Details

Time bar (total: 31.0s)

sample362.0ms

Algorithm
intervals
Results
218.0ms106×body1280valid
80.0ms67×body640valid
28.0ms39×body320valid
7.0ms14×body160valid
6.0ms30×body80valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune61.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize78.0ms

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))))
4.0b
(sin (- lambda1 lambda2))
4.1b
(cos (- lambda1 lambda2))

rewrite25.0ms

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)))))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms
(sin (- lambda1 lambda2))
8.0ms
(cos (- lambda1 lambda2))

series255.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
171.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(sin (- lambda1 lambda2))
37.0ms
(cos (- lambda1 lambda2))

simplify2.7s

Counts
52 → 52
Iterations
IterNodes
done5002
42583
31176
2476
1207
097

prune593.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0b
(sin (- lambda1 lambda2))

rewrite38.0ms

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×associate-+r+ sin-sum
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 49
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
14.0ms
(sin (- lambda1 lambda2))

series483.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
71.0ms
(* (sin lambda1) (sin lambda2))
359.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
31.0ms
(sin (- lambda1 lambda2))

simplify3.5s

Counts
61 → 61
Iterations
IterNodes
done5000
34234
2794
1275
0120

prune614.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite43.0ms

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×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+ sin-mult
Counts
4 → 57
Calls
4 calls:
10.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
19.0ms
(* (sin lambda1) (sin lambda2))
12.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (cos lambda1) (sin lambda2))
40.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
75.0ms
(* (sin lambda1) (sin lambda2))
296.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify3.1s

Counts
69 → 69
Iterations
IterNodes
done5002
34076
2964
1328
0133

prune734.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos lambda1))
0.3b
(cbrt (cos lambda1))
0.3b
(cbrt (cos lambda1))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube add-exp-log
3×pow1/3
2×associate-+r+
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+
Counts
4 → 46
Calls
4 calls:
2.0ms
(cbrt (cos lambda1))
9.0ms
(cbrt (cos lambda1))
2.0ms
(cbrt (cos lambda1))
14.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series700.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(cbrt (cos lambda1))
132.0ms
(cbrt (cos lambda1))
128.0ms
(cbrt (cos lambda1))
309.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.5s

Counts
58 → 58
Iterations
IterNodes
done5005
33231
2606
1198
079

prune634.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done38
138
027

end0.0ms

sample12.7s

Algorithm
intervals
Results
7.7s3635×body1280valid
2.9s2270×body640valid
1.2s1014×body320valid
226.0ms674×body80valid
206.0ms405×body160valid
14.0ms2×body2560valid