Details

sample177.0ms

Algorithm

intervals

Results

70.0ms	259×	body	80	valid
31.0ms	39×	body	640	valid
30.0ms	25×	body	1280	valid
9.0ms	17×	body	320	valid
4.0ms	9×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1878
4	761
3	231
2	72
1	34
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize54.0ms

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)))
3.3b	(cos (/ (+ phi2 phi1) 2))

rewrite66.0ms

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` `insert-posit16` `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 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
37.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
20.0ms	(cos (/ (+ phi2 phi1) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

486.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
588.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
109.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
40.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4185
2	1076
1	360
0	144

prune689.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
0.4b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
3.3b	(cos (/ (+ phi2 phi1) 2))
3.3b	(cos (/ (+ phi2 phi1) 2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

20.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
47.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
10.0ms	(cos (/ (+ phi2 phi1) 2))
11.0ms	(cos (/ (+ phi2 phi1) 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

904.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
649.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
23.0ms	(cos (/ (+ phi2 phi1) 2))
33.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1160
1	334
0	127

prune774.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

localize69.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2))) R))
0.4b	(expm1 (cos (/ (+ phi2 phi1) 2)))
3.3b	(cos (/ (+ phi2 phi1) 2))
3.3b	(cos (/ (+ phi2 phi1) 2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
1×	`expm1-log1p` `associate-r` `*-commutative` `expm1-udef`

Counts

4 → 56

Calls

4 calls:

51.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2))) R))
0.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
10.0ms	(cos (/ (+ phi2 phi1) 2))
11.0ms	(cos (/ (+ phi2 phi1) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2))) R))
77.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
25.0ms	(cos (/ (+ phi2 phi1) 2))
39.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.9s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	3103
2	881
1	303
0	122

prune621.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.4b	(log1p (cos (/ (+ phi2 phi1) 2)))
3.3b	(cos (/ (+ phi2 phi1) 2))
3.3b	(cos (/ (+ phi2 phi1) 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 44

Calls

4 calls:

0.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms	(log1p (cos (/ (+ phi2 phi1) 2)))
11.0ms	(cos (/ (+ phi2 phi1) 2))
11.0ms	(cos (/ (+ phi2 phi1) 2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
59.0ms	(log1p (cos (/ (+ phi2 phi1) 2)))
38.0ms	(cos (/ (+ phi2 phi1) 2))
23.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
4	1577
3	558
2	252
1	135
0	68

prune530.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

regimes995.0ms

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.5s	1299×	body	640	valid
1.5s	8247×	body	80	valid
1.3s	841×	body	1280	valid
466.0ms	735×	body	320	valid
108.0ms	374×	body	160	valid