Details

Time bar (total: 3.9m)

sample163.0ms

Algorithm
intervals
Results
40.0ms282×body80valid
33.0ms41×body640valid
22.0ms26×body1280valid
14.0ms32×body320valid
3.0ms9×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done2001
52001
4757
3225
266
132
017

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize54.0ms

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))))

rewrite158.0ms

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:
36.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
12.0ms
(cos (/ (+ phi1 phi2) 2))
8.0ms
(cos (/ (+ phi1 phi2) 2))
94.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series736.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
28.0ms
(cos (/ (+ phi1 phi2) 2))
29.0ms
(cos (/ (+ phi1 phi2) 2))
568.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.3s

Counts
131 → 131
Iterations
IterNodes
done2000
22000
11296
0446

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 23.9b

localize76.0ms

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))))

rewrite532.0ms

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:
14.0ms
(cos (/ (+ phi1 phi2) 2))
13.0ms
(cos (/ (+ phi1 phi2) 2))
14.0ms
(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 (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

series655.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(cos (/ (+ phi1 phi2) 2))
37.0ms
(cos (/ (+ phi1 phi2) 2))
42.0ms
(cos (/ (+ phi1 phi2) 2))
540.0ms
(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))))

simplify1.5s

Counts
116 → 116
Iterations
IterNodes
done2002
22002
11273
0427

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 23.6b

localize83.0ms

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))))

rewrite611.0ms

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:
15.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(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 (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))))) (* (- phi1 phi2) (- phi1 phi2))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2))
39.0ms
(cos (/ (+ phi1 phi2) 2))
32.0ms
(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))))

simplify1.4s

Counts
116 → 116
Iterations
IterNodes
done2001
22001
11285
0429

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.6b

localize102.0ms

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

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
19506×associate-*l/
12996×frac-times
12960×flip3-- flip--
10866×associate-*r/
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:
7.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))
135.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2))) (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))))
619.0ms
(cbrt (* (+ (* (- phi1 phi2) (- phi1 phi2)) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2))) (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))) (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2))) (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
22.0ms
(cos (/ (+ phi1 phi2) 2))
28.0ms
(cos (/ (+ phi1 phi2) 2))
867.0ms
(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2))) (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))))
834.0ms
(cbrt (* (+ (* (- phi1 phi2) (- phi1 phi2)) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2))) (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))) (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2))) (cbrt (* (cbrt (cos (/ (+ phi1 phi2) 2))) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))))))

simplify45.2s

Counts
4607 → 4607
Iterations
IterNodes
done12389
012389

prune2.7m

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 19.5b

regimes938.0ms

Accuracy

44.7% (9.9b remaining)

Error of 29.4b against oracle of 19.6b and baseline of 37.4b

bsearch3.0ms

simplify6.0ms

Iterations
IterNodes
done33
133
025

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.5s8349×body80valid
991.0ms783×body1280valid
885.0ms1259×body640valid
452.0ms762×body320valid
130.0ms396×body160valid