Details

sample67.0ms

Algorithm

intervals

Results

20.0ms	280×	body	80	valid
11.0ms	28×	body	1280	valid
10.0ms	35×	body	640	valid
5.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify51.0ms

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

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: 40.4b

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))))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
34×	`associate-*r/`
5×	`*-commutative`
2×	`swap-sqr` `associate-r` `associate-l`
1×	`pow2` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 83

Calls

4 calls:

14.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(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:

94.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(cos (/ (+ phi1 phi2) 2.0))
403.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1276	3364
1	5001	3324

prune333.0ms

Filtered

95 candidates to 49 candidates (51.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	6	96

Merged error: 27.2b

Counts

96 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
130×	`associate-*r/`
74×	`associate-*l/`
73×	`cos-mult`
1×	`pow2` `sqr-cos` `flip3-+` `pow1/2` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

6.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(sqrt (+ (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series728.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
632.0ms	(sqrt (+ (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify92.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2381	6920
1	5001	6884

prune537.0ms

Filtered

155 candidates to 70 candidates (45.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	152	9	161

Merged error: 20.7b

Counts

161 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
0.0b	(* (- phi1 phi2) (- phi1 phi2))
1.6b	(- (+ (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))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`flip3--` `flip--`
36×	`sqrt-div`
32×	`frac-add`
28×	`associate-*r/`
20×	`frac-times`
10×	`associate-*l/`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate--l+` `*-commutative` `flip-+`
1×	`+-commutative` `pow2` `pow1/2`

Counts

4 → 58

Calls

4 calls:

12.0ms	(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
4.0ms	(* (- phi1 phi2) (- phi1 phi2))
5.0ms	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
10.0ms	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
23.0ms	(* (- phi1 phi2) (- phi1 phi2))
26.0ms	(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
160.0ms	(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

simplify76.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	561	1915
1	2596	1903
2	5001	1903

prune489.0ms

Filtered

70 candidates to 46 candidates (65.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	66	13	79

Merged error: 20.5b

Counts

79 → 13

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	10	10
Picked	1	1
Done	2	2
Total	13	13

Merged error: 20.5b

Counts

13 → 13

regimes516.0ms

Accuracy

32.1% (13.0b remaining)

Error of 32.8b against oracle of 19.9b and baseline of 39.0b

bsearch323.0ms

Steps

Iters	Range		Point
8	2.7417959789681252e+82	2.3073686895453515e+85	4.211839799598552e+84
8	-3.506678384146156e-180	-2.1352498248621693e-183	-3.4664449046846123e-180
6	-6.269179574948309e-83	-1.164072771538563e-83	-1.1800918383419089e-83
9	-3.38508247816858e+146	-1.7270806460785741e+137	-3.3249148060297065e+146

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	58
1	76	58
2	81	58
3	91	58
4	97	58
5	97	58

end0.0ms

sample1.9s

Algorithm

intervals

Results

562.0ms	8520×	body	80	valid
379.0ms	1332×	body	640	valid
321.0ms	774×	body	1280	valid
149.0ms	700×	body	320	valid
50.0ms	358×	body	160	valid