Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

sample29.0ms

Algorithm

intervals

Results

8.0ms	217×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	9×	body	320	valid
1.0ms	24×	body	80	invalid
1.0ms	9×	body	160	valid

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4893	13
1	4893	13

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 14.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 z t) y)
3.3b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.6b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `associate-l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
4×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 69

Calls

3 calls:

12.0ms	(*.f64 (-.f64 z t) y)
11.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
10.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series60.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(*.f64 (-.f64 z t) y)
37.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
16.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4992	863
1	4992	863

prune116.0ms

Filtered

57 candidates to 78 candidates (-36.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 3.9b

Counts

79 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (-.f64 a t))
4.0b	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
7.7b	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
30×	`associate-r_binary64`
27×	`cbrt-prod_binary64`
25×	`add-exp-log_binary64`
23×	`add-cube-cbrt_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
9×	`add-log-exp_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a t))
3.0ms	(cbrt.f64 (-.f64 a t))
29.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
7.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (-.f64 a t))
24.0ms	(cbrt.f64 (-.f64 a t))
24.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t))))
41.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5704	2301

prune167.0ms

Filtered

111 candidates to 138 candidates (-24.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	135	11	146

Merged error: 3.9b

Counts

146 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 (-.f64 a t)))
0.6b	(cbrt.f64 (cbrt.f64 (-.f64 a t)))
4.0b	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))))) (/.f64 y (cbrt.f64 (-.f64 a t))))
7.9b	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

388×	`cbrt-div_binary64`
139×	`frac-times_binary64`
112×	`flip3--_binary64` `flip--_binary64`
89×	`associate-l_binary64`
82×	`associate-/r/_binary64`
53×	`associate-*r/_binary64`
49×	`add-exp-log_binary64`
47×	`associate-*l/_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`cbrt-prod_binary64`
37×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
30×	`associate-r_binary64` `add-cbrt-cube_binary64`
25×	`add-cube-cbrt_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64`
13×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`add-log-exp_binary64`
6×	`pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 209

Calls

4 calls:

4.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a t)))
4.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a t)))
85.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))))) (/.f64 y (cbrt.f64 (-.f64 a t))))
8.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a t)))
29.0ms	(cbrt.f64 (cbrt.f64 (-.f64 a t)))
26.0ms	(.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))))) (/.f64 y (cbrt.f64 (-.f64 a t))))
39.0ms	(-.f64 (+.f64 x y) (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 a t))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (cbrt.f64 (-.f64 a t)))))) (/.f64 y (cbrt.f64 (-.f64 a t)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5245	4008

prune277.0ms

Filtered

182 candidates to 221 candidates (-21.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	221	11	232

Merged error: 3.9b

Counts

232 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

5.1b	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
5.1b	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
5.1b	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
7.4b	(-.f64 (+.f64 x y) (.f64 (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

135×	`cbrt-prod_binary64`
72×	`times-frac_binary64`
67×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
57×	`cbrt-div_binary64`
49×	`add-cube-cbrt_binary64`
34×	`frac-times_binary64`
30×	`frac-sub_binary64`
26×	`associate-*l/_binary64`
22×	`associate-*r/_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
9×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r/_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/3_binary64` `div-inv_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 160

Calls

4 calls:

6.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
6.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
6.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
11.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
50.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
47.0ms	(cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))
50.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t)))))) (cbrt.f64 (/.f64 y (cbrt.f64 (-.f64 a t))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5552	4482

prune158.0ms

Filtered

138 candidates to 172 candidates (-24.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	170	13	183

Merged error: 3.9b

Counts

183 → 13

regimes593.0ms

Accuracy

6.3% (7.2b remaining)

Error of 11.2b against oracle of 4.0b and baseline of 11.7b

bsearch42.0ms

Steps

Iters	Range		Point
9	8.947138904414113e-81	7.810369709778065e-73	4.771245480372301e-73
7	-1.3911552327400735e-186	-1.6079339032526417e-188	-2.504837340528092e-188

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	290	58
1	290	58

end0.0ms

sample793.0ms

Algorithm

intervals

Results

273.0ms	6608×	body	80	valid
75.0ms	469×	body	640	valid
50.0ms	271×	body	1280	valid
43.0ms	387×	body	320	valid
31.0ms	715×	body	80	invalid
22.0ms	250×	body	160	valid
3.0ms	15×	body	2560	valid

Details

analyze1.0s

sample29.0ms

simplify125.0ms

prune9.0ms

localize10.0ms

rewrite35.0ms

series60.0ms

simplify44.0ms

prune116.0ms

localize17.0ms

rewrite49.0ms

series115.0ms

simplify45.0ms

prune167.0ms

localize19.0ms

rewrite127.0ms

series118.0ms

simplify82.0ms

prune277.0ms

localize20.0ms

rewrite39.0ms

series194.0ms

simplify49.0ms

prune158.0ms

regimes593.0ms

bsearch42.0ms

simplify8.0ms

end0.0ms

sample793.0ms

Profiling