Details

analyze64.0ms

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

sample14.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	9
1	38	9

prune6.0ms

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: 0.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
0.2b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
3×	`flip3-+_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64`
2×	`associate-+l+_binary64`

Counts

3 → 38

Calls

3 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
10.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

series24.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (.f64 x x) (.f64 y y))
10.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
8.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

simplify53.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5136	513

prune60.0ms

Filtered

33 candidates to 47 candidates (-42.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	8	48

Merged error: 0.1b

Counts

48 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`swap-sqr_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
10.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4959	1363
1	4959	1363

prune96.0ms

Filtered

66 candidates to 110 candidates (-66.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 y y) 3)
0.3b	(.f64 (.f64 y y) 3)
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

6.0ms	(.f64 (.f64 y y) 3)
6.0ms	(.f64 (.f64 y y) 3)
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 (.f64 y y) 3)
3.0ms	(.f64 (.f64 y y) 3)
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

simplify78.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4993	654
1	4993	654

prune94.0ms

Filtered

54 candidates to 80 candidates (-48.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	80	10	90

Merged error: 0.0b

Counts

90 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 y (sqrt.f64 3))
0.4b	(*.f64 y (sqrt.f64 3))
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 y (sqrt.f64 3)) (.f64 y (sqrt.f64 3)))))
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64`
12×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(*.f64 y (sqrt.f64 3))
5.0ms	(*.f64 y (sqrt.f64 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 y (sqrt.f64 3)) (.f64 y (sqrt.f64 3)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 y (sqrt.f64 3))
4.0ms	(*.f64 y (sqrt.f64 3))
13.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 y (sqrt.f64 3)) (.f64 y (sqrt.f64 3)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

simplify53.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5090	672

prune78.0ms

Filtered

58 candidates to 86 candidates (-48.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	86	10	96

Merged error: 0.0b

Counts

96 → 10

regimes263.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	25
1	13	25

end0.0ms

sample353.0ms

Algorithm

intervals

Results

225.0ms	8000×	body	80	valid
0.0ms	8×	body	80	invalid

Details

analyze64.0ms

sample14.0ms

simplify6.0ms

prune6.0ms

localize6.0ms

rewrite23.0ms

series24.0ms

simplify53.0ms

prune60.0ms

localize10.0ms

rewrite37.0ms

series35.0ms

simplify56.0ms

prune96.0ms

localize8.0ms

rewrite22.0ms

series24.0ms

simplify78.0ms

prune94.0ms

localize13.0ms

rewrite23.0ms

series30.0ms

simplify53.0ms

prune78.0ms

regimes263.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample353.0ms

Profiling