Details

sample155.0ms

Algorithm

intervals

Results

62.0ms	252×	body	80	valid
23.0ms	31×	body	640	valid
23.0ms	23×	body	1280	valid
14.0ms	28×	body	320	valid
3.0ms	9×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
5	1878
4	761
3	231
2	72
1	34
0	17

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
3.1b	(cos (/ (+ phi2 phi1) 2.0))

rewrite78.0ms

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` `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 (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
11.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
38.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
25.0ms	(cos (/ (+ phi2 phi1) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

587.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
698.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
101.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
45.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify2.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	4293
2	1093
1	359
0	142

prune711.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
3.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

5.0ms	(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
8.0ms	(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
24.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

895.0ms	(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
622.0ms	(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
173.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5153
3	3851
2	1072
1	414
0	183

prune924.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

11.0ms	(* (hypot (* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
72.0ms	(* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2))
34.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))

series946.0ms

Counts

4 → 12

Calls

4 calls:

674.0ms	(* (hypot (* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
174.0ms	(* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2))
47.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
51.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5009
3	3230
2	988
1	398
0	197

prune1.1s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 4.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- lambda1 lambda2))
0.5b	(cbrt (- lambda1 lambda2))
0.5b	(cbrt (- lambda1 lambda2))
3.1b	(cos (/ (+ phi2 phi1) 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

7.0ms	(cbrt (- lambda1 lambda2))
14.0ms	(cbrt (- lambda1 lambda2))
6.0ms	(cbrt (- lambda1 lambda2))
17.0ms	(cos (/ (+ phi2 phi1) 2.0))

series720.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (- lambda1 lambda2))
245.0ms	(cbrt (- lambda1 lambda2))
221.0ms	(cbrt (- lambda1 lambda2))
43.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5003
4	2085
3	845
2	395
1	201
0	99

prune715.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 4.5b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.4s	8245×	body	80	valid
1.3s	821×	body	1280	valid
1.0s	1265×	body	640	valid
937.0ms	743×	body	320	valid
92.0ms	344×	body	160	valid