Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample11.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 30.7b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

29.6b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64` `flip-+_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4818	91
1	4818	91

prune33.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	6	17

Merged error: 0.1b

Counts

17 → 6

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
29.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))
29.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64`
71×	`pow1_binary64`
33×	`sqrt-prod_binary64`
32×	`sqrt-div_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`pow-prod-down_binary64`
22×	`pow1/2_binary64`
20×	`associate-*r/_binary64`
14×	`pow-prod-up_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `flip-+_binary64`
8×	`pow-sqr_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
4.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
4.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
4.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4895	929
1	4895	929

prune72.0ms

Filtered

70 candidates to 136 candidates (-94.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	136	6	142

Merged error: 0.1b

Counts

142 → 6

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 2))

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:

5.0ms

(*.f64 x (sqrt.f64 2))

series5.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(*.f64 x (sqrt.f64 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4888	133
1	4888	133

prune26.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	24	7	31

Merged error: 0.1b

Counts

31 → 7

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

6.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
10.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

series12.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
5.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify62.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5070	343

prune34.0ms

Filtered

28 candidates to 56 candidates (-100.0%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	56	7	63

Merged error: 0.1b

Counts

63 → 7

regimes41.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.6b

bsearch11.0ms

Steps

Iters	Range		Point
9	-8.8864683877263e-309	3.48992956228169e-302	1.5307481317311e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	13
1	32	13

end0.0ms

sample271.0ms

Algorithm

intervals

Results

182.0ms	8000×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample11.0ms

simplify5.0ms

prune5.0ms

localize4.0ms

rewrite5.0ms

series4.0ms

simplify65.0ms

prune33.0ms

localize7.0ms

rewrite43.0ms

series20.0ms

simplify87.0ms

prune72.0ms

localize3.0ms

rewrite6.0ms

series5.0ms

simplify34.0ms

prune26.0ms

localize5.0ms

rewrite18.0ms

series12.0ms

simplify62.0ms

prune34.0ms

regimes41.0ms

bsearch11.0ms

simplify2.0ms

end0.0ms

sample271.0ms

Profiling