Details

sample5.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 43.652344%

Results

24.0ms	195×	body	80	valid
13.0ms	29×	body	640	valid
9.0ms	90×	body	80	invalid
8.0ms	12×	body	1280	invalid
7.0ms	11×	body	1280	valid
6.0ms	12×	body	640	invalid
4.0ms	11×	body	320	valid
2.0ms	10×	body	160	valid
2.0ms	6×	body	320	invalid
0.0ms	2×	body	160	invalid

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

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))))

rewrite52.0ms

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))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(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))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* (- 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))
134.0ms	(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

prune244.0ms

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))))

rewrite73.0ms

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))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(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))))

series173.0ms

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))
132.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify109.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2553	7988
1	5002	7819

prune354.0ms

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))))

rewrite96.0ms

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:

14.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))))
44.0ms	(+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))))
21.0ms	(cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))
13.0ms	(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))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ (cos (+ (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0))) (cos (- (/ (+ phi1 phi2) 2.0) (/ (+ phi1 phi2) 2.0)))))
8.0ms	(+ (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)))
518.0ms	(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))))

simplify116.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (88.0ms)

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

prune301.0ms

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))

rewrite6.0ms

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))

simplify45.0ms

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

prune28.0ms

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

regimes1.4s

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

sample8.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 43.652344%

Results

620.0ms	5938×	body	80	valid
394.0ms	813×	body	640	valid
344.0ms	484×	body	1280	valid
257.0ms	2529×	body	80	invalid
225.0ms	464×	body	640	invalid
217.0ms	319×	body	1280	invalid
170.0ms	499×	body	320	valid
77.0ms	241×	body	320	invalid
63.0ms	266×	body	160	valid
22.0ms	99×	body	160	invalid

Details

sample5.4s

simplify51.0ms

prune5.0ms

localize16.0ms

rewrite52.0ms

series175.0ms

simplify61.0ms

prune244.0ms

localize20.0ms

rewrite73.0ms

series173.0ms

simplify109.0ms

prune354.0ms

localize21.0ms

rewrite96.0ms

series565.0ms

simplify116.0ms

prune301.0ms

localize4.0ms

rewrite6.0ms

series7.0ms

simplify45.0ms

prune28.0ms

regimes1.4s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample8.5s

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