Details

Time bar (total: 32.0s)

sample392.0ms

Algorithm
intervals
Results
258.0ms118×body1280valid
77.0ms71×body640valid
26.0ms37×body320valid
5.0ms12×body160valid
4.0ms18×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01420
12020
22120
done2120

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.7b
(sin (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))

rewrite53.0ms

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:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
11.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms
(sin (- lambda1 lambda2))
26.0ms
(cos (- lambda1 lambda2))

series243.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
146.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
48.0ms
(sin (- lambda1 lambda2))
32.0ms
(cos (- lambda1 lambda2))

simplify4.7s

Counts
52 → 52
Iterations

Useful iterations: 3 (353.0ms)

IterNodesCost
097702
1204687
2458615
3967613
42013613
54634613
done5000613

prune345.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.8b
(cos (- lambda1 lambda2))

rewrite125.0ms

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×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 54
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
85.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(cos (- lambda1 lambda2))

series403.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
217.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
149.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(cos (- lambda1 lambda2))

simplify2.4s

Counts
66 → 66
Iterations

Useful iterations: 3 (936.0ms)

IterNodesCost
01211182
12891166
28701032
327531030
done50001030

prune411.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))

rewrite166.0ms

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
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 63
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
130.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
23.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))

series773.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
248.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
85.0ms
(* (sin lambda1) (sin lambda2))
410.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))

simplify3.6s

Counts
75 → 75
Iterations

Useful iterations: 2 (247.0ms)

IterNodesCost
01421487
13431463
211401274
346031274
done50001274

prune570.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos phi1) 3)
0.4b
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
0.6b
(pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3)
1.1b
(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite133.0ms

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:
4.0ms
(pow (cos phi1) 3)
39.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
26.0ms
(pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3)
63.0ms
(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series2.5s

Counts
4 → 12
Calls
4 calls:
31.0ms
(pow (cos phi1) 3)
1.8s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
314.0ms
(pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3)
316.0ms
(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify1.6s

Counts
87 → 87
Iterations

Useful iterations: 2 (387.0ms)

IterNodesCost
02111843
16141658
224401494
done50011494

prune927.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes950.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03180
14280
done4280

end0.0ms

sample11.5s

Algorithm
intervals
Results
6.5s3555×body1280valid
3.2s2408×body640valid
760.0ms975×body320valid
542.0ms375×body160valid
153.0ms687×body80valid