Details

analyze365.0ms

Algorithm

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
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
48.4%	45.8%	5.8%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

sample16.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
1.0ms	23×	body	80	invalid

simplify154.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	5198	7

prune3.0ms

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

Merged error: 13.8b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (+.f64 y z))
13.0b	(/.f64 (*.f64 x (+.f64 y z)) z)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `associate-*r/_binary64`
3×	`associate-/r_binary64` `associate-l*_binary64` `times-frac_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

2 → 46

Calls

2 calls:

7.0ms	(*.f64 x (+.f64 y z))
7.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)

series18.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(*.f64 x (+.f64 y z))
11.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)

simplify71.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4994	376
1	4994	376

prune56.0ms

Filtered

35 candidates to 52 candidates (-48.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	4	53

Merged error: 0.0b

Counts

53 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 z (+.f64 y z))
3.6b	(/.f64 x (/.f64 z (+.f64 y z)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac_binary64`
94×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
22×	`associate-/r*_binary64`
16×	`distribute-lft-out_binary64`
11×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

2 → 123

Calls

2 calls:

8.0ms	(/.f64 z (+.f64 y z))
10.0ms	(/.f64 x (/.f64 z (+.f64 y z)))

series18.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/.f64 z (+.f64 y z))
12.0ms	(/.f64 x (/.f64 z (+.f64 y z)))

simplify82.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4955	1556
1	4955	1556

prune107.0ms

Filtered

95 candidates to 129 candidates (-35.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	128	5	133

Merged error: 0b

Counts

133 → 5

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 x y) z))
5.2b	(/.f64 (*.f64 x y) z)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64`
2×	`pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

2 → 33

Calls

2 calls:

6.0ms	(+.f64 x (/.f64 (*.f64 x y) z))
5.0ms	(/.f64 (*.f64 x y) z)

series13.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(+.f64 x (/.f64 (*.f64 x y) z))
6.0ms	(/.f64 (*.f64 x y) z)

simplify63.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5188	299

prune36.0ms

Filtered

26 candidates to 39 candidates (-50.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	39	5	44

Merged error: 0b

Counts

44 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.1b	(/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (+.f64 z y))))
4.0b	(.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 z y)) (cbrt.f64 (+.f64 z y)))) (/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (+.f64 z y)))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

597×	`times-frac_binary64`
377×	`*-un-lft-identity_binary64`
327×	`cbrt-prod_binary64`
299×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
167×	`associate-r_binary64`
78×	`add-exp-log_binary64`
50×	`cbrt-div_binary64`
39×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64`
36×	`add-cbrt-cube_binary64`
28×	`associate-/r/_binary64`
27×	`associate-/r*_binary64`
25×	`flip3-+_binary64` `flip-+_binary64`
22×	`pow1_binary64`
21×	`associate-*r/_binary64`
18×	`cbrt-undiv_binary64` `div-exp_binary64`
16×	`frac-times_binary64`
15×	`div-inv_binary64`
13×	`pow-prod-down_binary64`
12×	`associate-*l/_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
2×	`pow1/3_binary64`
1×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 460

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
14.0ms	(/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (+.f64 z y))))
64.0ms	(.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 z y)) (cbrt.f64 (+.f64 z y)))) (/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (+.f64 z y)))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt.f64 x)
18.0ms	(cbrt.f64 x)
42.0ms	(/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (+.f64 z y))))
27.0ms	(.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 z y)) (cbrt.f64 (+.f64 z y)))) (/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (+.f64 z y)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

472 → 472

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5162	10179

prune412.0ms

Filtered

379 candidates to 472 candidates (-24.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	472	0	472
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	472	5	477

Merged error: 0b

Counts

477 → 5

regimes173.0ms

Accuracy

43% (1.8b remaining)

Error of 1.8b against oracle of 0.0b and baseline of 3.2b

bsearch27.0ms

Steps

Iters	Range		Point
7	5.1982257203976994e-68	5.351229234830876e-66	3.2862580425901126e-67
9	-7.806486572883347e-46	-1.1022488371132745e-50	-4.719214907735761e-47

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	23
1	21	23

end0.0ms

sample400.0ms

Algorithm

intervals

Results

202.0ms	8000×	body	80	valid
17.0ms	700×	body	80	invalid

Details

analyze365.0ms

sample16.0ms

simplify154.0ms

prune3.0ms

localize5.0ms

rewrite16.0ms

series18.0ms

simplify71.0ms

prune56.0ms

localize6.0ms

rewrite23.0ms

series18.0ms

simplify82.0ms

prune107.0ms

localize5.0ms

rewrite12.0ms

series13.0ms

simplify63.0ms

prune36.0ms

localize13.0ms

rewrite113.0ms

series107.0ms

simplify86.0ms

prune412.0ms

regimes173.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample400.0ms

Profiling