Details

Time bar (total: 36.2s)

sample141.0ms

Algorithm
intervals
Results
39.0ms284×body80valid
35.0ms41×body640valid
18.0ms21×body1280valid
10.0ms21×body320valid
2.0ms8×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
13232
26932
324032
496032
done500032

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.1b
(cos (/ (+ phi1 phi2) 2.0))
3.1b
(cos (/ (+ phi1 phi2) 2.0))
35.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite311.0ms

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:
72.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
187.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series946.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
56.0ms
(cos (/ (+ phi1 phi2) 2.0))
47.0ms
(cos (/ (+ phi1 phi2) 2.0))
670.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify684.0ms

Counts
147 → 147
Iterations

Useful iterations: done (673.0ms)

IterNodesCost
04557854
113677209
done50006873

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.6b

localize47.0ms

Local error

Found 4 expressions with local error:

3.1b
(cos (* 0.5 (+ phi2 phi1)))
3.1b
(cos (* 0.5 (+ phi2 phi1)))
3.1b
(cos (* 0.5 (+ phi2 phi1)))
35.5b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite557.0ms

Algorithm
rewrite-expression-head
Rules
20×flip3-- flip--
18×sqrt-div
16×frac-add
8×frac-times
6×add-sqr-sqrt cos-sum
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log associate-*r/ associate-*l/ add-cbrt-cube add-log-exp
3×distribute-rgt-in distribute-lft-in sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 58
Calls
4 calls:
20.0ms
(cos (* 0.5 (+ phi2 phi1)))
20.0ms
(cos (* 0.5 (+ phi2 phi1)))
22.0ms
(cos (* 0.5 (+ phi2 phi1)))
488.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series982.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(cos (* 0.5 (+ phi2 phi1)))
48.0ms
(cos (* 0.5 (+ phi2 phi1)))
36.0ms
(cos (* 0.5 (+ phi2 phi1)))
854.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts
70 → 70
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02105872
15505441
230374389
done50014387

prune719.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.9b

localize69.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.1b
(cos (* 0.5 (+ phi2 phi1)))
3.1b
(cos (* 0.5 (+ phi2 phi1)))
35.5b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
21×flip3-- flip--
18×sqrt-div
16×frac-add
9×add-log-exp
8×frac-times
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log cos-sum associate-*r/ associate-*l/ add-cbrt-cube
3×sqrt-prod
2×distribute-rgt-in distribute-lft-in diff-log
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate--l+ sum-log flip-+
Counts
4 → 63
Calls
4 calls:
564.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
10.0ms
(cos (* 0.5 (+ phi2 phi1)))
10.0ms
(cos (* 0.5 (+ phi2 phi1)))
988.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series5.1s

Counts
4 → 12
Calls
4 calls:
903.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
43.0ms
(cos (* 0.5 (+ phi2 phi1)))
50.0ms
(cos (* 0.5 (+ phi2 phi1)))
4.1s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.4s

Counts
75 → 75
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02978799
17878164
242138025
done50008023

prune944.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.9b

localize97.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos (* 0.5 (+ phi2 phi1))) 2)
2.4b
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
3.1b
(cos (* 0.5 (+ phi2 phi1)))
35.5b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
21×flip3-- flip--
18×sqrt-div
16×frac-add
9×add-log-exp
8×add-sqr-sqrt frac-times
7×add-cube-cbrt *-un-lft-identity
6×pow1
5×add-exp-log
4×associate-*r/ associate-*l/ add-cbrt-cube
3×unpow-prod-down pow-unpow sqrt-prod
2×cos-sum diff-log
1×distribute-rgt-in pow-to-exp sub-neg rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 flip3-+ pow1/2 pow-exp associate--l+ sum-log flip-+ unpow2 sqr-pow
Counts
4 → 72
Calls
4 calls:
15.0ms
(pow (cos (* 0.5 (+ phi2 phi1))) 2)
560.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
14.0ms
(cos (* 0.5 (+ phi2 phi1)))
1.0s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series6.5s

Counts
4 → 12
Calls
4 calls:
55.0ms
(pow (cos (* 0.5 (+ phi2 phi1))) 2)
1.3s
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
34.0ms
(cos (* 0.5 (+ phi2 phi1)))
5.2s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify675.0ms

Counts
84 → 84
Iterations

Useful iterations: done (662.0ms)

IterNodesCost
034910783
19959999
done50009811

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 16.9b

regimes1.5s

Accuracy

50.9% (9.1b remaining)

Error of 28.7b against oracle of 19.6b and baseline of 38.1b

bsearch3.0ms

simplify16.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
060157
179153
280153
done80153

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.9s8415×body80valid
952.0ms1288×body640valid
807.0ms755×body320valid
779.0ms778×body1280valid
163.0ms338×body160valid