Details

sample36.0ms

Algorithm

intervals

Results

9.0ms	194×	body	80	valid
6.0ms	22×	body	2560	valid
6.0ms	9×	body	5120	valid
3.0ms	13×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	5×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 37.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
232.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	260	458
1	982	428
2	3667	421
3	5001	420

prune173.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	7	67

Merged error: 17.1b

Counts

67 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.9b	(sqrt (+ (* re re) (* im im)))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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 → 126

Calls

4 calls:

18.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
49.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune257.0ms

Filtered

138 candidates to 73 candidates (52.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	137	8	145

Merged error: 17.1b

Counts

145 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
12.4b	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
27.9b	(sqrt (+ (* re re) (* im im)))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`cube-div` `rem-sqrt-square`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `sqrt-pow2` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
16.0ms	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
50.0ms	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	381	993
1	1279	875
2	5002	845

prune294.0ms

Filtered

104 candidates to 64 candidates (61.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	103	9	112

Merged error: 17.1b

Counts

112 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

4.7b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
7.0b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.9b	(sqrt (+ (* re re) (* im im)))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-prod` `add-log-exp`
4×	`add-exp-log` `log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-cbrt-cube`
2×	`rem-sqrt-square` `log-div` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `flip--` `flip-+` `difference-of-squares`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

16.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
14.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
47.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify113.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (105.0ms)

Iter	Nodes	Cost
0	191	746
1	442	597
2	1109	556
3	3525	548
4	5002	542

prune221.0ms

Filtered

73 candidates to 58 candidates (79.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	71	11	82

Merged error: 17.1b

Counts

82 → 11

regimes231.0ms

Accuracy

56.9% (9.1b remaining)

Error of 26.8b against oracle of 17.7b and baseline of 38.8b

bsearch79.0ms

Steps

Iters	Range		Point
8	-3.118349744238045e-230	-8.18437998310851e-233	-8.31798967334541e-233
6	-2.331637994940635e+74	-4.69191261873295e+73	-1.9404776396786571e+74

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample913.0ms

Algorithm

intervals

Results

301.0ms	6071×	body	80	valid
184.0ms	671×	body	2560	valid
108.0ms	461×	body	1280	valid
90.0ms	273×	body	5120	valid
54.0ms	287×	body	640	valid
22.0ms	149×	body	320	valid
8.0ms	88×	body	160	valid

Details

sample36.0ms

simplify8.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series342.0ms

simplify106.0ms

prune173.0ms

localize12.0ms

rewrite44.0ms

series154.0ms

simplify49.0ms

prune257.0ms

localize16.0ms

rewrite34.0ms

series235.0ms

simplify52.0ms

prune294.0ms

localize19.0ms

rewrite40.0ms

series172.0ms

simplify113.0ms

prune221.0ms

regimes231.0ms

bsearch79.0ms

simplify1.0ms

end0.0ms

sample913.0ms

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