Details

sample118.0ms

Algorithm

intervals

Results

40.0ms	262×	body	80	valid
21.0ms	44×	body	640	valid
11.0ms	18×	body	1280	valid
9.0ms	22×	body	320	valid
3.0ms	10×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1037
3	259
2	76
1	34
0	17

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize52.0ms

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)))
2.2b	(cos (/ (+ phi2 phi1) 2.0))

rewrite54.0ms

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))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
21.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
25.0ms	(cos (/ (+ phi2 phi1) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

588.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
698.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
140.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
36.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify1.3s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
2	1577
1	359
0	142

prune746.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
2.2b	(cos (* 0.5 (+ phi1 phi2)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
12×	`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×	`cos-sum` `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 → 87

Calls

4 calls:

0.0ms	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
12.0ms	(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
42.0ms	(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
9.0ms	(cos (* 0.5 (+ phi1 phi2)))

series1.8s

Counts

4 → 12

Calls

4 calls:

882.0ms	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
639.0ms	(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
188.0ms	(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
45.0ms	(cos (* 0.5 (+ phi1 phi2)))

simplify1.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1929
1	426
0	195

prune916.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 0.5 phi1)) (cos (* 0.5 phi2)))
0.1b	(- (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
0.2b	(* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))
0.2b	(* (- (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))) (- lambda1 lambda2))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`flip3--` `associate-l` `cos-mult` `flip--` `sin-mult`
8×	`frac-times`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `frac-sub` `log1p-expm1-u` `sub-div`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/`
1×	`fma-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

19.0ms	(* (cos (* 0.5 phi1)) (cos (* 0.5 phi2)))
40.0ms	(- (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
20.0ms	(* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))
148.0ms	(* (- (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))) (- lambda1 lambda2))

series806.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (cos (* 0.5 phi1)) (cos (* 0.5 phi2)))
156.0ms	(- (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
96.0ms	(* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))
468.0ms	(* (- (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))) (- lambda1 lambda2))

simplify2.9s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	3032
1	601
0	241

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 0.5 phi2)) (cos (* 0.5 phi1)))
0.1b	(- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
0.2b	(* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))
0.2b	(* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))) (- lambda1 lambda2))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`flip3--` `associate-l` `cos-mult` `flip--` `sin-mult`
8×	`frac-times`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `frac-sub` `log1p-expm1-u` `sub-div`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/`
1×	`fma-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

29.0ms	(* (cos (* 0.5 phi2)) (cos (* 0.5 phi1)))
56.0ms	(- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
40.0ms	(* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))
223.0ms	(* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))) (- lambda1 lambda2))

series714.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (cos (* 0.5 phi2)) (cos (* 0.5 phi1)))
132.0ms	(- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2))))
81.0ms	(* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))
414.0ms	(* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi1)) (sin (* 0.5 phi2)))) (- lambda1 lambda2))

simplify2.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	3098
1	617
0	247

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes866.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	26
1	26
0	20

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.6s	8366×	body	80	valid
1.4s	1309×	body	640	valid
1.1s	782×	body	1280	valid
336.0ms	768×	body	320	valid
107.0ms	398×	body	160	valid