Details

sample108.0ms

Algorithm

intervals

Results

26.0ms	30×	body	1280	valid
25.0ms	255×	body	80	valid
21.0ms	42×	body	640	valid
5.0ms	17×	body	320	valid
3.0ms	13×	body	160	valid

simplify941.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	259	16
4	1037	16
done	5001	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize41.0ms

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
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))
12.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
38.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
19.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

577.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
715.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
155.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify780.0ms

Counts

75 → 75

Iterations

Useful iterations: done (776.0ms)

Iter	Nodes	Cost
0	142	1279
1	362	1255
2	1593	1098
done	5002	1096

prune701.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize30.0ms

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

rewrite411.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
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))
6.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
20.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
383.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

574.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
772.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
124.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
36.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify742.0ms

Counts

75 → 75

Iterations

Useful iterations: done (739.0ms)

Iter	Nodes	Cost
0	141	1279
1	364	1255
2	1551	1100
done	5002	1096

prune659.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.6b

localize41.0ms

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`associate-r` `add-cube-cbrt`
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` `pow-pow` `flip3--` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip--` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

50.0ms	(* (- 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)
9.0ms	(cos (/ (+ phi1 phi2) 2.0))

series336.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
40.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
79.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
52.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.8s

Counts

109 → 109

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	130	1572
1	324	1273
2	1961	1143
done	5001	1141

prune819.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 3.6b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

10.0ms	(* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))

series295.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))
39.0ms	(cos (/ (+ phi1 phi2) 2.0))
45.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify3.8s

Counts

81 → 81

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	73	1163
1	161	1067
2	519	973
3	3306	841
done	5000	830

prune656.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 3.6b

regimes1.1s

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: 0 (0.0ms)

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

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.9s	8252×	body	80	valid
1.3s	1308×	body	640	valid
778.0ms	827×	body	1280	valid
439.0ms	715×	body	320	valid
102.0ms	391×	body	160	valid