2b (80.1%)

Compiler

Compiled 72404 to 55837 computations (22.9% saved)

bsearch156.0ms (0.6%)

Steps

Iters	Range		Point
8	6452015.598640546	17838438981.706886	279504563.64143807
4	-2.5818420275574264e+65	-2.790998873094731e+60	-2.3506583458343944e+61

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	130
1	91	130

end4.0ms (0%)

Compiler: Compiled 84 to 41 computations (51.2% saved)

sample3.2s (12%)

Algorithm

1×

intervals

Results

1.3s	2249×	body	1024	valid
515.0ms	4084×	body	128	valid
414.0ms	1080×	body	512	valid
151.0ms	585×	body	256	valid
91.0ms	663×	body	128	invalid
13.0ms	136×	body	128	nan
2.0ms	2×	body	2048	valid

Compiler

Compiled 368 to 274 computations (25.5% saved)

Details

analyze2.0s (7.6%)

sample102.0ms (0.4%)

simplify136.0ms (0.5%)

prune11.0ms (0%)

localize28.0ms (0.1%)

rewrite311.0ms (1.2%)

series1.6s (5.9%)

simplify103.0ms (0.4%)

prune347.0ms (1.3%)

localize19.0ms (0.1%)

rewrite416.0ms (1.6%)

series2.0s (7.5%)

simplify105.0ms (0.4%)

prune504.0ms (1.9%)

localize23.0ms (0.1%)

rewrite578.0ms (2.2%)

series2.0s (7.5%)

simplify116.0ms (0.4%)

prune572.0ms (2.2%)

localize19.0ms (0.1%)

rewrite440.0ms (1.7%)

series1.9s (7.1%)

simplify87.0ms (0.3%)

prune472.0ms (1.8%)

regimes9.3s (35.1%)

bsearch156.0ms (0.6%)

simplify4.0ms (0%)

end4.0ms (0%)

sample3.2s (12%)

Profiling