Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
5.0ms	24×	body	2560	valid
3.0ms	11×	body	5120	valid
3.0ms	16×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	2×	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 40.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

28.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	271	577
1	909	551
2	3188	541
3	5001	540

prune155.0ms

Filtered

73 candidates to 52 candidates (28.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	7	74

Merged error: 19.6b

Counts

74 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.2b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
30.0b	(sqrt (+ (* re re) (* im im)))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

238×	`sqrt-prod`
166×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
71×	`associate-l`
62×	`distribute-lft-out`
61×	`swap-sqr`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`difference-of-squares`
18×	`add-cube-cbrt` `pow1/2` `unswap-sqr`
14×	`associate-r`
9×	`pow-prod-up`
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/` `*-commutative` `distribute-lft-out--`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `flip--` `cbrt-unprod`

Counts

4 → 193

Calls

4 calls:

48.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
70.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
53.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify264.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	268	1581
1	851	1452
2	4937	1427
3	5001	1427

prune250.0ms

Filtered

205 candidates to 74 candidates (63.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	204	8	212

Merged error: 19.6b

Counts

212 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
7.0b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.9b	(cbrt (+ (* re re) (* im im)))
30.9b	(cbrt (+ (* re re) (* im im)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`cbrt-prod`
16×	`associate-l`
15×	`sqrt-prod` `distribute-lft-out`
14×	`associate-r`
10×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `cbrt-div` `swap-sqr` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
4×	`difference-of-squares`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `sqrt-div` `associate-*r/` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

23.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
30.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
19.0ms	(cbrt (+ (* re re) (* im im)))
17.0ms	(cbrt (+ (* re re) (* im im)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
87.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
98.0ms	(cbrt (+ (* re re) (* im im)))
103.0ms	(cbrt (+ (* re re) (* im im)))

simplify140.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	317	1162
1	1145	1100
2	4616	1049
3	5002	1049

prune267.0ms

Filtered

99 candidates to 67 candidates (32.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	98	9	107

Merged error: 19.6b

Counts

107 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
11.4b	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
30.0b	(sqrt (+ (* re re) (* im im)))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

109×	`sqrt-prod`
84×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
33×	`unpow-prod-down`
26×	`difference-of-squares`
24×	`unswap-sqr`
15×	`distribute-lft-out`
14×	`associate-l`
11×	`add-cube-cbrt` `sqrt-pow1`
10×	`pow1`
7×	`pow-pow`
6×	`swap-sqr` `add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube` `sqr-pow`
4×	`sqrt-div`
3×	`pow-unpow`
2×	`rem-sqrt-square` `flip3-+` `unpow3` `flip-+` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `sqrt-pow2` `flip--` `rem-cube-cbrt`

Counts

4 → 120

Calls

4 calls:

24.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
75.0ms	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))
17.0ms	(sqrt (+ (* re re) (* im im)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
52.0ms	(- (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
42.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	364	1526
1	1107	1326
2	5001	1187

prune253.0ms

Filtered

132 candidates to 64 candidates (51.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	131	10	141

Merged error: 19.6b

Counts

141 → 10

regimes234.0ms

Accuracy

38.4% (13.0b remaining)

Error of 30.6b against oracle of 17.7b and baseline of 38.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	45	36

end0.0ms

sample700.0ms

Algorithm

intervals

Results

206.0ms	6026×	body	80	valid
142.0ms	696×	body	2560	valid
83.0ms	473×	body	1280	valid
76.0ms	296×	body	5120	valid
37.0ms	279×	body	640	valid
14.0ms	144×	body	320	valid
6.0ms	86×	body	160	valid