Details

Time bar (total: 35.3s)

sample207.0ms

Algorithm
intervals
Results
86.0ms266×body80valid
32.0ms46×body640valid
28.0ms29×body1280valid
14.0ms27×body320valid
3.0ms8×body160valid

simplify5.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
13232
26932
323832
474232
5197232
6448632
done500132

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
38.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite234.0ms

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:
25.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
17.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
158.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series886.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
33.0ms
(cos (/ (+ phi1 phi2) 2.0))
646.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify743.0ms

Counts
127 → 127
Iterations

Useful iterations: done (733.0ms)

IterNodesCost
04417086
112696625
done50006386

prune757.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.0b

localize36.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.8b
(- (* lambda1 lambda1) (* lambda2 lambda2))
28.6b
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
38.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
60×associate-*l/
48×flip3-- flip--
42×sqrt-div
40×frac-add
36×frac-times
18×associate-*r/
11×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×add-log-exp
5×pow1
4×times-frac associate-/r*
3×sqrt-prod
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+ associate-/l/ distribute-lft-out
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp clear-num cbrt-unprod div-inv associate-/l* difference-of-squares
Counts
4 → 102
Calls
4 calls:
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(- (* lambda1 lambda1) (* lambda2 lambda2))
41.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
158.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
52.0ms
(cos (/ (+ phi1 phi2) 2.0))
57.0ms
(- (* lambda1 lambda1) (* lambda2 lambda2))
191.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
858.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify709.0ms

Counts
114 → 114
Iterations

Useful iterations: done (699.0ms)

IterNodesCost
03705387
110755085
done50004855

prune779.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 27.0b

localize33.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.8b
(- (* lambda1 lambda1) (* lambda2 lambda2))
28.6b
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))
38.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite680.0ms

Algorithm
rewrite-expression-head
Rules
60×associate-*l/
48×flip3-- flip--
42×sqrt-div
40×frac-add
36×frac-times
18×associate-*r/
11×*-un-lft-identity
9×add-exp-log
8×add-sqr-sqrt add-cbrt-cube
7×add-cube-cbrt
6×add-log-exp
5×pow1
4×times-frac associate-/r*
3×sqrt-prod
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+ associate-/l/ distribute-lft-out
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp clear-num cbrt-unprod div-inv associate-/l* difference-of-squares
Counts
4 → 102
Calls
4 calls:
14.0ms
(cos (/ (+ phi1 phi2) 2.0))
8.0ms
(- (* lambda1 lambda1) (* lambda2 lambda2))
53.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))
591.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
40.0ms
(cos (/ (+ phi1 phi2) 2.0))
39.0ms
(- (* lambda1 lambda1) (* lambda2 lambda2))
215.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))
802.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify756.0ms

Counts
114 → 114
Iterations

Useful iterations: done (749.0ms)

IterNodesCost
03755648
110745061
done50004855

prune876.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 27.0b

localize25.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
38.0b
(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))))

rewrite843.0ms

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:
20.0ms
(cos (/ (+ phi1 phi2) 2.0))
19.0ms
(cos (/ (+ phi1 phi2) 2.0))
19.0ms
(cos (/ (+ phi1 phi2) 2.0))
490.0ms
(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))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
57.0ms
(cos (/ (+ phi1 phi2) 2.0))
51.0ms
(cos (/ (+ phi1 phi2) 2.0))
676.0ms
(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))))

simplify1.4s

Counts
688 → 688
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0291093206
done500087709

prune11.5s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 27.0b

regimes928.0ms

Accuracy

71.9% (4.0b remaining)

Error of 28.6b against oracle of 24.6b and baseline of 38.8b

bsearch6.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03077
13977
done3977

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.4s8440×body80valid
810.0ms1279×body640valid
762.0ms734×body1280valid
404.0ms707×body320valid
148.0ms351×body160valid