Details

analyze184.0ms (7.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4920	34
1	4920	34
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample21.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	3×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify75.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune4.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

15.3b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
30.8b	(/.f64 (.f64 b b) (.f64 a a))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549`
4×	`prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `div-exp_binary64_4562` `add-sqr-sqrt_binary64_4533` `cbrt-undiv_binary64_4545`
3×	`pow1_binary64_4572` `*-un-lft-identity_binary64_4511` `sqrt-prod_binary64_4527` `add-cube-cbrt_binary64_4546`
2×	`add-log-exp_binary64_4550`
1×	`associate-/l_binary64_4456` `frac-2neg_binary64_4522` `rem-sqrt-square_binary64_4524` `associate-/r_binary64_4455` `pow1/2_binary64_4591` `sqrt-pow1_binary64_4529` `clear-num_binary64_4510` `times-frac_binary64_4517` `div-inv_binary64_4508`

Counts

2 → 34

Calls

2 calls:

7.0ms	(/.f64 (.f64 b b) (.f64 a a))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

series52.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
20.0ms	(/.f64 (.f64 b b) (.f64 a a))

simplify88.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4903	452
1	4903	452

prune37.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Error

Counts

41 → 3

Compiler

Compiled 548 to 362 computations (33.9% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))
0.4b	(pow.f64 (/.f64 b a) 2)
6.4b	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64_4590`
22×	`add-sqr-sqrt_binary64_4533`
21×	`*-un-lft-identity_binary64_4511` `add-cube-cbrt_binary64_4546`
19×	`log-pow_binary64_4600`
18×	`exp-prod_binary64_4563` `times-frac_binary64_4517`
6×	`pow1_binary64_4572` `add-exp-log_binary64_4549`
3×	`add-cbrt-cube_binary64_4547` `add-log-exp_binary64_4550` `log-prod_binary64_4597` `pow-unpow_binary64_4588` `sqrt-prod_binary64_4527`
2×	`unpow2_binary64_4576` `pow-exp_binary64_4579` `sqr-pow_binary64_4483` `div-inv_binary64_4508`
1×	`div-exp_binary64_4562` `pow-to-exp_binary64_4580` `rem-log-exp_binary64_4552` `rem-sqrt-square_binary64_4524` `pow1/2_binary64_4591` `sqrt-pow1_binary64_4529` `pow-pow_binary64_4583`

Counts

3 → 72

Calls

3 calls:

7.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
5.0ms	(pow.f64 (/.f64 b a) 2)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

series75.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

32.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
28.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))
14.0ms	(pow.f64 (/.f64 b a) 2)

simplify61.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5039	858

prune76.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

Counts

84 → 3

Compiler

Compiled 1206 to 806 computations (33.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 1 (pow.f64 (/.f64 a b) 2)))))
0.4b	(pow.f64 (/.f64 a b) 2)
0.6b	(/.f64 1 (pow.f64 (/.f64 a b) 2))

rewrite28.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`times-frac_binary64_4517`
65×	`unpow-prod-down_binary64_4590`
64×	`add-sqr-sqrt_binary64_4533`
63×	`*-un-lft-identity_binary64_4511` `add-cube-cbrt_binary64_4546`
22×	`add-exp-log_binary64_4549`
18×	`associate-/r*_binary64_4455`
12×	`div-exp_binary64_4562`
8×	`pow-exp_binary64_4579`
6×	`div-inv_binary64_4508`
5×	`pow1_binary64_4572` `unpow2_binary64_4576` `add-cbrt-cube_binary64_4547` `sqr-pow_binary64_4483`
4×	`1-exp_binary64_4555` `pow-to-exp_binary64_4580` `rec-exp_binary64_4561`
3×	`associate-/l*_binary64_4456` `add-log-exp_binary64_4550` `pow-unpow_binary64_4588` `sqrt-prod_binary64_4527`
1×	`inv-pow_binary64_4596` `frac-2neg_binary64_4522` `pow-flip_binary64_4585` `rem-sqrt-square_binary64_4524` `pow1/2_binary64_4591` `sqrt-pow1_binary64_4529` `clear-num_binary64_4510` `pow-pow_binary64_4583` `cbrt-undiv_binary64_4545`

Counts

3 → 142

Calls

3 calls:

9.0ms	(/.f64 1 (pow.f64 (/.f64 a b) 2))
5.0ms	(pow.f64 (/.f64 a b) 2)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 1 (pow.f64 (/.f64 a b) 2)))))

series65.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

28.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 1 (pow.f64 (/.f64 a b) 2)))))
22.0ms	(/.f64 1 (pow.f64 (/.f64 a b) 2))
15.0ms	(pow.f64 (/.f64 a b) 2)

simplify84.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5012	2188

prune139.0ms (5.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	151	3	154

Error

Counts

154 → 3

Compiler

Compiled 2445 to 1607 computations (34.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
0.0b	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
0.4b	(pow.f64 (/.f64 b a) 2)
0.4b	(pow.f64 (/.f64 b a) 2)

rewrite42.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`sqrt-prod_binary64_4527`
72×	`add-sqr-sqrt_binary64_4533`
33×	`*-un-lft-identity_binary64_4511` `sqrt-pow1_binary64_4529` `add-cube-cbrt_binary64_4546`
30×	`pow1_binary64_4572`
26×	`unpow-prod-down_binary64_4590`
18×	`times-frac_binary64_4517`
17×	`pow1/2_binary64_4591`
15×	`swap-sqr_binary64_4478`
12×	`add-exp-log_binary64_4549`
9×	`pow-prod-up_binary64_4581` `unswap-sqr_binary64_4479` `associate-l_binary64_4452` `associate-r_binary64_4451` `rem-sqrt-square_binary64_4524`
6×	`add-cbrt-cube_binary64_4547` `pow-unpow_binary64_4588`
5×	`pow-sqr_binary64_4484` `pow-prod-down_binary64_4582`
4×	`sqr-abs_binary64_4526` `pow-exp_binary64_4579` `add-log-exp_binary64_4550`
2×	`unpow2_binary64_4576` `sqr-pow_binary64_4483` `div-exp_binary64_4562` `pow-to-exp_binary64_4580` `pow-pow_binary64_4583` `div-inv_binary64_4508`
1×	`pow-plus_binary64_4574` `sqrt-unprod_binary64_4531` `pow2_binary64_4592` `prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `rem-square-sqrt_binary64_4523` `*-commutative_binary64_4442`

Counts

4 → 150

Calls

4 calls:

11.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
5.0ms	(pow.f64 (/.f64 b a) 2)
5.0ms	(pow.f64 (/.f64 b a) 2)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))

series85.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))))
25.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
14.0ms	(pow.f64 (/.f64 b a) 2)
14.0ms	(pow.f64 (/.f64 b a) 2)

simplify60.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5064	2353

prune198.0ms (8.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	162	3	165

Error

Counts

165 → 3

Compiler

Compiled 3491 to 2450 computations (29.8% saved)

regimes157.0ms (6.5%)

Accuracy

Total 0.0b remaining (85%)

Threshold costs 0.0b (85%)

Compiler

Compiled 1145 to 1014 computations (11.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	18
1	22	18

end0.0ms (0%)

sample812.0ms (33.7%)

Algorithm

1×

intervals

Results

272.0ms	8000×	body	128	valid
158.0ms	8000×	pre	128	true
3.0ms	138×	pre	128	false

Compiler

Compiled 152 to 139 computations (8.6% saved)

Details

analyze184.0ms (7.6%)

sample21.0ms (0.9%)

simplify75.0ms (3.1%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

rewrite10.0ms (0.4%)

series52.0ms (2.2%)

simplify88.0ms (3.6%)

prune37.0ms (1.6%)

localize11.0ms (0.4%)

rewrite19.0ms (0.8%)

series75.0ms (3.1%)

simplify61.0ms (2.5%)

prune76.0ms (3.1%)

localize8.0ms (0.3%)

rewrite28.0ms (1.2%)

series65.0ms (2.7%)

simplify84.0ms (3.5%)

prune139.0ms (5.8%)

localize10.0ms (0.4%)

rewrite42.0ms (1.7%)

series85.0ms (3.5%)

simplify60.0ms (2.5%)

prune198.0ms (8.2%)

regimes157.0ms (6.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample812.0ms (33.7%)

Profiling