Details

Time bar (total: 40.7s)

sample1.0s

Algorithm
intervals
Results
707.0ms164×body1280valid
144.0ms55×body640valid
26.0ms26×body320valid
7.0ms10×body160valid
0.0ms1×body80valid

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01719
12619
23319
33519
done3519

prune492.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.3b
(cos (- lambda1 lambda2))

rewrite122.0ms

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×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
75.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
25.0ms
(cos (- lambda1 lambda2))

series301.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
84.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
31.0ms
(cos (- lambda1 lambda2))

simplify8.2s

Counts
69 → 69
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01211225
12621213
28101035
321211033
436111033
done50011033

prune486.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.2b
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity cos-mult
5×associate-*r* associate-*l*
4×add-log-exp
3×*-commutative
2×frac-times associate-*r/ associate-*l/ sin-mult
1×acos-asin unswap-sqr
Counts
4 → 76
Calls
4 calls:
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
65.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
94.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
220.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
132.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
22.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify1.3s

Counts
88 → 88
Iterations

Useful iterations: 2 (265.0ms)

IterNodesCost
01672204
14201939
216211567
done50011567

prune878.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b
(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
0.8b
(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
1.3b
(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod cos-mult
5×add-log-exp
4×log-pow
3×acos-asin frac-times log-prod associate-*r/ associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-+ exp-diff frac-add flip-+ sin-mult
1×distribute-rgt-in log-div distribute-lft-in rem-log-exp associate-*l* associate-*l/ *-commutative rem-exp-log
Counts
4 → 63
Calls
4 calls:
108.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
10.0ms
(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
19.0ms
(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
7.0ms
(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
320.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
77.0ms
(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
34.0ms
(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
36.0ms
(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

simplify1.4s

Counts
75 → 75
Iterations

Useful iterations: 2 (219.0ms)

IterNodesCost
01612258
14182201
216041871
done50001871

prune865.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.5b
(asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))
1.0b
(- (/ PI 2) (asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1 add-exp-log add-cbrt-cube
9×*-un-lft-identity
7×add-cube-cbrt
6×associate-*r* cos-mult add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×frac-times associate-*r/ sin-mult
2×asin-acos flip3-+ frac-add *-commutative flip-+ difference-of-squares
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in times-frac diff-log associate-*l/ flip-- distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 70
Calls
4 calls:
26.0ms
(* (sin lambda1) (sin lambda2))
75.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms
(asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))
32.0ms
(- (/ PI 2) (asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (sin lambda1) (sin lambda2))
287.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
35.0ms
(asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))
93.0ms
(- (/ PI 2) (asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: 2 (296.0ms)

IterNodesCost
01892127
14992017
218281809
done50011809

prune669.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 4.1b

regimes1.9s

Accuracy

0% (0.6b remaining)

Error of 4.2b against oracle of 3.5b and baseline of 4.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02630
13430
done3430

end0.0ms

sample19.5s

Algorithm
intervals
Results
13.7s4728×body1280valid
3.9s2153×body640valid
917.0ms718×body320valid
156.0ms269×body160valid
35.0ms127×body80valid
32.0ms7×body2560valid