Details

Time bar (total: 12.1s)

sample251.0ms

Algorithm
intervals
Results
166.0ms146×body1280valid
53.0ms75×body640valid
9.0ms23×body320valid
3.0ms10×body160valid
0.0ms2×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02712
13912
24412
34512
44512
done4512

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.9b
(cos (- lambda1 lambda2))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 72
Calls
4 calls:
15.0ms
(* (sin phi1) (sin phi2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
13.0ms
(cos (- lambda1 lambda2))

series120.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin phi1) (sin phi2))
48.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms
(cos (- lambda1 lambda2))

simplify59.0ms

Counts
84 → 84
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0323995
1789819
22620818
35002793
done5002793

prune342.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 72
Calls
4 calls:
11.0ms
(* (sin phi1) (sin phi2))
14.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series195.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin phi1) (sin phi2))
58.0ms
(* (sin lambda1) (sin lambda2))
71.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify78.0ms

Counts
84 → 84
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02741015
1872860
22115860
33356860
45001860
done5001860

prune453.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
0.3b
(pow (* (sin lambda1) (sin lambda2)) 3)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
26.6b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 add-exp-log add-cbrt-cube
8×cbrt-prod add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod sin-mult rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 75
Calls
4 calls:
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
8.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
4.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series208.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
69.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
51.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify46.0ms

Counts
87 → 87
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03011137
11083991
25001990
done5001990

prune514.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.9b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite26.0ms

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
4×expm1-log1p-u log1p-expm1-u
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 → 66
Calls
4 calls:
14.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
3.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series157.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
48.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
17.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify126.0ms

Counts
78 → 78
Iterations

Useful iterations: 4 (44.0ms)

IterNodesCost
01931705
14381457
210561453
314691453
437541449
550011449
done50011449

prune385.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

regimes899.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03219
13219
done3219

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.7s4712×body1280valid
1.4s2171×body640valid
295.0ms695×body320valid
79.0ms291×body160valid
34.0ms11×body2560valid
17.0ms121×body80valid