Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	271×	body	80	valid
11.0ms	39×	body	640	valid
10.0ms	25×	body	1280	valid
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify57.0ms

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: 3.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-l/` `-commutative`
1×	`hypot-udef` `flip3--` `flip--`

Counts

4 → 5

Calls

4 calls:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
2.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
5.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))

series922.0ms

Counts

4 → 12

Calls

4 calls:

364.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
441.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
86.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	210	148
1	659	128
2	2836	116
3	5002	112

prune55.0ms

Filtered

17 candidates to 15 candidates (88.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	14	3	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	4	18

Merged error: 3.3b

Counts

18 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot (- lambda1 lambda2) (- phi1 phi2))
0.0b	(* (hypot (- lambda1 lambda2) (- phi1 phi2)) R)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

1×	`hypot-udef` `*-commutative`

Counts

2 → 2

Calls

2 calls:

1.0ms	(hypot (- lambda1 lambda2) (- phi1 phi2))
2.0ms	(* (hypot (- lambda1 lambda2) (- phi1 phi2)) R)

series288.0ms

Counts

2 → 6

Calls

2 calls:

139.0ms	(hypot (- lambda1 lambda2) (- phi1 phi2))
149.0ms	(* (hypot (- lambda1 lambda2) (- phi1 phi2)) R)

simplify118.0ms

Algorithm

egg-herbie

Counts

8 → 8

Iterations

Useful iterations: 4 (113.0ms)

Iter	Nodes	Cost
0	102	46
1	280	45
2	913	41
3	4238	36
4	5001	35

prune21.0ms

Filtered

8 candidates to 7 candidates (87.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	8	0	8
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	8	4	12

Merged error: 3.3b

Counts

12 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (- phi2 phi1) R)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-*l/`
1×	`flip3--` `*-commutative` `flip--`

Counts

1 → 3

Calls

1 calls:

3.0ms

(* (- phi2 phi1) R)

series29.0ms

Counts

1 → 3

Calls

1 calls:

29.0ms

(* (- phi2 phi1) R)

simplify69.0ms

Algorithm

egg-herbie

Counts

6 → 6

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	14
1	91	12
2	222	12
3	600	12
4	2162	12
5	5002	12

prune14.0ms

Filtered

6 candidates to 4 candidates (66.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	6	0	6
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	6	4	10

Merged error: 3.3b

Counts

10 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (* 0.5 (+ phi2 phi1)))
3.1b	(* (+ (/ lambda2 lambda1) 1) (/ (* R phi1) lambda1))
4.3b	(/ (* R phi1) lambda1)
7.0b	(fma (- (/ phi2 (cos (* 0.5 (+ phi2 phi1))))) (* (+ (/ lambda2 lambda1) 1) (/ (* R phi1) lambda1)) (- (* lambda2 (* (cos (* 0.5 (+ phi2 phi1))) R))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`frac-times`
8×	`associate-/l*`
6×	`flip3-+` `flip-+`
5×	`associate-r/` `clear-num` `-commutative`
4×	`cos-sum` `frac-2neg`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-*l/` `div-inv`
1×	`associate-r` `un-div-inv` `fma-udef`

Counts

4 → 30

Calls

4 calls:

4.0ms	(cos (* 0.5 (+ phi2 phi1)))
7.0ms	(* (+ (/ lambda2 lambda1) 1) (/ (* R phi1) lambda1))
3.0ms	(/ (* R phi1) lambda1)
1.0ms	(fma (- (/ phi2 (cos (* 0.5 (+ phi2 phi1))))) (* (+ (/ lambda2 lambda1) 1) (/ (* R phi1) lambda1)) (- (* lambda2 (* (cos (* 0.5 (+ phi2 phi1))) R))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (* 0.5 (+ phi2 phi1)))
52.0ms	(* (+ (/ lambda2 lambda1) 1) (/ (* R phi1) lambda1))
18.0ms	(/ (* R phi1) lambda1)
276.0ms	(fma (- (/ phi2 (cos (* 0.5 (+ phi2 phi1))))) (* (+ (/ lambda2 lambda1) 1) (/ (* R phi1) lambda1)) (- (* lambda2 (* (cos (* 0.5 (+ phi2 phi1))) R))))

simplify36.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	259	289
1	1180	282
2	5002	267

prune125.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	42	4	46

Merged error: 3.3b

Counts

46 → 4

regimes134.0ms

Accuracy

0% (0.1b remaining)

Error of 3.8b against oracle of 3.7b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	8
1	17	8

end0.0ms

sample2.1s

Algorithm

intervals

Results

563.0ms	8407×	body	80	valid
527.0ms	781×	body	1280	valid
384.0ms	1308×	body	640	valid
159.0ms	735×	body	320	valid
48.0ms	332×	body	160	valid