Details

sample65.0ms

Algorithm

intervals

Results

17.0ms	263×	body	80	valid
14.0ms	48×	body	640	valid
10.0ms	24×	body	1280	valid
3.0ms	16×	body	320	valid
2.0ms	13×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	195	16
4	491	16
5	1386	16
6	4985	16
done	5000	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize14.0ms

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)))
4.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

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))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
11.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series968.0ms

Counts

4 → 12

Calls

4 calls:

382.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
463.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
91.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
33.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.6s

Counts

75 → 75

Iterations

Useful iterations: 3 (648.0ms)

Iter	Nodes	Cost
0	139	1279
1	321	1271
2	977	1077
3	3582	1060
done	5000	1060

prune292.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
6.0ms	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
14.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series980.0ms

Counts

4 → 12

Calls

4 calls:

389.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
471.0ms	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
92.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.2s

Counts

83 → 83

Iterations

Useful iterations: 3 (833.0ms)

Iter	Nodes	Cost
0	157	1525
1	362	1408
2	1105	1251
3	4458	1219
done	5000	1219

prune318.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
4.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`associate-*l/`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

20.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
1.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
1.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series201.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
28.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
54.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.8s

Counts

109 → 109

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	131	1572
1	276	1275
2	888	1143
3	4842	1138
done	5000	1138

prune388.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.6b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

6.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
19.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
12.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series199.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
92.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
27.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.6s

Counts

85 → 85

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	120	1104
1	226	993
2	594	873
3	1787	868
4	4301	865
done	5001	865

prune332.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.1b

regimes375.0ms

Accuracy

0% (0.1b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	21	16
done	21	16

end0.0ms

sample1.9s

Algorithm

intervals

Results

556.0ms	8468×	body	80	valid
392.0ms	1316×	body	640	valid
334.0ms	784×	body	1280	valid
146.0ms	685×	body	320	valid
50.0ms	371×	body	160	valid