Details

Time bar (total: 29.0s)

sample359.0ms

Algorithm
intervals
Results
238.0ms120×body1280valid
71.0ms75×body640valid
18.0ms29×body320valid
5.0ms13×body160valid
3.0ms19×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.0b
(cos (- lambda1 lambda2))
2.1b
(sin (- lambda1 lambda2))

rewrite27.0ms

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
(cos (- lambda1 lambda2))
10.0ms
(sin (- lambda1 lambda2))

series252.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
186.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))
25.0ms
(sin (- lambda1 lambda2))

simplify2.6s

Counts
52 → 52
Iterations
IterNodes
done5001
42583
31180
2482
1207
097

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (cos lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.0b
(cos (- lambda1 lambda2))

rewrite55.0ms

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×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-+ sin-cos-mult unswap-sqr
Counts
4 → 49
Calls
4 calls:
24.0ms
(* (sin lambda1) (cos lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))

series261.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (sin lambda1) (cos lambda2))
23.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
145.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms
(cos (- lambda1 lambda2))

simplify2.9s

Counts
61 → 61
Iterations
IterNodes
done5004
44646
31854
2692
1281
0123

prune715.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize129.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (cos lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

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:
18.0ms
(* (sin lambda1) (cos lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
18.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin lambda1) (cos lambda2))
26.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
61.0ms
(* (sin lambda1) (sin lambda2))
170.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify2.3s

Counts
68 → 68
Iterations
IterNodes
done5001
33255
2873
1321
0135

prune702.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize199.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
0.4b
(* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)))
0.4b
(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
1.2b
(- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1))

rewrite746.0ms

Algorithm
rewrite-expression-head
Rules
127×pow1
72×pow-prod-down
49×add-cbrt-cube add-exp-log
33×prod-exp cbrt-unprod
26×cos-mult
21×associate-*l/
18×associate-*r/
9×pow-sqr pow-prod-up
8×frac-times add-log-exp
7×frac-add
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-*r*
3×distribute-rgt-in sub-neg distribute-lft-in pow-plus flip3-- flip--
2×sqr-cos associate-+r+ cube-unmult associate-*l* *-commutative
1×pow2 +-commutative sum-log flip3-+ diff-log swap-sqr sum-cubes flip-+
Counts
4 → 126
Calls
4 calls:
397.0ms
(+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
175.0ms
(* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)))
142.0ms
(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
27.0ms
(- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1))

series1.1s

Counts
4 → 12
Calls
4 calls:
283.0ms
(+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
354.0ms
(* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)))
186.0ms
(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
243.0ms
(- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1))

simplify3.0s

Counts
138 → 138
Iterations
IterNodes
done5000
23693
1724
0228

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes884.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations
IterNodes
done48
148
034

end0.0ms

sample10.6s

Algorithm
intervals
Results
6.6s3592×body1280valid
2.7s2352×body640valid
513.0ms922×body320valid
283.0ms700×body80valid
150.0ms433×body160valid
3.0ms1×body2560valid