Details

sample67.0ms

Algorithm

intervals

Results

16.0ms	254×	body	80	valid
13.0ms	49×	body	640	valid
11.0ms	27×	body	1280	valid
4.0ms	20×	body	320	valid
2.0ms	17×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	257	16
4	826	16
5	2355	16
done	5000	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
25.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

396.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
490.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
94.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.6s

Counts

75 → 75

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	139	1279
1	327	1271
2	960	1077
3	3194	1060
done	5000	1059

prune262.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
22.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series981.0ms

Counts

4 → 12

Calls

4 calls:

384.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
477.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
89.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.6s

Counts

75 → 75

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	139	1279
1	327	1271
2	960	1077
3	3194	1060
done	5000	1059

prune287.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`associate-*l/`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

30.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
5.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series199.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
27.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
52.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify739.0ms

Counts

109 → 109

Iterations

Useful iterations: done (736.0ms)

Iter	Nodes	Cost
0	131	1572
1	267	1275
2	862	1143
done	5000	1138

prune371.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `cos-mult`

Counts

4 → 39

Calls

4 calls:

4.0ms	(cbrt (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series205.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.1s

Counts

51 → 51

Iterations

Useful iterations: 4 (166.0ms)

Iter	Nodes	Cost
0	55	582
1	103	561
2	177	497
3	338	490
4	649	486
5	1007	486
6	1872	486
done	5000	486

prune251.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.6b

regimes387.0ms

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	21	16
done	21	16

end0.0ms

sample1.9s

Algorithm

intervals

Results

532.0ms	8367×	body	80	valid
360.0ms	1269×	body	640	valid
319.0ms	794×	body	1280	valid
142.0ms	676×	body	320	valid
49.0ms	370×	body	160	valid