Details

sample70.0ms

Algorithm

intervals

Results

18.0ms	265×	body	80	valid
14.0ms	32×	body	1280	valid
11.0ms	36×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	11×	body	160	valid

simplify785.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	196	16
4	497	16
5	1405	16
done	5000	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize17.0ms

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)))
3.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

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))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
12.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

433.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
517.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
109.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
36.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.7s

Counts

75 → 75

Iterations

Useful iterations: 3 (469.0ms)

Iter	Nodes	Cost
0	139	1279
1	326	1271
2	1056	1077
3	4415	1060
done	5000	1060

prune316.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

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))
3.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
11.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

384.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
539.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
89.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify459.0ms

Counts

75 → 75

Iterations

Useful iterations: done (457.0ms)

Iter	Nodes	Cost
0	138	1279
1	325	1271
2	1089	1077
done	5000	1064

prune280.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.4b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite30.0ms

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:

17.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
1.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series194.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
26.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
52.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify503.0ms

Counts

109 → 109

Iterations

Useful iterations: done (500.0ms)

Iter	Nodes	Cost
0	131	1572
1	286	1275
2	1049	1143
done	5000	1138

prune360.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))

series188.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.3s

Counts

52 → 52

Iterations

Useful iterations: 4 (184.0ms)

Iter	Nodes	Cost
0	48	501
1	89	494
2	165	444
3	378	437
4	1092	433
5	3311	433
done	5000	433

prune226.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.5b

regimes402.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.7b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	17	16
done	17	16

end0.0ms

sample1.9s

Algorithm

intervals

Results

544.0ms	8349×	body	80	valid
389.0ms	1321×	body	640	valid
353.0ms	842×	body	1280	valid
155.0ms	750×	body	320	valid
55.0ms	381×	body	160	valid