Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

sample36.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5022	33

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 0.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (pow.f64 (fabs.f64 x) 5) 5.0)
0.1b	(.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (*.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))))
0.1b	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
1.0b	(sqrt.f64 PI.f64)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

77×	`times-frac_binary64`
69×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
32×	`associate-*r/_binary64`
24×	`unpow-prod-down_binary64`
22×	`associate-l_binary64`
19×	`add-exp-log_binary64` `associate-/l*_binary64`
16×	`frac-add_binary64`
13×	`add-cbrt-cube_binary64` `sqrt-prod_binary64`
12×	`flip3-+_binary64` `cube-prod_binary64` `flip-+_binary64`
8×	`sqr-pow_binary64` `frac-times_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 183

Calls

4 calls:

8.0ms	(/.f64 (pow.f64 (fabs.f64 x) 5) 5.0)
26.0ms	(.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (*.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))))
6.0ms	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
2.0ms	(sqrt.f64 PI.f64)

series115.0ms

Counts

4 → 10

Calls

4 calls:

15.0ms	(/.f64 (pow.f64 (fabs.f64 x) 5) 5.0)
89.0ms	(.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (*.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))))
11.0ms	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
0.0ms	(sqrt.f64 PI.f64)

simplify73.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4975	4274
1	4975	4274

prune359.0ms

Filtered

133 candidates to 193 candidates (-45.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	191	3	194

Merged error: 0b

Counts

194 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
0.3b	(.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (*.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0))))))
0.3b	(.f64 (.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))))) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0))))))
1.0b	(sqrt.f64 PI.f64)

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

544×	`associate-*r/_binary64`
304×	`frac-add_binary64` `sqrt-div_binary64`
228×	`flip3-+_binary64` `flip-+_binary64`
216×	`frac-times_binary64`
64×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
27×	`associate-*l/_binary64`
23×	`add-exp-log_binary64` `associate-l_binary64` `sqrt-prod_binary64`
20×	`add-cbrt-cube_binary64`
12×	`pow1_binary64` `associate-r_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-/l*_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`unswap-sqr_binary64`
5×	`div-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`associate-/r*_binary64` `cbrt-undiv_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`

Counts

4 → 326

Calls

4 calls:

6.0ms	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
27.0ms	(.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (*.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0))))))
50.0ms	(.f64 (.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))))) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0))))))
2.0ms	(sqrt.f64 PI.f64)

series218.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
114.0ms	(.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (*.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0))))))
93.0ms	(.f64 (.f64 (/.f64 1.0 (sqrt.f64 PI.f64)) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))))) (sqrt.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0))))))
0.0ms	(sqrt.f64 PI.f64)

simplify211.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5015	32569

prune8.8s

Filtered

271 candidates to 336 candidates (-24.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	336	3	339

Merged error: 0b

Counts

339 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (pow.f64 (fabs.f64 x) 5) 5.0)
0.1b	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
0.3b	(/.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`
22×	`associate-/l*_binary64`
16×	`add-exp-log_binary64`
15×	`sqrt-prod_binary64`
12×	`associate-/r_binary64` `associate-r/_binary64` `cube-prod_binary64`
10×	`add-cbrt-cube_binary64`
8×	`associate-/l/_binary64` `frac-add_binary64` `sqr-pow_binary64`
7×	`div-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 170

Calls

4 calls:

5.0ms	(/.f64 (pow.f64 (fabs.f64 x) 5) 5.0)
6.0ms	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
24.0ms	(/.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))) (sqrt.f64 PI.f64))
2.0ms	(sqrt.f64 PI.f64)

series101.0ms

Counts

4 → 10

Calls

4 calls:

15.0ms	(/.f64 (pow.f64 (fabs.f64 x) 5) 5.0)
11.0ms	(/.f64 (pow.f64 (fabs.f64 x) 3) 3.0)
75.0ms	(/.f64 (+.f64 (.f64 2.0 (+.f64 (fabs.f64 x) (/.f64 (pow.f64 (fabs.f64 x) 3) 3.0))) (.f64 1.0 (+.f64 (/.f64 (pow.f64 (fabs.f64 x) 5) 5.0) (/.f64 (pow.f64 (fabs.f64 x) 7) 21.0)))) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)

simplify51.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5607	3447

prune276.0ms

Filtered

119 candidates to 180 candidates (-51.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	180	3	183

Merged error: 0b

Counts

183 → 3

regimes63.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	33
1	32	33

end0.0ms

sample913.0ms

Algorithm

intervals

Results

722.0ms	8000×	body	80	valid
85.0ms	8000×	pre	80	true

Details

analyze5.0ms

sample36.0ms

simplify56.0ms

prune7.0ms

localize19.0ms

rewrite50.0ms

series115.0ms

simplify73.0ms

prune359.0ms

localize22.0ms

rewrite128.0ms

series218.0ms

simplify211.0ms

prune8.8s

localize20.0ms

rewrite44.0ms

series101.0ms

simplify51.0ms

prune276.0ms

regimes63.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample913.0ms

Profiling