Details

analyze2.4s (12.9%)

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)

sample118.0ms (0.6%)

Algorithm

1×

intervals

Results

44.0ms	64×	body	1024	valid
21.0ms	39×	body	512	valid
20.0ms	131×	body	128	valid
8.0ms	22×	body	256	valid
4.0ms	30×	body	128	invalid
0.0ms	3×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify170.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (159.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune9.0ms (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

10.5b

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 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
4.6b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite262.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

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))
9.0ms	(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 3459 to 1606 computations (53.6% saved)

series1.2s (6.4%)

Error

0.1b

Counts

4 → 51

Calls

4 calls:

480.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
263.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
253.0ms	(/.f64 x (tan.f64 B))
139.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4288 to 3116 computations (27.3% saved)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5183	3735

prune311.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	156	10	166
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	10	168

Error

0.0b

Counts

168 → 10

Compiler

Compiled 4946 to 2447 computations (50.5% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
14.4b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite221.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`unpow-prod-down_binary64` `associate-r_binary64`
6×	`prod-exp_binary64` `associate-/r*_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `sqr-pow_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `associate-l_binary64`
2×	`cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `*-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 93

Calls

4 calls:

10.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
10.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
9.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 2798 to 1468 computations (47.5% saved)

series1.4s (7.2%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

478.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
321.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
240.0ms	(/.f64 x (tan.f64 B))
215.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))

Compiler

Compiled 4721 to 3530 computations (25.2% saved)

simplify110.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4936	3592
1	4936	3592

prune234.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	148	10	158

Error

0.0b

Counts

158 → 10

Compiler

Compiled 4393 to 2396 computations (45.5% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
0.3b	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
14.4b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite318.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 141

Calls

4 calls:

10.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
10.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
9.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
7.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))

Compiler

Compiled 4637 to 2517 computations (45.7% saved)

series1.3s (6.8%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

469.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
251.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
241.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
235.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))

Compiler

Compiled 4939 to 3748 computations (24.1% saved)

simplify127.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4919	4463
1	4919	4463

prune335.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	196	10	206

Error

0.0b

Counts

206 → 10

Compiler

Compiled 6063 to 3290 computations (45.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
4.6b	(.f64 (/.f64 F (sin.f64 B)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))))))
14.1b	(sqrt.f64 (/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))))

rewrite312.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

68×	`add-sqr-sqrt_binary64`
55×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`
18×	`associate-r_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
9×	`pow1_binary64`
8×	`unswap-sqr_binary64`
6×	`associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64`
3×	`sqrt-pow1_binary64` `sqrt-div_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `cbrt-undiv_binary64`
2×	`inv-pow_binary64` `pow-flip_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow1/2_binary64` `pow-prod-down_binary64` `frac-times_binary64` `associate-l/_binary64` `associate-r/_binary64` `*-commutative_binary64` `1-exp_binary64` `rec-exp_binary64`

Counts

4 → 145

Calls

4 calls:

19.0ms	(.f64 (/.f64 F (sin.f64 B)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))))))
7.0ms	(sqrt.f64 (/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))))
7.0ms	(/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
5.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4884 to 2547 computations (47.9% saved)

series1.0s (5.3%)

Error

0.0b

Counts

4 → 57

Calls

4 calls:

464.0ms	(.f64 (/.f64 F (sin.f64 B)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))))))
163.0ms	(sqrt.f64 (/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))))
156.0ms	(/.f64 1 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
118.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4652 to 3427 computations (26.3% saved)

simplify173.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4931	5410
1	4931	5410

prune321.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	202	10	212

Error

0.0b

Counts

212 → 10

Compiler

Compiled 6311 to 3282 computations (48% saved)

regimes1.4s (7.5%)

Accuracy

Total 0.2b remaining (89.7%)

Threshold costs 0.2b (89.7%)

Compiler

Compiled 11740 to 8980 computations (23.5% saved)

bsearch139.0ms (0.7%)

Steps

Iters	Range		Point
8	46318825.02109967	497725499837.33624	94181933.04629011
7	-7.570107378107944e+84	-4.1945670733272555e+83	-7.377918106249466e+84

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	72
1	54	72

end0.0ms (0%)

sample6.9s (36.3%)

Algorithm

1×

intervals

Results

1.5s	2135×	body	1024	valid
710.0ms	4153×	body	128	valid
566.0ms	1142×	body	512	valid
187.0ms	564×	body	256	valid
112.0ms	700×	body	128	invalid
16.0ms	131×	body	128	nan
7.0ms	6×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 2995 to 2285 computations (23.7% saved)

Details

analyze2.4s (12.9%)

sample118.0ms (0.6%)

simplify170.0ms (0.9%)

prune9.0ms (0%)

localize18.0ms (0.1%)

rewrite262.0ms (1.4%)

series1.2s (6.4%)

simplify74.0ms (0.4%)

prune311.0ms (1.6%)

localize37.0ms (0.2%)

rewrite221.0ms (1.2%)

series1.4s (7.2%)

simplify110.0ms (0.6%)

prune234.0ms (1.2%)

localize31.0ms (0.2%)

rewrite318.0ms (1.7%)

series1.3s (6.8%)

simplify127.0ms (0.7%)

prune335.0ms (1.8%)

localize16.0ms (0.1%)

rewrite312.0ms (1.6%)

series1.0s (5.3%)

simplify173.0ms (0.9%)

prune321.0ms (1.7%)

regimes1.4s (7.5%)

bsearch139.0ms (0.7%)

simplify8.0ms (0%)

end0.0ms (0%)

sample6.9s (36.3%)

Profiling