Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	249×	body	80	valid
13.0ms	42×	body	640	valid
8.0ms	19×	body	1280	valid
6.0ms	28×	body	320	valid
1.0ms	9×	body	160	valid

simplify57.0ms

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

prune4.0ms

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: 38.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite56.0ms

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:

14.0ms	(* (* (- 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))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
419.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify69.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune427.0ms

Filtered

147 candidates to 77 candidates (52.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Merged error: 23.9b

Counts

148 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

97×	`flip3--` `flip--`
82×	`associate-r/` `associate-l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `*-commutative` `flip-+`

Counts

4 → 113

Calls

4 calls:

8.0ms	(* (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))
23.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
411.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1321	3716
1	5001	3613

prune500.0ms

Filtered

125 candidates to 86 candidates (68.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	125	8	133

Merged error: 23.9b

Counts

133 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(cos (/ (+ phi1 phi2) 2.0))
406.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1349	3745
1	5002	3672

prune442.0ms

Filtered

128 candidates to 69 candidates (53.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	127	9	136

Merged error: 23.9b

Counts

136 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite66.0ms

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)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(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))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
33.0ms	(cos (/ (+ phi1 phi2) 2.0))
419.0ms	(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 (43.0ms)

Iter	Nodes	Cost
0	2471	7439
1	5001	7337

prune620.0ms

Filtered

204 candidates to 102 candidates (50.0%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	204	9	213

Merged error: 23.9b

Counts

213 → 9

regimes612.0ms

Accuracy

75.2% (3.4b remaining)

Error of 28.3b against oracle of 24.9b and baseline of 38.6b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	53
1	33	53

end0.0ms

sample2.0s

Algorithm

intervals

Results

624.0ms	8471×	body	80	valid
423.0ms	1311×	body	640	valid
357.0ms	795×	body	1280	valid
166.0ms	725×	body	320	valid
62.0ms	389×	body	160	valid

Details

sample66.0ms

simplify57.0ms

prune4.0ms

localize21.0ms

rewrite56.0ms

series568.0ms

simplify69.0ms

prune427.0ms

localize17.0ms

rewrite53.0ms

series628.0ms

simplify60.0ms

prune500.0ms

localize21.0ms

rewrite44.0ms

series511.0ms

simplify60.0ms

prune442.0ms

localize17.0ms

rewrite66.0ms

series523.0ms

simplify104.0ms

prune620.0ms

regimes612.0ms

bsearch4.0ms

simplify2.0ms

end0.0ms

sample2.0s

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