Details

sample97.0ms

Algorithm

intervals

Results

28.0ms	299×	body	80	valid
24.0ms	25×	body	1280	valid
13.0ms	33×	body	640	valid
6.0ms	17×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
2.8b	(cos (/ (+ phi2 phi1) 2.0))

rewrite64.0ms

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 (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
10.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
36.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
16.0ms	(cos (/ (+ phi2 phi1) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

633.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
742.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
139.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
41.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify1.2s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
2	1577
1	359
0	142

prune738.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi2 phi1) 2.0)))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ phi2 phi1) 2.0)))
9.0ms	(cos (/ (+ phi2 phi1) 2.0))
15.0ms	(cos (/ (+ phi2 phi1) 2.0))
17.0ms	(cos (/ (+ phi2 phi1) 2.0))

series282.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (cos (/ (+ phi2 phi1) 2.0)))
49.0ms	(cos (/ (+ phi2 phi1) 2.0))
51.0ms	(cos (/ (+ phi2 phi1) 2.0))
39.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify1.8s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
4	2222
3	577
2	189
1	89
0	48

prune635.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.5b

localize121.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

15.0ms	(cos (/ (+ phi2 phi1) 2.0))
8.0ms	(cos (/ (+ phi2 phi1) 2.0))
8.0ms	(cos (/ (+ phi2 phi1) 2.0))
9.0ms	(cos (/ (+ phi2 phi1) 2.0))

series160.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cos (/ (+ phi2 phi1) 2.0))
37.0ms	(cos (/ (+ phi2 phi1) 2.0))
38.0ms	(cos (/ (+ phi2 phi1) 2.0))
38.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify1.5s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	1464
3	378
2	122
1	54
0	29

prune666.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 1.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
0.3b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

8.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
19.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
8.0ms	(cos (/ (+ phi2 phi1) 2.0))
9.0ms	(cos (/ (+ phi2 phi1) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
732.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
30.0ms	(cos (/ (+ phi2 phi1) 2.0))
32.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify1.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
2	1563
1	333
0	127

prune610.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 1.5b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.6s	8464×	body	80	valid
1.3s	1272×	body	640	valid
1.2s	751×	body	1280	valid
398.0ms	762×	body	320	valid
89.0ms	350×	body	160	valid