Details

Time bar (total: 35.8s)

sample501.0ms

Algorithm
intervals
Results
251.0ms122×body1280valid
179.0ms71×body640valid
33.0ms33×body320valid
8.0ms13×body160valid
4.0ms17×body80valid

simplify18.0ms

Counts
1 → 1
Iterations
IterNodes
321
221
120
014

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize48.0ms

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))))
4.0b
(cos (- lambda1 lambda2))
4.2b
(sin (- lambda1 lambda2))

rewrite41.0ms

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 insert-posit16
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 → 44
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms
(cos (- lambda1 lambda2))
9.0ms
(sin (- lambda1 lambda2))

series257.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
189.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(cos (- lambda1 lambda2))
27.0ms
(sin (- lambda1 lambda2))

simplify1.1s

Counts
56 → 56
Iterations
IterNodes
42207
31046
2467
1209
0101

prune772.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b
(cos (- lambda1 lambda2))

rewrite102.0ms

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
4×insert-posit16
3×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative sum-log flip3-+ flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ flip-- unswap-sqr
Counts
4 → 58
Calls
4 calls:
79.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
12.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms
(cos (- lambda1 lambda2))

series367.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
153.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms
(cos (- lambda1 lambda2))

simplify1.4s

Counts
70 → 70
Iterations
IterNodes
32949
2898
1310
0128

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

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
4×insert-posit16
3×distribute-rgt-in distribute-lft-in
2×associate-+r+ sub-neg pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-+ flip3-- flip-+ flip-- sin-mult
Counts
4 → 67
Calls
4 calls:
68.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))))))
11.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
56.0ms
(* (sin lambda1) (sin lambda2))
290.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify5.5s

Counts
79 → 79
Iterations
IterNodes
37521
21313
1378
0148

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16
2×associate-+r+ *-commutative
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ associate-*r/ flip-+ sin-cos-mult sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
0.0ms
(atan2 (+ (* (cos phi2) (* (sin lambda1) (cos lambda2))) (* (cos phi2) (- (* (cos lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
20.0ms
(* (sin lambda1) (sin lambda2))
56.0ms
(* (cos phi2) (* (sin lambda1) (cos lambda2)))
18.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series540.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(atan2 (+ (* (cos phi2) (* (sin lambda1) (cos lambda2))) (* (cos phi2) (- (* (cos lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
59.0ms
(* (sin lambda1) (sin lambda2))
129.0ms
(* (cos phi2) (* (sin lambda1) (cos lambda2)))
325.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.5s

Counts
74 → 74
Iterations
IterNodes
35224
21033
1351
0142

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes659.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations
IterNodes
451
351
250
144
026

end0.0ms

sample17.2s

Algorithm
intervals
Results
10.7s3589×body1280valid
4.6s2325×body640valid
1.0s962×body320valid
289.0ms407×body160valid
237.0ms717×body80valid