Details

Time bar (total: 29.6s)

sample335.0ms

Algorithm
intervals
Results
168.0ms104×body1280valid
104.0ms78×body640valid
32.0ms40×body320valid
7.0ms15×body160valid
4.0ms19×body80valid

simplify51.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize47.0ms

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))))
3.2b
(sin (- lambda1 lambda2))
3.3b
(cos (- lambda1 lambda2))

rewrite75.0ms

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)))))
32.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

series206.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
138.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms
(sin (- lambda1 lambda2))
31.0ms
(cos (- lambda1 lambda2))

simplify2.4s

Counts
56 → 56
Iterations
IterNodes
done5001
42565
31169
2480
1211
0101

prune686.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize76.0ms

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b
(cos (- lambda1 lambda2))

rewrite59.0ms

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×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 52
Calls
4 calls:
12.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
17.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
28.0ms
(cos (- lambda1 lambda2))

series253.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (cos lambda1) (sin lambda2))
22.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
155.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms
(cos (- lambda1 lambda2))

simplify2.0s

Counts
64 → 64
Iterations
IterNodes
done5005
32585
2726
1276
0122

prune675.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

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

rewrite62.0ms

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
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-+ flip-+ sin-mult
Counts
4 → 59
Calls
4 calls:
26.0ms
(* (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)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
22.0ms
(* (sin lambda1) (sin lambda2))
12.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series335.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (cos lambda1) (sin lambda2))
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
79.0ms
(* (sin lambda1) (sin lambda2))
164.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify2.3s

Counts
71 → 71
Iterations
IterNodes
done5012
33046
2872
1323
0133

prune793.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1))))
0.4b
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))
0.4b
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))
1.1b
(- (cos phi1) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
769×pow1
456×pow-prod-down
247×add-cbrt-cube add-exp-log
195×prod-exp cbrt-unprod
111×pow-prod-up
45×pow-sqr
25×associate-*l/
20×cos-mult
15×pow-plus
7×frac-times associate-*r/
6×add-log-exp
5×pow2
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt insert-posit16
3×associate-*r* associate-*l* *-commutative
2×swap-sqr
1×sub-neg flip3-- diff-log cube-unmult flip--
Counts
4 → 316
Calls
4 calls:
742.0ms
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1))))
166.0ms
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))
226.0ms
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))
14.0ms
(- (cos phi1) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))

series741.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1))))
167.0ms
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))
141.0ms
(* (* (* (cos phi2) (cos lambda2)) (cos lambda1)) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))
257.0ms
(- (cos phi1) (* (* (cos phi2) (cos lambda2)) (cos lambda1)))

simplify3.2s

Counts
328 → 328
Iterations
IterNodes
done5014
22869
1599
0206

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes920.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations
IterNodes
done48
148
033

end0.0ms

sample11.3s

Algorithm
intervals
Results
6.3s3533×body1280valid
3.0s2331×body640valid
1.3s975×body320valid
249.0ms439×body160valid
163.0ms722×body80valid