Details

Time bar (total: 23.1s)

sample133.0ms

Algorithm
intervals
Results
44.0ms284×body80valid
27.0ms47×body640valid
14.0ms17×body1280valid
8.0ms20×body320valid
4.0ms12×body160valid

simplify916.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
38.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite323.0ms

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:
97.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
181.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series947.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
48.0ms
(cos (/ (+ phi1 phi2) 2.0))
37.0ms
(cos (/ (+ phi1 phi2) 2.0))
669.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify779.0ms

Counts
147 → 147

prune702.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
38.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1
5×add-exp-log add-cbrt-cube
4×add-log-exp
3×unpow-prod-down pow-unpow cube-prod sqrt-prod
1×cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 unpow3 pow-exp flip-+ rem-cube-cbrt sqr-pow
Counts
4 → 116
Calls
4 calls:
7.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
16.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
175.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series788.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
40.0ms
(cos (/ (+ phi1 phi2) 2.0))
35.0ms
(cos (/ (+ phi1 phi2) 2.0))
622.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify706.0ms

Counts
128 → 128

prune750.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 28.6b

localize42.0ms

Local error

Found 4 expressions with local error:

4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
38.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite903.0ms

Algorithm
rewrite-expression-head
Rules
128×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:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
812.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series776.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(cos (/ (+ phi1 phi2) 2.0))
47.0ms
(cos (/ (+ phi1 phi2) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
662.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify796.0ms

Counts
112 → 112

prune948.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 28.6b

localize85.0ms

Local error

Found 4 expressions with local error:

4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
39.8b
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
39.8b
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite930.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×cbrt-div
128×frac-times frac-add
64×associate-*r/
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
2×flip3-+ pow1/3 flip-+
Counts
4 → 168
Calls
4 calls:
18.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
397.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
454.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
700.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
795.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify911.0ms

Counts
180 → 180

prune2.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 28.6b

regimes1.0s

Accuracy

33.8% (9.0b remaining)

Error of 34.5b against oracle of 25.4b and baseline of 39.1b

bsearch112.0ms

Steps
ItersRangePoint
9
7.026962070260041e-10
0.1320695871758506
0.1234906905453276

simplify979.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.9s8420×body80valid
1.2s1296×body640valid
819.0ms764×body1280valid
388.0ms765×body320valid
127.0ms368×body160valid