Details

sample73.0ms

Algorithm

intervals

Results

20.0ms	279×	body	80	valid
13.0ms	30×	body	1280	valid
12.0ms	37×	body	640	valid
6.0ms	26×	body	320	valid
3.0ms	16×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	8
1	78	8
2	261	8
3	834	8
4	2600	8
5	5001	8

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 3.3b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series539.0ms

Counts

3 → 9

Calls

3 calls:

427.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
85.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	290	525
1	1003	448
2	4763	442
3	5001	440

prune204.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	51	11	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	11	63

Merged error: 3.2b

Counts

63 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`associate-*l/`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

10.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series187.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
26.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
47.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	715
1	1100	668
2	5002	655

prune296.0ms

Filtered

109 candidates to 68 candidates (62.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	108	12	120

Merged error: 3.2b

Counts

120 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
0.5b	(pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)
2.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
39×	`unpow-prod-down` `cube-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log` `cube-mult` `unpow3` `sqr-pow`
6×	`pow-unpow` `add-cbrt-cube`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp`
2×	`pow-pow` `rem-cube-cbrt`
1×	`pow1/3`

Counts

4 → 122

Calls

4 calls:

6.0ms	(cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series171.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))
46.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
69.0ms	(pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	291	976
1	946	906
2	5002	872

prune283.0ms

Filtered

134 candidates to 59 candidates (44.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	134	12	146

Merged error: 3.2b

Counts

146 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.1b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`associate-*l/`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

5.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
12.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series186.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
85.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
29.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	224	596
1	703	507
2	3169	501
3	5002	501

prune241.0ms

Filtered

85 candidates to 67 candidates (78.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	84	13	97

Merged error: 3.2b

Counts

97 → 13

regimes365.0ms

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample2.0s

Algorithm

intervals

Results

620.0ms	8392×	body	80	valid
432.0ms	1301×	body	640	valid
378.0ms	815×	body	1280	valid
170.0ms	726×	body	320	valid
62.0ms	371×	body	160	valid

Details

sample73.0ms

simplify59.0ms

prune8.0ms

localize16.0ms

rewrite16.0ms

series539.0ms

simplify96.0ms

prune204.0ms

localize16.0ms

rewrite22.0ms

series187.0ms

simplify48.0ms

prune296.0ms

localize22.0ms

rewrite22.0ms

series171.0ms

simplify48.0ms

prune283.0ms

localize16.0ms

rewrite30.0ms

series186.0ms

simplify67.0ms

prune241.0ms

regimes365.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.0s

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