Details

Time bar (total: 29.8s)

sample568.0ms

Algorithm
intervals
Results
368.0ms143×body1280valid
85.0ms88×body640valid
12.0ms17×body320valid
3.0ms6×body160valid
1.0ms2×body80valid

simplify29.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize38.0ms

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)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b
(cos (- lambda1 lambda2))

rewrite123.0ms

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:
42.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms
(* (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)))))
57.0ms
(cos (- lambda1 lambda2))

series268.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
55.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
48.0ms
(cos (- lambda1 lambda2))

simplify1.7s

Counts
69 → 69

prune484.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin lambda1) (sin lambda2))
0.9b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt *-un-lft-identity
7×associate-*r* associate-*l*
4×add-log-exp
3×*-commutative sin-mult
2×cos-mult unswap-sqr
1×acos-asin frac-times associate-*r/ associate-*l/
Counts
4 → 70
Calls
4 calls:
82.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
15.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
27.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
131.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
82.0ms
(* (sin lambda1) (sin lambda2))
39.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify702.0ms

Counts
82 → 82

prune697.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
0.5b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
0.9b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
5×add-log-exp
4×log-pow
3×acos-asin log-prod associate-*r* associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log sin-mult unswap-sqr
Counts
4 → 55
Calls
4 calls:
26.0ms
(* (sin lambda1) (sin lambda2))
7.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
11.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (sin lambda1) (sin lambda2))
78.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
49.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
41.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify1.3s

Counts
67 → 67

prune716.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.9b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))))) R)
0.3b
(exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
0.5b
(log (exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))))
0.9b
(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

rewrite60.0ms

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:
38.0ms
(* (log (exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))))) R)
5.0ms
(exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
9.0ms
(log (exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))))
6.0ms
(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (log (exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))))) R)
73.0ms
(exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
36.0ms
(log (exp (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))))
42.0ms
(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

simplify1.5s

Counts
70 → 70

prune597.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.9b

regimes1.9s

Accuracy

7% (0.3b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify209.0ms

end0.0ms

sample17.4s

Algorithm
intervals
Results
11.6s4780×body1280valid
3.5s2132×body640valid
985.0ms691×body320valid
393.0ms119×body80valid
176.0ms273×body160valid
53.0ms11×body2560valid