Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	190×	body	80	valid
8.0ms	30×	body	2560	valid
3.0ms	15×	body	1280	valid
3.0ms	9×	body	5120	valid
2.0ms	10×	body	640	valid
0.0ms	2×	body	320	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: 37.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (sqrt (+ (* re re) (* im im))) re)
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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 (+ (* re re) (* im im))) re)
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series341.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
244.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	234	381
1	812	362
2	3077	355
3	5001	353

prune144.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 18.2b

Counts

53 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))
0.4b	(* (sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-pow1`
67×	`pow1`
37×	`sqrt-prod`
32×	`sqrt-div`
30×	`add-sqr-sqrt`
23×	`pow-prod-down`
22×	`pow1/2`
16×	`associate-*r/`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow-prod-up`
9×	`swap-sqr`
8×	`pow-sqr`
7×	`flip3--` `associate-r` `associate-l` `flip--`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

9.0ms	(sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))
24.0ms	(* (sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))
249.0ms	(* (sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))
36.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	421	1366
1	1813	1252
2	5002	1197

prune319.0ms

Filtered

140 candidates to 79 candidates (56.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	140	6	146

Merged error: 18.2b

Counts

146 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

11.0b	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

24.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
42.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify143.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (136.0ms)

Iter	Nodes	Cost
0	148	643
1	378	541
2	1206	463
3	4691	456
4	5001	450

prune223.0ms

Filtered

69 candidates to 56 candidates (81.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	67	8	75

Merged error: 18.2b

Counts

75 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

11.0b	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

20.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify142.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (135.0ms)

Iter	Nodes	Cost
0	148	643
1	378	541
2	1206	463
3	4691	456
4	5001	450

prune252.0ms

Filtered

69 candidates to 58 candidates (84.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	67	10	77

Merged error: 18.2b

Counts

77 → 10

regimes396.0ms

Accuracy

58.3% (8.6b remaining)

Error of 26.3b against oracle of 17.8b and baseline of 38.4b

bsearch96.0ms

Steps

Iters	Range		Point
9	-3.726832345198518e-301	-5.5837829303726255e-306	-2.805428795031093e-305
7	-3.446092505479231e+101	-1.5233748944127634e+99	-4.710851114955975e+99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	32
1	41	32

end0.0ms

sample873.0ms

Algorithm

intervals

Results

280.0ms	6039×	body	80	valid
200.0ms	739×	body	2560	valid
98.0ms	447×	body	1280	valid
85.0ms	270×	body	5120	valid
48.0ms	278×	body	640	valid
18.0ms	146×	body	320	valid
7.0ms	81×	body	160	valid

Details

sample34.0ms

simplify8.0ms

prune3.0ms

localize10.0ms

rewrite22.0ms

series341.0ms

simplify91.0ms

prune144.0ms

localize15.0ms

rewrite45.0ms

series551.0ms

simplify63.0ms

prune319.0ms

localize14.0ms

rewrite38.0ms

series162.0ms

simplify143.0ms

prune223.0ms

localize18.0ms

rewrite33.0ms

series166.0ms

simplify142.0ms

prune252.0ms

regimes396.0ms

bsearch96.0ms

simplify2.0ms

end0.0ms

sample873.0ms

Profiling