Details

sample83.0ms

Algorithm

intervals

Results

19.0ms	260×	body	80	valid
17.0ms	33×	body	1280	valid
13.0ms	36×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	8
1	78	8
2	261	8
3	834	8
4	2600	8
5	5001	8
done	5001	8

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize18.0ms

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)))
3.3b	(cos (/ (+ phi1 phi2) 2.0))

rewrite42.0ms

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)
23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

394.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
485.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
92.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify36.0ms

Counts

75 → 75

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	328	677
1	1130	579
2	5001	569
done	5001	569

prune262.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0))))
3.3b	(cos (/ (+ phi1 phi2) 2.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log`
11×	`pow1` `add-sqr-sqrt` `add-cbrt-cube`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`add-cube-cbrt`
6×	`prod-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`associate-l/` `-commutative`
1×	`hypot-udef` `flip3--` `1-exp` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2))
10.0ms	(* (hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2)) R)
35.0ms	(* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0))))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series989.0ms

Counts

4 → 12

Calls

4 calls:

389.0ms	(hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2))
478.0ms	(* (hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2)) R)
94.0ms	(* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0))))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify38.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	372	730
1	1278	613
2	5002	603
done	5002	603

prune260.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (* 1 (log (exp (cos (/ (+ phi1 phi2) 2.0))))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.3b	(cos (/ (+ phi1 phi2) 2.0))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

11.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
53.0ms	(* (- lambda1 lambda2) (* 1 (log (exp (cos (/ (+ phi1 phi2) 2.0))))))
20.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series197.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
92.0ms	(* (- lambda1 lambda2) (* 1 (log (exp (cos (/ (+ phi1 phi2) 2.0))))))
27.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify95.0ms

Counts

88 → 88

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	309	677
1	936	567
2	3806	559
3	5002	539
done	5002	539

prune299.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (exp (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (log (exp (exp (cos (/ (+ phi1 phi2) 2.0))))))
0.5b	(exp (exp (cos (/ (+ phi1 phi2) 2.0))))
3.3b	(cos (/ (+ phi1 phi2) 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

10×	`log-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity` `log-pow`
7×	`pow1`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`rem-log-exp`
1×	`rem-exp-log`

Counts

4 → 57

Calls

4 calls:

7.0ms	(log (exp (exp (cos (/ (+ phi1 phi2) 2.0)))))
7.0ms	(log (log (exp (exp (cos (/ (+ phi1 phi2) 2.0))))))
26.0ms	(exp (exp (cos (/ (+ phi1 phi2) 2.0))))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series186.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(log (exp (exp (cos (/ (+ phi1 phi2) 2.0)))))
27.0ms	(log (log (exp (exp (cos (/ (+ phi1 phi2) 2.0))))))
80.0ms	(exp (exp (cos (/ (+ phi1 phi2) 2.0))))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify126.0ms

Counts

69 → 69

Iterations

Useful iterations: 4 (121.0ms)

Iter	Nodes	Cost
0	169	451
1	369	390
2	986	390
3	3356	388
4	5001	378
done	5001	378

prune266.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 2.5b

regimes406.0ms

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	9
1	24	9
2	24	9
done	24	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

551.0ms	8377×	body	80	valid
380.0ms	1279×	body	640	valid
344.0ms	821×	body	1280	valid
150.0ms	717×	body	320	valid
48.0ms	337×	body	160	valid