Details

Time bar (total: 34.3s)

sample305.0ms

Algorithm
intervals
Results
187.0ms108×body1280valid
67.0ms76×body640valid
20.0ms30×body320valid
7.0ms34×body80valid
3.0ms8×body160valid

simplify66.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
014584
120584
223559
done23559

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize65.0ms

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))))
3.4b
(sin (- lambda1 lambda2))
3.5b
(cos (- lambda1 lambda2))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cos-sum sin-sum
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×cos-diff fma-def
2×associate-+r+ sub-neg
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
21.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

series255.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
160.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms
(sin (- lambda1 lambda2))
33.0ms
(cos (- lambda1 lambda2))

simplify3.0s

Counts
81 → 81
Iterations

Useful iterations: done (3.0s)

IterNodesCost
019139334
137234856
272730570
3194430520
done500028597

prune891.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize101.0ms

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 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b
(cos (- lambda1 lambda2))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×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 → 68
Calls
4 calls:
18.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
21.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms
(cos (- lambda1 lambda2))

series256.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (cos lambda1) (sin lambda2))
28.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
138.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms
(cos (- lambda1 lambda2))

simplify3.4s

Counts
80 → 80
Iterations

Useful iterations: done (3.4s)

IterNodesCost
019436230
140433185
294330698
3327430513
done500029513

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def
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 → 68
Calls
4 calls:
14.0ms
(* (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))))))
20.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (cos lambda1) (sin lambda2))
39.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
88.0ms
(* (sin lambda1) (sin lambda2))
408.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify4.0s

Counts
80 → 80
Iterations

Useful iterations: done (4.0s)

IterNodesCost
014133743
134631568
2102130658
3409130618
done500030593

prune899.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (expm1 (log1p (* (cos lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(log1p (* (cos lambda1) (sin lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log add-log-exp
5×expm1-log1p-u
4×log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×associate-+r+
1×distribute-rgt-in +-commutative log1p-udef sum-log distribute-lft-in flip3-+ pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (expm1 (log1p (* (cos lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.0ms
(log1p (* (cos lambda1) (sin lambda2)))
19.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series580.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (expm1 (log1p (* (cos lambda1) (sin lambda2)))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
127.0ms
(log1p (* (cos lambda1) (sin lambda2)))
77.0ms
(* (sin lambda1) (sin lambda2))
330.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify3.7s

Counts
71 → 71
Iterations

Useful iterations: 3 (2.0s)

IterNodesCost
013534434
131830129
286629134
3394229069
done500029069

prune790.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0251199
1331199
done331199

end0.0ms

sample12.8s

Algorithm
intervals
Results
8.3s3532×body1280valid
3.0s2358×body640valid
639.0ms948×body320valid
366.0ms423×body160valid
140.0ms739×body80valid