Details

analyze3.0ms

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

sample10.0ms

Algorithm

intervals

Results

5.0ms

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

prune8.0ms

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: 29.2b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

28.1b

(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)))

simplify67.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4818	91
1	4818	91

prune18.0ms

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: 0.2b

Counts

17 → 6

localize6.0ms

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)))))
28.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.1b	(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:

9.0ms	(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)))))
5.0ms	(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)))

simplify86.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4895	929
1	4895	929

prune42.0ms

Filtered

70 candidates to 136 candidates (-94.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	136	6	142

Merged error: 0.2b

Counts

142 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
28.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1_binary64`
11×	`sqrt-prod_binary64`
10×	`unpow-prod-down_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64` `add-sqr-sqrt_binary64`
6×	`associate-*r/_binary64` `sqrt-div_binary64`
5×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow-unpow_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 67

Calls

4 calls:

5.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
4.0ms	(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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4781	572
1	4781	572

prune44.0ms

Filtered

60 candidates to 79 candidates (-31.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	79	6	85

Merged error: 0.2b

Counts

85 → 6

localize3.0ms

Local error

Found 1 expressions with local error:

0.5b	(*.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:

5.0ms

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

simplify35.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4888	133
1	4888	133

prune10.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	22	9	31

Merged error: 0.1b

Counts

31 → 9

regimes33.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.3b

bsearch12.0ms

Steps

Iters	Range		Point
10	-2.097651272328278e-306	5.665522876388207e-297	3.15504167189217e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	22
1	38	22

end0.0ms

sample258.0ms

Algorithm

intervals

Results

172.0ms

8000×

body

valid

Details

analyze3.0ms

sample10.0ms

simplify5.0ms

prune8.0ms

localize4.0ms

rewrite5.0ms

series4.0ms

simplify67.0ms

prune18.0ms

localize6.0ms

rewrite43.0ms

series20.0ms

simplify86.0ms

prune42.0ms

localize13.0ms

rewrite22.0ms

series45.0ms

simplify68.0ms

prune44.0ms

localize3.0ms

rewrite6.0ms

series5.0ms

simplify35.0ms

prune10.0ms

regimes33.0ms

bsearch12.0ms

simplify2.0ms

end0.0ms

sample258.0ms

Profiling