Details

Time bar (total: 25.5s)

sample283.0ms

Algorithm
intervals
Results
204.0ms153×body1280valid
55.0ms76×body640valid
5.0ms11×body320valid
1.0ms11×body80valid
1.0ms5×body160valid

simplify34.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12724
24524
37024
47224
done7224

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))
3.5b
(sin (- lambda1 lambda2))

rewrite32.0ms

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 sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
11.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series191.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
91.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify5.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (801.0ms)

IterNodesCost
0116760
1260748
2850644
32518642
44691642
done5001642

prune335.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.1b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))

rewrite35.0ms

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* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×cos-diff associate-*l/
2×cos-sum flip3-+ sin-neg *-commutative distribute-rgt-neg-out flip-+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in unsub-neg sum-log sin-cos-mult unswap-sqr
Counts
4 → 64
Calls
4 calls:
5.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
13.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
10.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(cos (- lambda1 lambda2))

series345.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
137.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
92.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms
(cos (- lambda1 lambda2))

simplify2.7s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01311163
13451143
21257987
34677950
done5000950

prune434.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×flip3-+ sin-cos-mult flip-+
3×frac-times associate-*r/ associate-*l/ *-commutative sin-mult
2×frac-add sin-neg cos-mult distribute-rgt-neg-out unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in unsub-neg sum-log
Counts
4 → 79
Calls
4 calls:
5.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
13.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms
(* (sin lambda1) (sin lambda2))
18.0ms
(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
136.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
45.0ms
(* (sin lambda1) (sin lambda2))
178.0ms
(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))

simplify967.0ms

Counts
91 → 91
Iterations

Useful iterations: done (964.0ms)

IterNodesCost
01841636
15251595
221131395
done50001363

prune591.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
0.2b
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b
(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
87×pow1
78×cos-mult sin-mult
74×associate-*r/
66×frac-times
44×associate-*l/
42×add-exp-log add-cbrt-cube
37×pow-prod-down frac-sub
34×sin-cos-mult
33×associate-/l/
22×prod-exp cbrt-unprod
21×sub-div
8×pow-sqr pow-prod-up
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate-*r*
5×flip3-- flip--
4×pow-plus associate-/r/ add-log-exp
3×cbrt-undiv times-frac div-exp associate-*l* associate-/r* *-commutative
2×pow2 distribute-rgt-in sub-neg distribute-lft-in swap-sqr
1×frac-2neg clear-num div-inv associate-/l* difference-of-squares
Counts
4 → 190
Calls
4 calls:
92.0ms
(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
77.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
15.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
13.0ms
(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

series1.0s

Counts
4 → 12
Calls
4 calls:
217.0ms
(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
707.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
57.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
54.0ms
(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

simplify1.8s

Counts
202 → 202
Iterations

Useful iterations: 2 (638.0ms)

IterNodesCost
03065917
18725008
243274302
done50004302

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes443.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03563
14761
done4761

end0.0ms

sample8.6s

Algorithm
intervals
Results
6.3s4639×body1280valid
1.5s1959×body640valid
271.0ms554×body320valid
88.0ms639×body80valid
61.0ms209×body160valid