Details

Time bar (total: 15.8s)

sample126.0ms

Algorithm
intervals
Results
47.0ms274×body80valid
20.0ms29×body1280valid
19.0ms40×body640valid
7.0ms23×body320valid
4.0ms18×body160valid

simplify61.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
142×associate-*l/
102×flip3-- flip--
68×frac-times
66×sqrt-div
64×frac-add
44×pow1
34×associate-*r/
17×pow-prod-down
16×add-exp-log add-cbrt-cube
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow-sqr pow-prod-up add-log-exp
3×sqrt-prod
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 135
Calls
4 calls:
139.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
146.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series872.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
42.0ms
(cos (/ (+ phi1 phi2) 2.0))
41.0ms
(cos (/ (+ phi1 phi2) 2.0))
639.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify66.0ms

Counts
147 → 147

prune769.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
198×flip3-- flip--
196×frac-times
138×sqrt-div
136×frac-add
130×associate-*l/
74×associate-*r/
73×cos-mult
12×pow1 add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
4×add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
1×pow2 rem-sqrt-square sqr-cos sqrt-pow1 flip3-+ pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 192
Calls
4 calls:
17.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
210.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series754.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
38.0ms
(cos (/ (+ phi1 phi2) 2.0))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))
618.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify136.0ms

Counts
204 → 204

prune979.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.5b

localize45.0ms

Local error

Found 4 expressions with local error:

3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (cos (/ (+ phi1 phi2) 2.0)) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite617.0ms

Algorithm
rewrite-expression-head
Rules
96×flip3-- associate-*l/ flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
15.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
17.0ms
(cos (/ (+ phi1 phi2) 2.0))
554.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (cos (/ (+ phi1 phi2) 2.0)) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series731.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
38.0ms
(cos (/ (+ phi1 phi2) 2.0))
35.0ms
(cos (/ (+ phi1 phi2) 2.0))
628.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (cos (/ (+ phi1 phi2) 2.0)) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify62.0ms

Counts
112 → 112

prune682.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.5b

localize35.0ms

Local error

Found 4 expressions with local error:

3.2b
(cos (/ (+ phi1 phi2) 2.0))
3.2b
(cos (/ (+ phi1 phi2) 2.0))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
64×associate-*r/
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 172
Calls
4 calls:
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
104.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
121.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts
4 → 12
Calls
4 calls:
39.0ms
(cos (/ (+ phi1 phi2) 2.0))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
648.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
580.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify86.0ms

Counts
184 → 184

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 25.5b

regimes745.0ms

Accuracy

71.3% (3.9b remaining)

Error of 29.5b against oracle of 25.5b and baseline of 39.2b

bsearch2.0ms

simplify57.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.7s8362×body80valid
1.4s1335×body640valid
1.0s790×body1280valid
498.0ms743×body320valid
127.0ms333×body160valid