Details

sample134.0ms

Algorithm

intervals

Results

26.0ms	276×	body	80	valid
20.0ms	44×	body	640	valid
19.0ms	30×	body	1280	valid
11.0ms	22×	body	320	valid
2.0ms	7×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

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: 40.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

12.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune246.0ms

Filtered

147 candidates to 77 candidates (47.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	7	148

Merged error: 25.3b

Counts

148 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
130×	`associate-*l/`
74×	`associate-*r/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `rem-sqrt-square` `sqr-cos` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

4.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify104.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2471	7439
1	5001	7337

prune328.0ms

Filtered

204 candidates to 102 candidates (50.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	204	7	211

Merged error: 25.3b

Counts

211 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* lambda2 lambda1))
0.0b	(* (- phi1 phi2) (- phi1 phi2))
2.0b	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
37.2b	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

27×	`flip3--` `flip--`
24×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
18×	`sqrt-div`
17×	`pow1`
16×	`frac-add`
12×	`frac-times`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
9×	`add-log-exp`
8×	`associate-l`
7×	`swap-sqr`
6×	`associate-r/` `associate-r` `associate-l/` `distribute-lft-out--`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `difference-of-squares`
3×	`sub-neg` `sqrt-prod`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `*-commutative`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `associate--l+` `sum-log` `pow-sqr` `pow-prod-up` `flip-+` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

5.0ms	(* 2 (* lambda2 lambda1))
9.0ms	(* (- phi1 phi2) (- phi1 phi2))
10.0ms	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
14.0ms	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 2 (* lambda2 lambda1))
4.0ms	(* (- phi1 phi2) (- phi1 phi2))
7.0ms	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
50.0ms	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

simplify96.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	650	1638
1	3417	1602
2	5002	1598

prune234.0ms

Filtered

120 candidates to 69 candidates (42.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	118	9	127

Merged error: 25.3b

Counts

127 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
6.1b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
37.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `exp-diff`
64×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`log-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

4 → 179

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
137.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
142.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify87.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1513	6939
1	5002	6823

prune308.0ms

Filtered

191 candidates to 99 candidates (48.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	187	13	200

Merged error: 25.3b

Counts

200 → 13

regimes1.3s

Accuracy

72.5% (3.9b remaining)

Error of 29.3b against oracle of 25.4b and baseline of 39.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	34
1	33	34

end0.0ms

sample2.8s

Algorithm

intervals

Results

797.0ms	8298×	body	80	valid
592.0ms	1306×	body	640	valid
523.0ms	799×	body	1280	valid
238.0ms	735×	body	320	valid
82.0ms	366×	body	160	valid

Details

sample134.0ms

simplify53.0ms

prune5.0ms

localize16.0ms

rewrite53.0ms

series181.0ms

simplify59.0ms

prune246.0ms

localize17.0ms

rewrite61.0ms

series158.0ms

simplify104.0ms

prune328.0ms

localize19.0ms

rewrite42.0ms

series64.0ms

simplify96.0ms

prune234.0ms

localize21.0ms

rewrite76.0ms

series289.0ms

simplify87.0ms

prune308.0ms

regimes1.3s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling