Details

Time bar (total: 19.7s)

sample372.0ms

Algorithm
intervals
Results
264.0ms136×body1280valid
70.0ms78×body640valid
11.0ms13×body320valid
4.0ms23×body80valid
2.0ms6×body160valid

simplify4.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b
(sin (- lambda1 lambda2))
2.8b
(cos (- lambda1 lambda2))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×sub-neg cos-sum sin-sum *-commutative
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff sin-cos-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
17.0ms
(* (cos phi1) (sin phi2))
35.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms
(sin (- lambda1 lambda2))
302.0ms
(cos (- lambda1 lambda2))

series198.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (cos phi1) (sin phi2))
106.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify106.0ms

Counts
71 → 71

prune361.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b
(cos (- lambda1 lambda2))

rewrite118.0ms

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*
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cos-diff associate-*l/ *-commutative
2×cos-sum unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ sin-cos-mult flip-+
Counts
4 → 69
Calls
4 calls:
50.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
14.0ms
(* (cos phi1) (sin phi2))
34.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

series323.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
51.0ms
(* (cos phi1) (sin phi2))
104.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

simplify47.0ms

Counts
81 → 81

prune513.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

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*
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×sin-cos-mult add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add cos-mult flip-+ unswap-sqr
1×distribute-rgt-in distribute-lft-in associate-*l/
Counts
4 → 71
Calls
4 calls:
0.0ms
(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
16.0ms
(* (cos phi1) (sin phi2))
13.0ms
(* (sin lambda1) (sin lambda2))
70.0ms
(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
54.0ms
(* (cos phi1) (sin phi2))
50.0ms
(* (sin lambda1) (sin lambda2))
201.0ms
(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify62.0ms

Counts
83 → 83

prune548.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×*-commutative sin-cos-mult add-log-exp
3×sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult unswap-sqr
Counts
4 → 87
Calls
4 calls:
13.0ms
(* (cos phi1) (sin phi2))
14.0ms
(* (sin lambda1) (sin lambda2))
49.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
59.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (cos phi1) (sin phi2))
49.0ms
(* (sin lambda1) (sin lambda2))
133.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
119.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify53.0ms

Counts
99 → 99

prune478.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes530.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample14.5s

Algorithm
intervals
Results
10.0s4574×body1280valid
3.0s2022×body640valid
526.0ms562×body320valid
430.0ms634×body80valid
85.0ms208×body160valid