Details

sample129.0ms

Algorithm

intervals

Results

55.0ms	265×	body	80	valid
23.0ms	26×	body	1280	valid
16.0ms	25×	body	640	valid
12.0ms	28×	body	320	valid
4.0ms	14×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1878
4	761
3	231
2	72
1	34
0	17

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
1.8b	(cos (/ (+ phi2 phi1) 2))

rewrite57.0ms

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` `insert-posit16` `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 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
32.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
17.0ms	(cos (/ (+ phi2 phi1) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

529.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
700.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
133.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
42.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4185
2	1076
1	360
0	144

prune700.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
1.8b	(cos (/ (+ phi1 phi2) 2))

rewrite83.0ms

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` `insert-posit16` `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 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
14.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
50.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
17.0ms	(cos (/ (+ phi1 phi2) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

611.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
689.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
117.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
38.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4260
2	1075
1	363
0	144

prune626.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
0.5b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))))
1.8b	(cos (/ (+ phi1 phi2) 2))
1.8b	(cos (/ (+ phi1 phi2) 2))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`pow1`
18×	`sqrt-prod`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`associate-l`
9×	`associate-r`
8×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `swap-sqr` `add-exp-log`
5×	`pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`associate-l/` `prod-exp` `-commutative` `cbrt-unprod`
1×	`pow2` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

42.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
20.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))))
17.0ms	(cos (/ (+ phi1 phi2) 2))
17.0ms	(cos (/ (+ phi1 phi2) 2))

series731.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
536.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))))
40.0ms	(cos (/ (+ phi1 phi2) 2))
39.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
3	2223
2	775
1	321
0	136

prune843.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) R)
0.4b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) R))
1.8b	(cos (/ (+ phi1 phi2) 2))
1.8b	(cos (/ (+ phi1 phi2) 2))

rewrite65.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

9.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) R)
22.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) R))
17.0ms	(cos (/ (+ phi1 phi2) 2))
16.0ms	(cos (/ (+ phi1 phi2) 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

891.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) R)
654.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) R))
22.0ms	(cos (/ (+ phi1 phi2) 2))
33.0ms	(cos (/ (+ phi1 phi2) 2))

simplify1.6s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1166
1	334
0	126

prune663.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.0b

regimes926.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.2s	1269×	body	640	valid
2.0s	8526×	body	80	valid
1.2s	794×	body	1280	valid
650.0ms	738×	body	320	valid
164.0ms	330×	body	160	valid