Details

sample208.0ms

Algorithm

intervals

Results

68.0ms	309×	body	80	valid
59.0ms	37×	body	640	valid
33.0ms	24×	body	1280	valid
16.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify729.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2141
4	757
3	225
2	66
1	32
0	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
2.4b	(cos (/ (+ phi1 phi2) 2))
2.4b	(cos (/ (+ phi1 phi2) 2))
40.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite230.0ms

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-cbrt-cube` `add-exp-log`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `insert-posit16` `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 → 139

Calls

4 calls:

89.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
9.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
114.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series734.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
36.0ms	(cos (/ (+ phi1 phi2) 2))
36.0ms	(cos (/ (+ phi1 phi2) 2))
528.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.6s

Counts

151 → 151

Iterations

Iter	Nodes
2	6665
1	1344
0	460

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 27.4b

localize59.0ms

Local error

Found 4 expressions with local error:

27.9b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
27.9b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
27.9b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
40.0b	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

29930×	`associate-*l/`
20428×	`frac-times`
16050×	`flip3--` `flip--`
15576×	`cbrt-div`
5990×	`associate-*r/`
5826×	`sqrt-div`
5824×	`frac-add`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 5894

Calls

4 calls:

58.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
58.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
57.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
857.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.7s

Counts

4 → 12

Calls

4 calls:

377.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
331.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
361.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
625.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.4m

Counts

5906 → 5906

Iterations

Iter	Nodes
1	57410
0	22401

prune1.3m

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 26.6b

localize65.0ms

Local error

Found 4 expressions with local error:

2.4b	(cos (/ (+ phi1 phi2) 2))
3.1b	(exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))))
28.0b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
40.0b	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite769.0ms

Algorithm

rewrite-expression-head

Rules

156×	`associate-*l/`
108×	`flip3--` `flip--`
85×	`pow1`
80×	`log-div`
72×	`frac-times` `exp-diff`
66×	`sqrt-div`
64×	`frac-add`
36×	`associate-*r/`
34×	`pow-prod-down`
32×	`log-pow`
19×	`exp-prod`
17×	`add-exp-log`
8×	`prod-exp` `pow-sqr` `pow-prod-up`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`rem-log-exp`
4×	`pow-plus` `add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `log-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `exp-sum` `flip-+` `rem-exp-log`

Counts

4 → 163

Calls

4 calls:

11.0ms	(cos (/ (+ phi1 phi2) 2))
147.0ms	(exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))))
88.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
514.0ms	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series777.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2))
135.0ms	(exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))))
146.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
470.0ms	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.1s

Counts

175 → 175

Iterations

Iter	Nodes
2	6133
1	1285
0	500

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 25.9b

localize64.0ms

Local error

Found 4 expressions with local error:

28.0b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
28.0b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
28.0b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
40.0b	(sqrt (+ (exp (cbrt (* (* (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

125×	`pow1`
51×	`pow-prod-down`
48×	`log-pow`
43×	`add-exp-log`
42×	`associate-*l/`
24×	`log-div` `prod-exp`
18×	`flip3--` `flip--`
15×	`rem-log-exp`
12×	`frac-times` `pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `pow-plus` `associate-*r/`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow2` `log-prod` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 130

Calls

4 calls:

54.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
55.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
55.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
8.0ms	(sqrt (+ (exp (cbrt (* (* (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

series852.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
136.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
139.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
418.0ms	(sqrt (+ (exp (cbrt (* (* (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.0s

Counts

142 → 142

Iterations

Iter	Nodes
3	4591
2	1000
1	348
0	129

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 25.9b

regimes1.3s

Accuracy

60.4% (5.4b remaining)

Error of 28.6b against oracle of 23.2b and baseline of 36.8b

bsearch2.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	27
1	27
0	22

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	8520×	body	80	valid
1.1s	1269×	body	640	valid
719.0ms	763×	body	1280	valid
376.0ms	756×	body	320	valid
119.0ms	370×	body	160	valid