Details

analyze342.0ms

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample37.0ms

Algorithm

intervals

Results

9.0ms	188×	body	80	valid
5.0ms	19×	body	2560	valid
5.0ms	15×	body	5120	valid
4.0ms	17×	body	1280	valid
3.0ms	256×	pre	80	true
1.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

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: 38.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (- (sqrt (+ (* re re) (* im im))) re))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`pow1`
7×	`add-cube-cbrt`
6×	`add-exp-log` `associate-r` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-*r/` `difference-of-squares`
3×	`sub-neg` `flip3--` `sqrt-pow1` `associate-l` `flip--`
2×	`pow1/2` `pow-prod-down` `distribute-lft-out--`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `flip3-+` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

12.0ms	(* 2.0 (- (sqrt (+ (* re re) (* im im))) re))
7.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* 2.0 (- (sqrt (+ (* re re) (* im im))) re))
24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4950	936
1	4950	936

prune127.0ms

Filtered

63 candidates to 79 candidates (-25.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Merged error: 8.6b

Counts

80 → 7

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (* 2.0 (- im re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

4.0ms

(sqrt (* 2.0 (- im re)))

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

(sqrt (* 2.0 (- im re)))

simplify32.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5318	162

prune40.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	15	8	23

Merged error: 8.6b

Counts

23 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- im re)))
0.0b	(log (sqrt (* 2.0 (- im re))))
3.5b	(exp (log (sqrt (* 2.0 (- im re)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
8×	`log-prod` `log-pow`
7×	`exp-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `sqrt-pow1` `sqrt-div` `associate-r/`
4×	`add-exp-log` `log-div` `exp-sum`
3×	`flip3--` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`exp-diff`
1×	`rem-log-exp` `rem-exp-log`

Counts

3 → 52

Calls

3 calls:

4.0ms	(sqrt (* 2.0 (- im re)))
5.0ms	(log (sqrt (* 2.0 (- im re))))
6.0ms	(exp (log (sqrt (* 2.0 (- im re)))))

series46.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(sqrt (* 2.0 (- im re)))
17.0ms	(log (sqrt (* 2.0 (- im re))))
15.0ms	(exp (log (sqrt (* 2.0 (- im re)))))

simplify32.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5208	620

prune106.0ms

Filtered

45 candidates to 61 candidates (-35.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	61	8	69

Merged error: 8.6b

Counts

69 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
11.0b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.8b	(sqrt (+ (* re re) (* im im)))
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 125

Calls

4 calls:

14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4925	1493
1	4925	1493

prune117.0ms

Filtered

74 candidates to 137 candidates (-85.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	136	9	145

Merged error: 8.6b

Counts

145 → 9

regimes313.0ms

Accuracy

42.6% (11.1b remaining)

Error of 20.7b against oracle of 9.7b and baseline of 28.9b

bsearch77.0ms

Steps

Iters	Range		Point
9	2.6764312614606914e+50	9.800889802775413e+57	2.7223419195749627e+50
7	-9.218399617431092e-33	-1.0597130700650951e-34	-1.3272029508543682e-33

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	42
1	36	42

end0.0ms

analyze337.0ms

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample1.1s

Algorithm

intervals

Results

301.0ms	6027×	body	80	valid
202.0ms	688×	body	2560	valid
119.0ms	501×	body	1280	valid
100.0ms	8000×	pre	80	true
94.0ms	277×	body	5120	valid
50.0ms	272×	body	640	valid
26.0ms	168×	body	320	valid
6.0ms	67×	body	160	valid

Details

analyze342.0ms

sample37.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite30.0ms

series45.0ms

simplify40.0ms

prune127.0ms

localize8.0ms

rewrite5.0ms

series15.0ms

simplify32.0ms

prune40.0ms

localize12.0ms

rewrite17.0ms

series46.0ms

simplify32.0ms

prune106.0ms

localize13.0ms

rewrite41.0ms

series25.0ms

simplify72.0ms

prune117.0ms

regimes313.0ms

bsearch77.0ms

simplify1.0ms

end0.0ms

analyze337.0ms

sample1.1s

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