Details

Time bar (total: 3.9m)

sample245.0ms

Algorithm
intervals
Results
71.0ms26×body1280valid
68.0ms282×body80valid
45.0ms41×body640valid
26.0ms32×body320valid
5.0ms9×body160valid

simplify711.0ms

Counts
1 → 1
Iterations
IterNodes
52141
4757
3225
266
132
017

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
2.0b
(cos (/ (+ phi1 phi2) 2))
2.0b
(cos (/ (+ phi1 phi2) 2))
34.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite176.0ms

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-cbrt-cube add-exp-log
5×associate-*l*
4×insert-posit16 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 → 119
Calls
4 calls:
24.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
9.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))
128.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series738.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
25.0ms
(cos (/ (+ phi1 phi2) 2))
26.0ms
(cos (/ (+ phi1 phi2) 2))
568.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.4s

Counts
131 → 131
Iterations
IterNodes
26515
11294
0446

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.8b

localize74.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (/ (+ phi1 phi2) 2))
2.0b
(cos (/ (+ phi1 phi2) 2))
2.0b
(cos (/ (+ phi1 phi2) 2))
34.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite571.0ms

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 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 104
Calls
4 calls:
8.0ms
(cos (/ (+ phi1 phi2) 2))
12.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(cos (/ (+ phi1 phi2) 2))
534.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

series660.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2))
32.0ms
(cos (/ (+ phi1 phi2) 2))
25.0ms
(cos (/ (+ phi1 phi2) 2))
572.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.5s

Counts
116 → 116
Iterations
IterNodes
26953
11271
0427

prune3.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.3b

localize100.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (/ (+ phi1 phi2) 2))
2.0b
(cos (/ (+ phi1 phi2) 2))
2.0b
(cos (/ (+ phi1 phi2) 2))
34.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite518.0ms

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 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 104
Calls
4 calls:
7.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(cos (/ (+ phi1 phi2) 2))
485.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))))) (* (- phi1 phi2) (- phi1 phi2))))

series692.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2))
24.0ms
(cos (/ (+ phi1 phi2) 2))
23.0ms
(cos (/ (+ phi1 phi2) 2))
615.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.3s

Counts
116 → 116
Iterations
IterNodes
26958
11283
0429

prune3.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.3b

localize94.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (/ (+ phi1 phi2) 2))
2.0b
(cos (/ (+ phi1 phi2) 2))
34.9b
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))))
43.6b
(cbrt (* (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))) (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
19506×associate-*l/
13026×associate-*r/
12996×frac-times
12960×flip3-- flip--
8640×frac-add
4488×cbrt-div sqrt-div
135×flip3-+ flip-+
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
1×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 pow3 rem-cbrt-cube
Counts
4 → 4595
Calls
4 calls:
12.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(cos (/ (+ phi1 phi2) 2))
145.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))))
546.0ms
(cbrt (* (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))) (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
33.0ms
(cos (/ (+ phi1 phi2) 2))
38.0ms
(cos (/ (+ phi1 phi2) 2))
874.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))))
1.5s
(cbrt (* (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))) (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))))))))

simplify30.7s

Counts
4607 → 4607
Iterations
IterNodes
118407
012395

prune2.8m

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 19.6b

regimes911.0ms

Accuracy

43.6% (10.3b remaining)

Error of 29.4b against oracle of 19.1b and baseline of 37.4b

bsearch2.0ms

simplify6.0ms

Iterations
IterNodes
233
133
025

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.7s8349×body80valid
909.0ms1259×body640valid
736.0ms783×body1280valid
416.0ms762×body320valid
173.0ms396×body160valid