Details

sample123.0ms

Algorithm

intervals

Results

37.0ms	44×	body	640	valid
27.0ms	244×	body	80	valid
15.0ms	23×	body	1280	valid
9.0ms	28×	body	320	valid
3.0ms	11×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize22.0ms

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)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite80.0ms

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:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
16.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
48.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

609.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
751.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
139.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts

75 → 75

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	139	1279
1	327	1271
2	960	1077
3	3194	1060
done	5000	1059

prune448.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log`
11×	`pow1` `add-sqr-sqrt` `add-cbrt-cube`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`associate-r` `associate-l` `prod-exp`
4×	`expm1-log1p-u` `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) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
32.0ms	(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
48.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
18.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

600.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
659.0ms	(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
139.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
39.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.4s

Counts

76 → 76

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	150	1364
1	346	1301
2	989	1075
3	3206	1058
done	5000	1057

prune466.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.1b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite149.0ms

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:

25.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
65.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
42.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))

series303.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
138.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
47.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
50.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.9s

Counts

85 → 85

Iterations

Useful iterations: done (1.9s)

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

prune520.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
0.2b	(pow E (cos (/ (+ phi1 phi2) 2.0)))
0.5b	(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
4.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

63.0ms	(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
13.0ms	(pow E (cos (/ (+ phi1 phi2) 2.0)))
52.0ms	(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))

series459.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
122.0ms	(pow E (cos (/ (+ phi1 phi2) 2.0)))
109.0ms	(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
53.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.8s

Counts

101 → 101

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	143	1538
1	276	1303
2	785	1167
3	2527	1147
done	5000	1132

prune560.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 3.9b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	18
1	22	16
done	22	16

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.7s	1295×	body	640	valid
1.6s	8470×	body	80	valid
992.0ms	776×	body	1280	valid
391.0ms	693×	body	320	valid
99.0ms	336×	body	160	valid