Details

sample5.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 43.652344%

Results

34.0ms	285×	body	80	valid
20.0ms	41×	body	640	valid
16.0ms	23×	body	1280	valid
6.0ms	17×	body	320	valid
3.0ms	12×	body	160	valid

simplify52.0ms

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

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: 39.4b

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))))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
36.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite54.0ms

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))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* (- 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))
136.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify61.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune232.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	5	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	6	148

Merged error: 26.2b

Counts

148 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
36.3b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

212×	`frac-times`
210×	`flip3--` `flip--`
142×	`associate-*l/`
138×	`sqrt-div`
136×	`frac-add`
81×	`cos-mult`
79×	`associate-*r/`
33×	`pow1`
16×	`add-exp-log` `add-cbrt-cube`
14×	`pow-prod-down`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-plus` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `sqr-cos` `pow-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `associate-l` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 213

Calls

4 calls:

15.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
135.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify111.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2553	7988
1	5002	7819

prune356.0ms

Filtered

114 candidates to 225 candidates (-97.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	225	6	231

Merged error: 26.2b

Counts

231 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))))
0.6b	(+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))))
3.8b	(cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))
36.3b	(sqrt (+ (/ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))))) 2) (* (- phi1 phi2) (- phi1 phi2))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

32×	`frac-times`
24×	`flip3--` `flip--`
16×	`associate-*l/`
11×	`flip3-+` `flip-+`
10×	`pow1` `-un-lft-identity` `sqrt-div` `associate-r/`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `frac-add`
6×	`add-cube-cbrt` `add-log-exp`
5×	`associate-r`
4×	`cos-sum`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`associate-+l-` `associate-+r-` `sum-cos` `count-2` `cos-2` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `cos-diff` `sub-neg` `rem-sqrt-square` `associate-+r+` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

15.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))))
45.0ms	(+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))))
22.0ms	(cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))
14.0ms	(sqrt (+ (/ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))))) 2) (* (- phi1 phi2) (- phi1 phi2))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))))
9.0ms	(+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))))
6.0ms	(cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))
537.0ms	(sqrt (+ (/ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))))) 2) (* (- phi1 phi2) (- phi1 phi2))))

simplify117.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	999	3121
1	4337	2817
2	5001	2763

prune296.0ms

Filtered

81 candidates to 111 candidates (-37.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	109	8	117

Merged error: 26.2b

Counts

117 → 8

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* R (- phi2 phi1))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-r*`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`

Counts

1 → 26

Calls

1 calls:

6.0ms

(* R (- phi2 phi1))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* R (- phi2 phi1))

simplify46.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	112	98
1	462	88
2	1883	88
3	5002	88

prune27.0ms

Filtered

17 candidates to 29 candidates (-70.6%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	20	9	29
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	21	16	37

Merged error: 26.2b

Counts

37 → 16

regimes1.6s

Accuracy

74.4% (3.6b remaining)

Error of 28.7b against oracle of 25.2b and baseline of 39.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	55
1	43	55
2	44	55
3	44	55

end0.0ms

sample8.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 43.652344%

Results

922.0ms	8467×	body	80	valid
635.0ms	1277×	body	640	valid
579.0ms	803×	body	1280	valid
268.0ms	740×	body	320	valid
97.0ms	365×	body	160	valid

Details

sample5.7s

simplify52.0ms

prune5.0ms

localize16.0ms

rewrite54.0ms

series178.0ms

simplify61.0ms

prune232.0ms

localize20.0ms

rewrite76.0ms

series177.0ms

simplify111.0ms

prune356.0ms

localize21.0ms

rewrite101.0ms

series586.0ms

simplify117.0ms

prune296.0ms

localize4.0ms

rewrite7.0ms

series7.0ms

simplify46.0ms

prune27.0ms

regimes1.6s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample8.7s

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