Details

sample185.0ms

Algorithm

intervals

Results

72.0ms	266×	body	80	valid
30.0ms	46×	body	640	valid
26.0ms	29×	body	1280	valid
12.0ms	27×	body	320	valid
3.0ms	8×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	257	16
4	826	16
5	2355	16
done	5000	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.4b	(cos (/ (+ phi1 phi2) 2.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r`
3×	`expm1-log1p-u` `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 → 53

Calls

3 calls:

15.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
39.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))

series988.0ms

Counts

3 → 9

Calls

3 calls:

766.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
172.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
50.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.4s

Counts

62 → 62

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	125	990
1	289	983
2	840	835
3	2758	824
done	5000	823

prune367.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

localize20.0ms

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)))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.4b	(cos (/ (+ phi1 phi2) 2.0))

rewrite136.0ms

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:

15.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
57.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
46.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))

series297.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
142.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
38.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
47.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.8s

Counts

85 → 85

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	120	1104
1	221	993
2	581	873
3	1674	868
done	5000	865

prune498.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))))
0.3b	(expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))))
3.4b	(cos (/ (+ phi1 phi2) 2.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

29.0ms	(* (- lambda1 lambda2) (log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))))
0.0ms	(expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms	(log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))))
21.0ms	(cos (/ (+ phi1 phi2) 2.0))

series689.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (- lambda1 lambda2) (log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))))
218.0ms	(expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))
201.0ms	(log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))))
48.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.4s

Counts

77 → 77

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	126	1204
1	252	1045
2	690	834
3	2006	827
done	5000	825

prune545.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log1p (exp (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))))
0.5b	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
0.5b	(log (expm1 (log1p (exp (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))))))
3.4b	(cos (/ (+ phi1 phi2) 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

0.0ms	(expm1 (log1p (exp (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))))
1.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
3.0ms	(log (expm1 (log1p (exp (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))))))
18.0ms	(cos (/ (+ phi1 phi2) 2.0))

series654.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(expm1 (log1p (exp (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))))
82.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
270.0ms	(log (expm1 (log1p (exp (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))))))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify3.0s

Counts

57 → 57

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	90	741
1	178	600
2	384	513
3	918	503
4	2195	492
done	5000	489

prune363.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

regimes644.0ms

Accuracy

0% (0.1b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	18	16
done	18	16

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.5s	8440×	body	80	valid
1.1s	1279×	body	640	valid
632.0ms	734×	body	1280	valid
297.0ms	707×	body	320	valid
129.0ms	351×	body	160	valid