Details

sample70.0ms

Algorithm

intervals

Results

18.0ms	282×	body	80	valid
11.0ms	27×	body	1280	valid
10.0ms	35×	body	640	valid
5.0ms	28×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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: 3.3b

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)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite48.0ms

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)
27.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

407.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
496.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
95.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.8s

Counts

75 → 75

Iterations

Useful iterations: done (1.8s)

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

prune277.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

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)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite49.0ms

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)
28.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

401.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
495.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
95.0ms	(* (- 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

prune309.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.1b

localize22.0ms

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))
0.4b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite57.0ms

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:

37.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series198.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
29.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
49.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify740.0ms

Counts

109 → 109

Iterations

Useful iterations: done (737.0ms)

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

prune410.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))
0.4b	(pow (* (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2)) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) 3)
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-prod-down` `pow-exp` `unpow2` `rem-cube-cbrt` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `cube-prod` `pow3` `prod-exp` `cbrt-unprod`

Counts

4 → 62

Calls

4 calls:

2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))
13.0ms	(pow (* (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2)) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) 3)
11.0ms	(cos (/ (+ phi1 phi2) 2.0))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series239.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))
56.0ms	(pow (* (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2)) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) 3)
28.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts

74 → 74

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	102	1085
1	212	901
2	549	688
3	2562	657
done	5001	639

prune347.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.1b

regimes389.0ms

Accuracy

0% (0.1b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample2.0s

Algorithm

intervals

Results

546.0ms	8358×	body	80	valid
348.0ms	1256×	body	640	valid
315.0ms	779×	body	1280	valid
152.0ms	757×	body	320	valid
54.0ms	413×	body	160	valid