Details

sample233.0ms

Algorithm

intervals

Results

97.0ms	261×	body	80	valid
49.0ms	43×	body	640	valid
37.0ms	26×	body	1280	valid
15.0ms	19×	body	320	valid
6.0ms	13×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	5440
5	1878
4	761
3	231
2	72
1	34
0	17

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize32.0ms

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)))
2.0b	(cos (/ (+ phi2 phi1) 2))

rewrite28.0ms

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))) (- phi1 phi2))
5.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
16.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
6.0ms	(cos (/ (+ phi2 phi1) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

512.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
621.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
158.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
45.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.4s

Counts

75 → 75

Iterations

Iter	Nodes
3	3962
2	1082
1	355
0	140

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
2.0b	(cos (/ (+ phi2 phi1) 2))
2.0b	(cos (/ (+ phi2 phi1) 2))
2.0b	(cos (/ (+ phi2 phi1) 2))

rewrite63.0ms

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`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 40

Calls

4 calls:

19.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
15.0ms	(cos (/ (+ phi2 phi1) 2))
14.0ms	(cos (/ (+ phi2 phi1) 2))
14.0ms	(cos (/ (+ phi2 phi1) 2))

series148.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
36.0ms	(cos (/ (+ phi2 phi1) 2))
25.0ms	(cos (/ (+ phi2 phi1) 2))
46.0ms	(cos (/ (+ phi2 phi1) 2))

simplify4.5s

Counts

52 → 52

Iterations

Iter	Nodes
8	3145
7	1396
6	874
5	656
4	441
3	226
2	118
1	75
0	47

prune881.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi2 phi1) 2))))
2.0b	(cos (/ (+ phi2 phi1) 2))
2.0b	(cos (/ (+ phi2 phi1) 2))
2.0b	(cos (/ (+ phi2 phi1) 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

18.0ms	(log (exp (cos (/ (+ phi2 phi1) 2))))
7.0ms	(cos (/ (+ phi2 phi1) 2))
6.0ms	(cos (/ (+ phi2 phi1) 2))
9.0ms	(cos (/ (+ phi2 phi1) 2))

series115.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(log (exp (cos (/ (+ phi2 phi1) 2))))
26.0ms	(cos (/ (+ phi2 phi1) 2))
28.0ms	(cos (/ (+ phi2 phi1) 2))
24.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.7s

Counts

56 → 56

Iterations

Iter	Nodes
8	2201
7	1092
6	664
5	474
4	336
3	190
2	115
1	83
0	51

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.4b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
2.0b	(cos (* 1/2 (+ phi1 phi2)))
2.0b	(cos (* 1/2 (+ phi1 phi2)))
2.1b	(cos (+ phi1 phi2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `cos-sum` `*-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`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`pow1/3`

Counts

4 → 45

Calls

4 calls:

1.0ms	(cbrt 2)
7.0ms	(cos (* 1/2 (+ phi1 phi2)))
7.0ms	(cos (* 1/2 (+ phi1 phi2)))
6.0ms	(cos (+ phi1 phi2))

series108.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(cbrt 2)
39.0ms	(cos (* 1/2 (+ phi1 phi2)))
39.0ms	(cos (* 1/2 (+ phi1 phi2)))
29.0ms	(cos (+ phi1 phi2))

simplify2.4s

Counts

55 → 55

Iterations

Iter	Nodes
8	2350
7	1581
6	1127
5	866
4	605
3	330
2	191
1	130
0	85

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

regimes719.0ms

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	24
1	24
0	19

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	8323×	body	80	valid
1.5s	1255×	body	640	valid
1.2s	804×	body	1280	valid
1.1s	751×	body	320	valid
217.0ms	348×	body	160	valid