Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	195×	body	80	valid
7.0ms	25×	body	2560	valid
3.0ms	12×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	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: 37.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.1b	(- (sqrt (+ (* re re) (* im im))) re)
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
171.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune167.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Merged error: 17.6b

Counts

67 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

10.1b	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
28.6b	(sqrt (+ (* re re) (* im im)))
28.6b	(sqrt (+ (* re re) (* im im)))
28.6b	(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)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify144.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (137.0ms)

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

prune219.0ms

Filtered

69 candidates to 56 candidates (81.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	67	9	76

Merged error: 17.6b

Counts

76 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (+ (* re re) (* im im)))
28.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(cbrt (+ (* re re) (* im im)))
29.6b	(cbrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

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

series260.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1469	416
3	5002	414

prune320.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	67	10	77

Merged error: 17.6b

Counts

77 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (+ (* re re) (* im im)))
28.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(cbrt (+ (* re re) (* im im)))
32.0b	(pow (+ (* re re) (* im im)) 1/3)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-prod`
5×	`add-exp-log`
4×	`sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `flip3-+` `flip-+`
2×	`rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `pow-pow` `unpow1/3` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 61

Calls

4 calls:

4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(pow (+ (* re re) (* im im)) 1/3)

series266.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
97.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(pow (+ (* re re) (* im im)) 1/3)

simplify81.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	189	439
1	661	385
2	2515	381
3	5001	379

prune333.0ms

Filtered

73 candidates to 61 candidates (83.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	73	10	83

Merged error: 17.6b

Counts

83 → 10

regimes521.0ms

Accuracy

56.7% (9.1b remaining)

Error of 27.0b against oracle of 17.9b and baseline of 38.9b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	36
1	37	36

end0.0ms

sample910.0ms

Algorithm

intervals

Results

292.0ms	6061×	body	80	valid
197.0ms	707×	body	2560	valid
102.0ms	457×	body	1280	valid
96.0ms	283×	body	5120	valid
51.0ms	278×	body	640	valid
19.0ms	145×	body	320	valid
6.0ms	69×	body	160	valid