Details

Time bar (total: 22.4s)

sample362.0ms

Algorithm
intervals
Results
218.0ms112×body1280valid
76.0ms75×body640valid
20.0ms30×body320valid
5.0ms28×body80valid
5.0ms11×body160valid

simplify13.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.6b
(cos (- lambda1 lambda2))
3.6b
(sin (- lambda1 lambda2))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×cos-diff
2×cos-sum associate-+r+ sub-neg sin-sum
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms
(cos (- lambda1 lambda2))
17.0ms
(sin (- lambda1 lambda2))

series204.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
123.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
25.0ms
(cos (- lambda1 lambda2))
34.0ms
(sin (- lambda1 lambda2))

simplify1.1s

Counts
52 → 52
Iterations
IterNodes
done5000
31522
2538
1207
097

prune555.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.4b
(+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1))
3.6b
(sin (- lambda1 lambda2))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
3×associate-*r* associate-*l*
2×sin-sum
1×+-commutative sum-log sub-neg flip3-+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 47
Calls
4 calls:
18.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
19.0ms
(+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1))
8.0ms
(sin (- lambda1 lambda2))

series308.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (sin lambda1) (sin lambda2))
24.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
196.0ms
(+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1))
29.0ms
(sin (- lambda1 lambda2))

simplify689.0ms

Counts
59 → 59
Iterations
IterNodes
done5000
2924
1275
0120

prune799.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.4b
(+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-+ flip-+ sin-cos-mult sin-mult
Counts
4 → 56
Calls
4 calls:
9.0ms
(* (sin lambda1) (cos lambda2))
9.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
39.0ms
(+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1))

series333.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (sin lambda1) (cos lambda2))
64.0ms
(* (sin lambda1) (sin lambda2))
38.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
174.0ms
(+ (* (cos lambda2) (* (cos phi2) (cos lambda1))) (cos phi1))

simplify611.0ms

Counts
68 → 68
Iterations
IterNodes
done5001
21116
1314
0132

prune724.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize140.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (cbrt (pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.4b
(+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1))
0.5b
(cbrt (pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3))
0.6b
(pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-cbrt-cube add-exp-log
4×cube-div
3×pow-unpow flip3-+ flip-+
2×cube-mult cbrt-div unpow3 sqr-pow
1×pow-to-exp +-commutative sum-log pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 66
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (cbrt (pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
20.0ms
(+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1))
26.0ms
(cbrt (pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3))
53.0ms
(pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3)

series709.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (cbrt (pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
210.0ms
(+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1))
183.0ms
(cbrt (pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3))
275.0ms
(pow (+ (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (cos phi1)) 3)

simplify2.7s

Counts
78 → 78
Iterations
IterNodes
done5001
21945
1354
0122

prune768.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes870.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done32
132
022

end0.0ms

sample11.0s

Algorithm
intervals
Results
6.7s3546×body1280valid
2.6s2370×body640valid
705.0ms921×body320valid
222.0ms752×body80valid
184.0ms411×body160valid