Details

Time bar (total: 38.2s)

sample190.0ms

Algorithm
intervals
Results
59.0ms47×body640valid
47.0ms273×body80valid
18.0ms18×body1280valid
10.0ms19×body320valid
5.0ms14×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01732
13232
26932
324032
496032
done500032

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
2.9b
(cos (/ (+ phi1 phi2) 2.0))
35.8b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite405.0ms

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:
140.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
198.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
203.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
50.0ms
(cos (/ (+ phi1 phi2) 2.0))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
846.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify977.0ms

Counts
147 → 147
Iterations

Useful iterations: done (956.0ms)

IterNodesCost
04557854
113677209
done50006873

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.7b

localize82.0ms

Local error

Found 4 expressions with local error:

2.9b
(cos (* 0.5 (+ phi2 phi1)))
2.9b
(cos (* 0.5 (+ phi2 phi1)))
2.9b
(cos (* 0.5 (+ phi2 phi1)))
35.8b
(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:
17.0ms
(cos (* 0.5 (+ phi2 phi1)))
18.0ms
(cos (* 0.5 (+ phi2 phi1)))
18.0ms
(cos (* 0.5 (+ phi2 phi1)))
499.0ms
(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))))

series1.1s

Counts
4 → 12
Calls
4 calls:
48.0ms
(cos (* 0.5 (+ phi2 phi1)))
44.0ms
(cos (* 0.5 (+ phi2 phi1)))
44.0ms
(cos (* 0.5 (+ phi2 phi1)))
931.0ms
(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))))

simplify2.2s

Counts
70 → 70
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02105872
15505441
230374389
done50014387

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.2b

localize135.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
2.9b
(cos (* 0.5 (+ phi2 phi1)))
2.9b
(cos (* 0.5 (+ phi2 phi1)))
35.8b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite808.0ms

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:
277.0ms
(- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
18.0ms
(cos (* 0.5 (+ phi2 phi1)))
18.0ms
(cos (* 0.5 (+ phi2 phi1)))
488.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.6s

Counts
4 → 12
Calls
4 calls:
800.0ms
(- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
49.0ms
(cos (* 0.5 (+ phi2 phi1)))
43.0ms
(cos (* 0.5 (+ phi2 phi1)))
1.7s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.8s

Counts
75 → 75
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02618496
17077909
238527815
done50017813

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.2b

localize212.0ms

Local error

Found 4 expressions with local error:

2.9b
(cos (* 0.5 (+ phi2 phi1)))
2.9b
(cos (* 0.5 (+ phi2 phi1)))
4.6b
(* (sin (* 0.5 phi2)) (pow lambda1 2))
35.8b
(sqrt (+ (+ (* (pow lambda1 2) (+ (* (pow (sin (* 0.5 phi2)) 2) (pow (sin (* 0.5 phi1)) 2)) (* (pow (cos (* 0.5 phi1)) 2) (pow (cos (* 0.5 phi2)) 2)))) (- (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* 2 (+ (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi2)) (pow lambda1 2))))) (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite543.0ms

Algorithm
rewrite-expression-head
Rules
80×frac-add
52×flip3-- flip--
50×sqrt-div
44×associate-*r/
25×flip3-+ flip-+
24×frac-times
15×add-sqr-sqrt
12×associate-*l/
9×add-exp-log
8×add-cube-cbrt *-un-lft-identity associate-*r*
6×add-cbrt-cube
5×pow1
4×unpow-prod-down cos-sum add-log-exp unswap-sqr
3×associate-*l* prod-exp sqrt-prod
2×distribute-rgt-in distribute-lft-in unpow2 sqr-pow
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp *-commutative cbrt-unprod
Counts
4 → 108
Calls
4 calls:
21.0ms
(cos (* 0.5 (+ phi2 phi1)))
20.0ms
(cos (* 0.5 (+ phi2 phi1)))
48.0ms
(* (sin (* 0.5 phi2)) (pow lambda1 2))
437.0ms
(sqrt (+ (+ (* (pow lambda1 2) (+ (* (pow (sin (* 0.5 phi2)) 2) (pow (sin (* 0.5 phi1)) 2)) (* (pow (cos (* 0.5 phi1)) 2) (pow (cos (* 0.5 phi2)) 2)))) (- (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* 2 (+ (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi2)) (pow lambda1 2))))) (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))))) (* (- phi1 phi2) (- phi1 phi2))))

series4.3s

Counts
4 → 12
Calls
4 calls:
44.0ms
(cos (* 0.5 (+ phi2 phi1)))
44.0ms
(cos (* 0.5 (+ phi2 phi1)))
98.0ms
(* (sin (* 0.5 phi2)) (pow lambda1 2))
4.1s
(sqrt (+ (+ (* (pow lambda1 2) (+ (* (pow (sin (* 0.5 phi2)) 2) (pow (sin (* 0.5 phi1)) 2)) (* (pow (cos (* 0.5 phi1)) 2) (pow (cos (* 0.5 phi2)) 2)))) (- (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* 2 (+ (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi2)) (pow lambda1 2))))) (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.2s

Counts
120 → 120
Iterations

Useful iterations: done (1.1s)

IterNodesCost
052531905
1157728023
done500125919

prune3.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 17.8b

regimes2.7s

Accuracy

43.8% (11.9b remaining)

Error of 29.5b against oracle of 17.6b and baseline of 38.8b

bsearch6.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
053116
175116
done75116

end0.0ms

sample7.1s

Algorithm
intervals
Results
2.4s8460×body80valid
1.7s1269×body640valid
1.1s777×body1280valid
610.0ms733×body320valid
132.0ms369×body160valid