Details

Time bar (total: 18.3s)

sample69.0ms

Algorithm
intervals
Results
19.0ms268×body80valid
11.0ms26×body1280valid
11.0ms36×body640valid
4.0ms19×body320valid
2.0ms13×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
13232
26932
317932
442232
5104032
6336532
done500032

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
35.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite103.0ms

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:
27.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
51.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
33.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
415.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify435.0ms

Counts
147 → 147
Iterations

Useful iterations: done (427.0ms)

IterNodesCost
04557854
112127209
done50007047

prune484.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.6b

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.6b
(cos (* 0.5 (+ phi2 phi1)))
3.6b
(cos (* 0.5 (+ phi2 phi1)))
35.6b
(sqrt (+ (- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
21×flip3-- flip--
18×sqrt-div
16×frac-add
8×frac-times
6×add-sqr-sqrt add-log-exp
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log cos-sum associate-*r/ associate-*l/ add-cbrt-cube
3×distribute-rgt-in distribute-lft-in sqrt-prod
2×associate--l+
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 63
Calls
4 calls:
39.0ms
(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.0ms
(cos (* 0.5 (+ phi2 phi1)))
3.0ms
(cos (* 0.5 (+ phi2 phi1)))
111.0ms
(sqrt (+ (- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series954.0ms

Counts
4 → 12
Calls
4 calls:
288.0ms
(- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
28.0ms
(cos (* 0.5 (+ phi2 phi1)))
33.0ms
(cos (* 0.5 (+ phi2 phi1)))
603.0ms
(sqrt (+ (- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify797.0ms

Counts
75 → 75
Iterations

Useful iterations: 2 (199.0ms)

IterNodesCost
02275490
15674982
225324684
done50004684

prune423.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
1.8b
(- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.6b
(cos (* 0.5 (+ phi2 phi1)))
35.6b
(sqrt (+ (- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
21×flip3-- flip--
18×sqrt-div
16×frac-add
8×add-sqr-sqrt frac-times
7×add-cube-cbrt *-un-lft-identity
6×pow1 add-log-exp
5×add-exp-log
4×associate-*r/ associate-*l/ add-cbrt-cube
3×unpow-prod-down pow-unpow sqrt-prod
2×distribute-rgt-in cos-sum distribute-lft-in associate--l+
1×pow-to-exp sub-neg rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 diff-log pow-exp flip-+ unpow2 sqr-pow
Counts
4 → 72
Calls
4 calls:
13.0ms
(pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
79.0ms
(- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
4.0ms
(cos (* 0.5 (+ phi2 phi1)))
164.0ms
(sqrt (+ (- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.5s

Counts
4 → 12
Calls
4 calls:
139.0ms
(pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)
975.0ms
(- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
26.0ms
(cos (* 0.5 (+ phi2 phi1)))
1.4s
(sqrt (+ (- (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.3s

Counts
84 → 84
Iterations

Useful iterations: 2 (312.0ms)

IterNodesCost
03117871
18106698
237846529
done50016529

prune647.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.8b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b
(log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)))
1.8b
(- (* (log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2))) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.6b
(cos (* 0.5 (+ phi2 phi1)))
35.6b
(sqrt (+ (- (* (log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2))) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
21×flip3-- flip--
18×sqrt-div
16×frac-add
9×add-sqr-sqrt log-pow
8×frac-times add-cube-cbrt exp-prod *-un-lft-identity
6×pow1 add-log-exp
4×add-exp-log associate-*r/ associate-*l/ add-cbrt-cube
3×unpow-prod-down log-prod sqrt-prod
2×distribute-rgt-in cos-sum distribute-lft-in associate--l+
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log rem-log-exp flip-+ unpow2 sqr-pow
Counts
4 → 74
Calls
4 calls:
12.0ms
(log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)))
43.0ms
(- (* (log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2))) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.0ms
(cos (* 0.5 (+ phi2 phi1)))
173.0ms
(sqrt (+ (- (* (log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2))) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.4s

Counts
4 → 12
Calls
4 calls:
131.0ms
(log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)))
950.0ms
(- (* (log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2))) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
26.0ms
(cos (* 0.5 (+ phi2 phi1)))
1.3s
(sqrt (+ (- (* (log (exp (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2))) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.2s

Counts
86 → 86
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
03298221
18167368
237656584
done50016584

prune687.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.8b

regimes638.0ms

Accuracy

50% (9.1b remaining)

Error of 29.0b against oracle of 19.9b and baseline of 38.0b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04792
16292
26492
done6492

end0.0ms

sample1.8s

Algorithm
intervals
Results
553.0ms8366×body80valid
385.0ms1326×body640valid
326.0ms787×body1280valid
149.0ms722×body320valid
53.0ms371×body160valid