Details

sample76.0ms

Algorithm

intervals

Results

20.0ms	272×	body	80	valid
14.0ms	32×	body	1280	valid
14.0ms	44×	body	640	valid
6.0ms	15×	body	320	valid
2.0ms	14×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	17
1	71	17
2	241	17
3	747	17
4	2196	17
5	5001	17

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: 38.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series553.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
410.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify57.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1312	3623
1	5002	3528

prune422.0ms

Filtered

127 candidates to 77 candidates (60.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	7	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	8	128

Merged error: 25.8b

Counts

128 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
416.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1349	3745
1	5002	3672

prune442.0ms

Filtered

128 candidates to 69 candidates (53.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	126	10	136

Merged error: 25.8b

Counts

136 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
413.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify69.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1278	4428
1	5001	4345

prune550.0ms

Filtered

112 candidates to 80 candidates (71.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	112	10	122

Merged error: 25.8b

Counts

122 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
13×	`log-pow`
12×	`exp-prod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `log-prod` `cube-prod` `sqrt-prod`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `rem-log-exp` `flip-+` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

4.0ms	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
22.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
416.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1360	3931
1	5002	3837

prune486.0ms

Filtered

129 candidates to 73 candidates (56.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	5	6
Picked	0	1	1
Done	1	2	3
Total	130	9	139

Merged error: 25.8b

Counts

139 → 9

regimes618.0ms

Accuracy

74% (3.4b remaining)

Error of 28.7b against oracle of 25.3b and baseline of 38.5b

bsearch4.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms

sample2.1s

Algorithm

intervals

Results

635.0ms	8533×	body	80	valid
434.0ms	1318×	body	640	valid
390.0ms	836×	body	1280	valid
173.0ms	718×	body	320	valid
59.0ms	365×	body	160	valid

Details

sample76.0ms

simplify52.0ms

prune3.0ms

localize16.0ms

rewrite46.0ms

series553.0ms

simplify57.0ms

prune422.0ms

localize24.0ms

rewrite44.0ms

series519.0ms

simplify60.0ms

prune442.0ms

localize22.0ms

rewrite55.0ms

series497.0ms

simplify69.0ms

prune550.0ms

localize25.0ms

rewrite50.0ms

series525.0ms

simplify67.0ms

prune486.0ms

regimes618.0ms

bsearch4.0ms

simplify1.0ms

end0.0ms

sample2.1s

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