Details

analyze366.0ms

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
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	75×	body	80	nan
1.0ms	21×	body	80	invalid

simplify137.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	6513	10

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: 23.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
3.0b	(-.f64 (.f64 y y) (.f64 z z))
24.7b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`sqrt-div_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`associate-*r/_binary64` `unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

3 → 53

Calls

3 calls:

9.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
4.0ms	(-.f64 (.f64 y y) (.f64 z z))
4.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
7.0ms	(-.f64 (.f64 y y) (.f64 z z))
8.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

simplify36.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4996	609
1	4996	609

prune64.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	58	4	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	5	63

Merged error: 0.2b

Counts

63 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

3.0b	(-.f64 (.f64 y y) (.f64 z z))
3.0b	(-.f64 (.f64 y y) (.f64 z z))
25.6b	(cbrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
25.6b	(cbrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `cbrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(-.f64 (.f64 y y) (.f64 z z))
4.0ms	(-.f64 (.f64 y y) (.f64 z z))
4.0ms	(cbrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
4.0ms	(cbrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(-.f64 (.f64 y y) (.f64 z z))
6.0ms	(-.f64 (.f64 y y) (.f64 z z))
23.0ms	(cbrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
21.0ms	(cbrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4840	684
1	4840	684

prune64.0ms

Filtered

54 candidates to 64 candidates (-18.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	64	5	69

Merged error: 0.2b

Counts

69 → 5

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify5.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Merged error: 0.2b

Counts

5 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 y z))
0.0b	(sqrt.f64 (+.f64 y z))
0.0b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
0.3b	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

28×	`sqrt-div_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`sqrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
15×	`pow1_binary64`
12×	`associate-*r/_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-l_binary64`
9×	`associate-r_binary64`
8×	`frac-times_binary64`
7×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
6×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-*l/_binary64`
2×	`distribute-lft-out_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`sqrt-unprod_binary64`

Counts

4 → 100

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 y z))
3.0ms	(sqrt.f64 (+.f64 y z))
13.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
12.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt.f64 (-.f64 y z))
7.0ms	(sqrt.f64 (+.f64 y z))
24.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
14.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

simplify35.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5230	1223

prune79.0ms

Filtered

83 candidates to 112 candidates (-34.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	112	5	117

Merged error: 0.2b

Counts

117 → 5

regimes661.0ms

Accuracy

96.8% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 25.0b

bsearch67.0ms

Steps

Iters	Range		Point
9	-2.0202767934438714e-221	-5.345090808404906e-227	-5.421599144526907e-227

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	11
1	31	11

end0.0ms

sample614.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
64.0ms	1762×	body	80	nan
25.0ms	688×	body	80	invalid

Details

analyze366.0ms

sample23.0ms

simplify137.0ms

prune3.0ms

localize7.0ms

rewrite19.0ms

series38.0ms

simplify36.0ms

prune64.0ms

localize10.0ms

rewrite19.0ms

series57.0ms

simplify54.0ms

prune64.0ms

localize2.0ms

rewrite0.0ms

series0.0ms

simplify5.0ms

prune6.0ms

localize8.0ms

rewrite39.0ms

series56.0ms

simplify35.0ms

prune79.0ms

regimes661.0ms

bsearch67.0ms

simplify2.0ms

end0.0ms

sample614.0ms

Profiling