Details

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

9.0ms	194×	body	80	valid
6.0ms	21×	body	2560	valid
3.0ms	14×	body	1280	valid
3.0ms	9×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

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

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: 39.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

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

series41.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
10.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	234	381
1	812	362
2	3077	355
3	5001	354

prune100.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	5	53

Merged error: 17.6b

Counts

53 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.8b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 66

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
29.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
24.0ms	(cbrt (+ (* re re) (* im im)))
23.0ms	(cbrt (+ (* re re) (* im im)))

simplify110.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	341	1002
1	1180	942
2	4515	900
3	5002	886

prune139.0ms

Filtered

66 candidates to 78 candidates (-18.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 17.6b

Counts

83 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
22.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	151	560
1	426	524
2	1225	500
3	5002	468

prune120.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	64	7	71

Merged error: 17.6b

Counts

71 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
5.6b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
22.4b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
5.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
22.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	412	1076
1	1494	991
2	5002	987

prune147.0ms

Filtered

78 candidates to 111 candidates (-42.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	108	10	118

Merged error: 6.5b

Counts

118 → 10

regimes328.0ms

Accuracy

40.8% (19.4b remaining)

Error of 26.6b against oracle of 7.1b and baseline of 39.9b

bsearch231.0ms

Steps

Iters	Range		Point
7	8355106611636677.0	1.8798288722006794e+18	38636472822869224.0
4	7.921561677907191e-25	1.1712415830611904e-24	1.0547731849269709e-24
7	3.1367703345281057e-143	2.1325094630940935e-141	3.185583124521705e-143
8	1.283739826604558e-207	1.4512130115630385e-204	3.974989552829448e-206
9	-9.400415056905811e-297	-1.1521681827193233e-301	-1.166134515309741e-300
9	-6.107610852753143e-165	-8.03951107182309e-171	-8.118211634895193e-171
7	-5.052728755528032e+54	-1.8783072856380372e+53	-4.996607267832153e+54

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	73
1	95	73
2	96	73
3	96	73

end0.0ms

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

292.0ms	5932×	body	80	valid
200.0ms	718×	body	2560	valid
111.0ms	500×	body	1280	valid
101.0ms	302×	body	5120	valid
56.0ms	311×	body	640	valid
22.0ms	163×	body	320	valid
8.0ms	74×	body	160	valid

Details

sample3.6s

simplify7.0ms

prune3.0ms

localize10.0ms

rewrite19.0ms

series41.0ms

simplify87.0ms

prune100.0ms

localize13.0ms

rewrite24.0ms

series109.0ms

simplify110.0ms

prune139.0ms

localize18.0ms

rewrite15.0ms

series83.0ms

simplify43.0ms

prune120.0ms

localize13.0ms

rewrite36.0ms

series45.0ms

simplify53.0ms

prune147.0ms

regimes328.0ms

bsearch231.0ms

simplify3.0ms

end0.0ms

sample4.6s

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