Details

Time bar (total: 31.1s)

sample440.0ms

Algorithm
intervals
Results
276.0ms109×body1280valid
103.0ms81×body640valid
26.0ms31×body320valid
7.0ms26×body80valid
5.0ms9×body160valid

simplify56.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize51.0ms

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))))
5.1b
(cos (- lambda1 lambda2))
5.2b
(sin (- lambda1 lambda2))

rewrite40.0ms

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)))))
19.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
12.0ms
(cos (- lambda1 lambda2))
8.0ms
(sin (- lambda1 lambda2))

series197.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
133.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))
30.0ms
(sin (- lambda1 lambda2))

simplify1.2s

Counts
56 → 56
Iterations
IterNodes
done2001
42001
31179
2486
1211
0101

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.2b
(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
4×insert-posit16
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 → 53
Calls
4 calls:
23.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
14.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
8.0ms
(sin (- lambda1 lambda2))

series438.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
325.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
39.0ms
(sin (- lambda1 lambda2))

simplify1.1s

Counts
65 → 65
Iterations
IterNodes
done2002
32002
2794
1280
0124

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos lambda1) (sin lambda2))
0.3b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite33.0ms

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×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 → 61
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (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))))))
9.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sin lambda1) (sin lambda2))
64.0ms
(* (cos lambda1) (sin lambda2))
30.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
329.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.2s

Counts
73 → 73
Iterations
IterNodes
done2011
32011
2954
1331
0137

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.4b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.5b
(* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b
(cbrt (* (* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
35×flip3-+ flip-+
32×frac-times
26×cbrt-div
16×associate-*l/
11×pow1
10×add-sqr-sqrt associate-*r/
8×*-un-lft-identity add-cube-cbrt add-log-exp
6×add-cbrt-cube add-exp-log
4×associate-+r+ insert-posit16
3×distribute-rgt-in distribute-lft-in swap-sqr associate-*r* associate-*l*
2×+-commutative sum-log
1×cbrt-prod pow2 pow-plus pow1/3 pow3 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up rem-cbrt-cube cbrt-unprod unswap-sqr
Counts
4 → 101
Calls
4 calls:
17.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
20.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
46.0ms
(* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
64.0ms
(cbrt (* (* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
316.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
359.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
405.0ms
(* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
334.0ms
(cbrt (* (* (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify1.6s

Counts
113 → 113
Iterations
IterNodes
done2000
22000
1606
0183

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes854.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done34
134
024

end0.0ms

sample14.8s

Algorithm
intervals
Results
9.0s3428×body1280valid
3.9s2431×body640valid
1.1s956×body320valid
320.0ms454×body160valid
249.0ms731×body80valid