Details

sample107.0ms

Algorithm

intervals

Results

29.0ms	264×	body	80	valid
23.0ms	49×	body	640	valid
12.0ms	17×	body	1280	valid
8.0ms	21×	body	320	valid
3.0ms	15×	body	160	valid

simplify862.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	259	16
4	1055	16
done	5001	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize22.0ms

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)))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite69.0ms

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)))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

572.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
780.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
121.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify785.0ms

Counts

75 → 75

Iterations

Useful iterations: done (783.0ms)

Iter	Nodes	Cost
0	139	1279
1	335	1271
2	1431	1079
done	5002	1069

prune434.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.4b

localize34.0ms

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)))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite99.0ms

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:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
15.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
57.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
22.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

645.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
846.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
143.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
46.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify824.0ms

Counts

75 → 75

Iterations

Useful iterations: done (822.0ms)

Iter	Nodes	Cost
0	138	1279
1	339	1271
2	1409	1079
done	5002	1070

prune487.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`associate-*l/`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

24.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
75.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
21.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
18.0ms	(cos (/ (+ phi1 phi2) 2.0))

series282.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
132.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
48.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
39.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify698.0ms

Counts

85 → 85

Iterations

Useful iterations: done (695.0ms)

Iter	Nodes	Cost
0	120	1104
1	245	993
2	879	875
done	5001	870

prune528.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (* (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (sqrt (exp (cos (/ (+ phi1 phi2) 2.0))))))
0.7b	(* (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))))
3.5b	(cos (/ (+ phi1 phi2) 2.0))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-pow1`
36×	`add-sqr-sqrt` `exp-prod`
35×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`log-pow`
18×	`sqrt-prod`
16×	`pow1/2` `pow-prod-up`
12×	`pow-prod-down` `pow-sqr`
9×	`add-exp-log`
8×	`swap-sqr`
6×	`associate-r` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow2` `pow-plus` `rem-log-exp` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 113

Calls

4 calls:

118.0ms	(log (* (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (sqrt (exp (cos (/ (+ phi1 phi2) 2.0))))))
131.0ms	(* (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))))
20.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))

series193.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(log (* (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (sqrt (exp (cos (/ (+ phi1 phi2) 2.0))))))
68.0ms	(* (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (sqrt (exp (cos (/ (+ phi1 phi2) 2.0)))))
42.0ms	(cos (/ (+ phi1 phi2) 2.0))
45.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify3.8s

Counts

125 → 125

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	118	1995
1	245	1290
2	797	1106
3	4001	1066
done	5001	1062

prune608.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.4b

regimes624.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	18
1	19	18
done	19	18

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	1363×	body	640	valid
1.7s	8277×	body	80	valid
621.0ms	779×	body	1280	valid
542.0ms	717×	body	320	valid
99.0ms	374×	body	160	valid