Details

Time bar (total: 23.2s)

sample247.0ms

Algorithm
intervals
Results
160.0ms144×body1280valid
45.0ms69×body640valid
8.0ms20×body320valid
5.0ms19×body160valid
3.0ms1×body2560valid
0.0ms3×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01719
12619
23319
33419
done3419

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b
(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 55
Calls
4 calls:
4.0ms
(* (sin phi1) (sin phi2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

series121.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin phi1) (sin phi2))
43.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms
(cos (- lambda1 lambda2))

simplify902.0ms

Counts
67 → 67
Iterations

Useful iterations: 3 (186.0ms)

IterNodesCost
01111035
12041027
2504889
31474887
done5000887

prune306.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r* cos-mult
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod sin-mult
4×frac-times associate-*r/ add-log-exp
3×*-commutative
2×distribute-rgt-in sub-neg flip3-- distribute-lft-in frac-sub flip-- sub-div unswap-sqr
1×acos-asin associate-*l/
Counts
4 → 76
Calls
4 calls:
4.0ms
(* (sin phi1) (sin phi2))
24.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin phi1) (sin phi2))
197.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
71.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify793.0ms

Counts
88 → 88
Iterations

Useful iterations: done (791.0ms)

IterNodesCost
01952211
14962178
218731781
done50001779

prune522.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))))
0.2b
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))) R)
0.6b
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))
1.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt log-prod *-un-lft-identity
8×pow1
7×exp-sum
6×add-exp-log associate-*l* add-cbrt-cube
4×exp-prod add-log-exp
3×associate-*r*
2×log-pow unswap-sqr
1×acos-asin rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Counts
4 → 57
Calls
4 calls:
3.0ms
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))))
8.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))) R)
1.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))

series149.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))))
69.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))) R)
47.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))

simplify7.1s

Counts
69 → 69
Iterations

Useful iterations: 4 (349.0ms)

IterNodesCost
0992419
11702325
23801985
36591913
410621907
524581907
done50001907

prune379.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))) R)
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))
1.1b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))))
1.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 58
Calls
4 calls:
6.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))) R)
1.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))
2.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))

series149.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))) R)
47.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))))
17.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))))
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))))

simplify3.3s

Counts
70 → 70
Iterations

Useful iterations: 5 (846.0ms)

IterNodesCost
01022374
11752277
23922001
36821929
411141929
531001927
done50001927

prune295.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.0b

regimes674.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02630
13430
done3430

end0.0ms

sample7.8s

Algorithm
intervals
Results
5.6s4698×body1280valid
1.4s2164×body640valid
306.0ms690×body320valid
80.0ms290×body160valid
56.0ms16×body2560valid
21.0ms145×body80valid