Details

sample102.0ms

Algorithm

intervals

Results

25.0ms	264×	body	80	valid
18.0ms	40×	body	640	valid
18.0ms	26×	body	1280	valid
11.0ms	22×	body	320	valid
3.0ms	16×	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

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: 36.1b

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))))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
32.8b	(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))))
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))))

series183.0ms

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))
141.0ms	(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 (26.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune268.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 23.7b

Counts

148 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
32.8b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite58.0ms

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)))
4.0ms	(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))))

series161.0ms

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))
143.0ms	(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

prune368.0ms

Filtered

102 candidates to 204 candidates (-100.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	202	10	212

Merged error: 23.7b

Counts

212 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
32.8b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series157.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1283	3713
1	5001	3633

prune271.0ms

Filtered

71 candidates to 120 candidates (-69.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	121	9	130

Merged error: 23.7b

Counts

130 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) 3)
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
32.8b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (cbrt (pow (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) 3))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
130×	`associate-*l/`
74×	`associate-*r/`
73×	`cube-div` `cos-mult`
72×	`cbrt-div`
13×	`pow1`
7×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
6×	`add-cube-cbrt` `pow-pow` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow-exp` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `unpow3` `cube-prod` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `flip-+` `sqr-pow`

Counts

4 → 192

Calls

4 calls:

4.0ms	(pow (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (cbrt (pow (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) 3))) (* (- phi1 phi2) (- phi1 phi2))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) 3)
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (cbrt (pow (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) 3))) (* (- phi1 phi2) (- phi1 phi2))))

simplify109.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2428	7839
1	5001	7758

prune392.0ms

Filtered

104 candidates to 204 candidates (-96.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	205	8	213

Merged error: 23.7b

Counts

213 → 8

regimes662.0ms

Accuracy

39.3% (8.2b remaining)

Error of 33.7b against oracle of 25.5b and baseline of 39.0b

bsearch60.0ms

Steps

Iters	Range		Point
6	2.339259205354612e+129	2.463774962507644e+130	4.352973789041405e+129

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	21
1	31	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

817.0ms	8465×	body	80	valid
584.0ms	1283×	body	640	valid
527.0ms	781×	body	1280	valid
228.0ms	679×	body	320	valid
79.0ms	350×	body	160	valid

Details

sample102.0ms

simplify51.0ms

prune5.0ms

localize16.0ms

rewrite52.0ms

series183.0ms

simplify59.0ms

prune268.0ms

localize18.0ms

rewrite58.0ms

series161.0ms

simplify104.0ms

prune368.0ms

localize22.0ms

rewrite44.0ms

series157.0ms

simplify55.0ms

prune271.0ms

localize21.0ms

rewrite60.0ms

series168.0ms

simplify109.0ms

prune392.0ms

regimes662.0ms

bsearch60.0ms

simplify1.0ms

end0.0ms

sample2.9s

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