Details

sample202.0ms

Algorithm

intervals

Results

51.0ms	271×	body	80	valid
41.0ms	32×	body	1280	valid
28.0ms	33×	body	640	valid
11.0ms	21×	body	320	valid
4.0ms	11×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3108
4	953
3	258
2	76
1	34
0	17

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
2.7b	(cos (/ (+ phi2 phi1) 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
3×	`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×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
25.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms	(cos (/ (+ phi2 phi1) 2))

series842.0ms

Counts

3 → 9

Calls

3 calls:

703.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
116.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
23.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	4005
2	945
1	307
0	128

prune576.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (cos (/ (+ phi1 phi2) 2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (/ (+ phi1 phi2) 2)) (- lambda1 lambda2))
2.7b	(cos (/ (+ phi1 phi2) 2))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`associate-r`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-l`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 78

Calls

3 calls:

7.0ms	(* (hypot (* (cos (/ (+ phi1 phi2) 2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
37.0ms	(* (cos (/ (+ phi1 phi2) 2)) (- lambda1 lambda2))
16.0ms	(cos (/ (+ phi1 phi2) 2))

series850.0ms

Counts

3 → 9

Calls

3 calls:

643.0ms	(* (hypot (* (cos (/ (+ phi1 phi2) 2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
178.0ms	(* (cos (/ (+ phi1 phi2) 2)) (- lambda1 lambda2))
29.0ms	(cos (/ (+ phi1 phi2) 2))

simplify1.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	5002
2	1228
1	419
0	182

prune758.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))

rewrite58.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 44

Calls

4 calls:

19.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
22.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
42.0ms	(cos (/ (+ phi2 phi1) 2))
45.0ms	(cos (/ (+ phi2 phi1) 2))
26.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
5	2556
4	800
3	324
2	133
1	80
0	49

prune624.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (log (exp (cos (/ (+ phi2 phi1) 2))))))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))

rewrite46.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*l/` `cos-mult`

Counts

4 → 43

Calls

4 calls:

20.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (log (exp (cos (/ (+ phi2 phi1) 2))))))
8.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))
9.0ms	(cos (/ (+ phi2 phi1) 2))

series125.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (log (exp (cos (/ (+ phi2 phi1) 2))))))
31.0ms	(cos (/ (+ phi2 phi1) 2))
31.0ms	(cos (/ (+ phi2 phi1) 2))
34.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5009
5	2582
4	753
3	308
2	149
1	89
0	52

prune536.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.3b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 4.0b against oracle of 3.8b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.1s	8378×	body	80	valid
1.8s	844×	body	1280	valid
1.3s	1236×	body	640	valid
501.0ms	722×	body	320	valid
202.0ms	356×	body	160	valid