Details

Time bar (total: 2.0m)

sample926.0ms

Algorithm
intervals
Results
613.0ms103×body1280valid
80.0ms68×body640valid
78.0ms30×body80valid
50.0ms39×body320valid
8.0ms16×body160valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
01420
12020
22120
done2120

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize652.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b
(sin (- lambda1 lambda2))
2.8b
(cos (- lambda1 lambda2))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
50.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
40.0ms
(sin (- lambda1 lambda2))
29.0ms
(cos (- lambda1 lambda2))

series764.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
409.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
212.0ms
(sin (- lambda1 lambda2))
77.0ms
(cos (- lambda1 lambda2))

simplify4.2s

Counts
52 → 52
Iterations

Useful iterations: 3 (928.0ms)

IterNodesCost
097702
1207687
2532615
31518613
done5000613

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.8b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b
(cos (- lambda1 lambda2))

rewrite325.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 48
Calls
4 calls:
52.0ms
(* (cos lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
55.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
212.0ms
(cos (- lambda1 lambda2))

series703.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (cos lambda1) (sin lambda2))
34.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
321.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
112.0ms
(cos (- lambda1 lambda2))

simplify8.6s

Counts
60 → 60
Iterations

Useful iterations: 3 (2.7s)

IterNodesCost
0115857
1262841
2815743
34052741
done5000741

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.7b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log flip-+ sin-mult
Counts
4 → 57
Calls
4 calls:
21.0ms
(* (cos lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
26.0ms
(* (sin lambda1) (sin lambda2))
151.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (cos lambda1) (sin lambda2))
47.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
156.0ms
(* (sin lambda1) (sin lambda2))
898.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify3.0s

Counts
69 → 69
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01311162
13181138
21226989
done5001985

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize382.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos phi1) 3)
0.5b
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
0.6b
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
0.7b
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite471.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt add-cbrt-cube add-log-exp
6×pow-unpow
4×unpow-prod-down cube-prod
3×cube-div pow-pow associate-*r/ pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp flip3-+ unpow3 associate--l+ flip-+ sqr-pow
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log pow-prod-down frac-add prod-exp sum-log cos-mult sum-cubes flip-- cbrt-unprod sin-mult distribute-lft-out
Counts
4 → 75
Calls
4 calls:
39.0ms
(pow (cos phi1) 3)
42.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
76.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
267.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series6.7s

Counts
4 → 12
Calls
4 calls:
54.0ms
(pow (cos phi1) 3)
5.2s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
639.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
763.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify7.2s

Counts
87 → 87
Iterations

Useful iterations: 2 (2.4s)

IterNodesCost
02041843
17121660
237591500
done50001500

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes2.2s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02336
13236
done3236

end0.0ms

sample1.2m

Algorithm
intervals
Results
53.0s3614×body1280valid
14.4s2337×body640valid
3.7s949×body320valid
1.6s399×body160valid
499.0ms701×body80valid