Details

Time bar (total: 15.1s)

sample72.0ms

Algorithm
intervals
Results
19.0ms48×body640valid
18.0ms263×body80valid
10.0ms24×body1280valid
3.0ms16×body320valid
2.0ms13×body160valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
13232
26932
317732
441432
5101432
6331232
done500132

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
41.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
130×associate-*l/
97×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
12×add-sqr-sqrt
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×add-exp-log add-cbrt-cube
5×associate-*l*
4×add-log-exp
3×associate-*r* sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 115
Calls
4 calls:
10.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
47.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
402.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify444.0ms

Counts
127 → 127
Iterations

Useful iterations: done (437.0ms)

IterNodesCost
04417086
111356625
done50006593

prune457.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 28.4b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(* R (- phi2 phi1))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×*-un-lft-identity associate-*r*
3×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- add-log-exp difference-of-squares unswap-sqr
Counts
1 → 26
Calls
1 calls:
10.0ms
(* R (- phi2 phi1))

series35.0ms

Counts
1 → 3
Calls
1 calls:
35.0ms
(* R (- phi2 phi1))

simplify1.9s

Counts
29 → 29
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
052217
1112206
2278186
3786186
42093186
done5000186

prune81.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 28.3b

localize23.0ms

Local error

Found 4 expressions with local error:

4.1b
(cos (/ (+ phi1 phi2) 2.0))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
41.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
176×associate-*l/
96×flip3-- 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:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
259.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series511.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
428.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify458.0ms

Counts
112 → 112
Iterations

Useful iterations: done (451.0ms)

IterNodesCost
04238318
111877826
done50017808

prune587.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 28.3b

localize25.0ms

Local error

Found 4 expressions with local error:

4.1b
(cos (/ (+ phi1 phi2) 2.0))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
41.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite379.0ms

Algorithm
rewrite-expression-head
Rules
2240×associate-*l/
1408×frac-times
1344×flip3-- flip--
1296×cbrt-div
642×sqrt-div
640×frac-add
560×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 → 676
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
180.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series505.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
419.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.2s

Counts
688 → 688
Iterations

Useful iterations: 0 (247.0ms)

IterNodesCost
0291093206
done500093206

prune1.8s

Pruning

17 alts after pruning (13 fresh and 4 done)

Merged error: 28.1b

regimes1.0s

Accuracy

81.6% (3.9b remaining)

Error of 29.1b against oracle of 25.2b and baseline of 46.5b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02269
12769
done2769

end0.0ms

sample1.9s

Algorithm
intervals
Results
584.0ms8468×body80valid
395.0ms1316×body640valid
335.0ms784×body1280valid
153.0ms685×body320valid
52.0ms371×body160valid