Details

analyze15.0ms

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune7.0ms

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: 39.7b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
36.5b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

2 → 54

Calls

2 calls:

10.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
7.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

series47.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
32.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4937	1096
1	4937	1096

prune86.0ms

Filtered

48 candidates to 60 candidates (-25.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	5	61

Merged error: 20.6b

Counts

61 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
36.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

2 → 47

Calls

2 calls:

12.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series57.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
25.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify55.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5143	838

prune49.0ms

Filtered

35 candidates to 53 candidates (-51.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Merged error: 20.6b

Counts

58 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
36.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod_binary64`
36×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 78

Calls

2 calls:

11.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series60.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
22.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify61.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5057	1814

prune71.0ms

Filtered

50 candidates to 84 candidates (-68.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	81	8	89

Merged error: 20.5b

Counts

89 → 8

localize4.0ms

Local error

Found 1 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 1/3))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

1 → 22

Calls

1 calls:

6.0ms

(*.f64 x (sqrt.f64 1/3))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(*.f64 x (sqrt.f64 1/3))

simplify52.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4902	133
1	4902	133

prune20.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	23	10	33

Merged error: 20.5b

Counts

33 → 10

regimes755.0ms

Accuracy

60.3% (7.8b remaining)

Error of 26.4b against oracle of 18.6b and baseline of 38.3b

bsearch30.0ms

Steps

Iters	Range		Point
8	9.687733552473191e+72	2.6371565179860673e+75	2.608580135401658e+75
8	-6.358702913804977e+89	-1.6776597388798722e+85	-1.123597247650645e+88

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	32
1	50	32

end0.0ms

sample545.0ms

Algorithm

intervals

Results

377.0ms

8000×

body

valid

Details

analyze15.0ms

sample20.0ms

simplify5.0ms

prune7.0ms

localize10.0ms

rewrite19.0ms

series47.0ms

simplify59.0ms

prune86.0ms

localize10.0ms

rewrite20.0ms

series57.0ms

simplify55.0ms

prune49.0ms

localize10.0ms

rewrite20.0ms

series60.0ms

simplify61.0ms

prune71.0ms

localize4.0ms

rewrite6.0ms

series5.0ms

simplify52.0ms

prune20.0ms

regimes755.0ms

bsearch30.0ms

simplify3.0ms

end0.0ms

sample545.0ms

Profiling