Details

Time bar (total: 52.4s)

sample767.0ms

Algorithm
intervals
Results
501.0ms142×body1280valid
141.0ms74×body640valid
59.0ms27×body320valid
4.0ms6×body160valid
4.0ms7×body80valid

simplify109.0ms

Calls
1 calls:
Slowest
108.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize65.0ms

Local error

Found 4 expressions with local error:

3.9b
(cos (- lambda1 lambda2))
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-*l* insert-posit16 add-log-exp
3×cos-diff associate-*r* pow-prod-down prod-exp cbrt-unprod
2×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult
Calls
4 calls:
Slowest
26.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(cos (- lambda1 lambda2))
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)))))

series206.0ms

Calls
4 calls:
Slowest
100.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
56.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
34.0ms
(cos (- lambda1 lambda2))
15.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.8s

Calls
30 calls:
Slowest
417.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
328.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
175.0ms
(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
76.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
69.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.5b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
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
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
4×associate-*r* insert-posit16 add-log-exp
3×*-commutative sin-mult
2×cos-mult
1×acos-asin frac-times associate-*l/ associate-*r/
Calls
4 calls:
Slowest
36.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
9.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series328.0ms

Calls
4 calls:
Slowest
139.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
111.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
48.0ms
(* (sin lambda1) (sin lambda2))
31.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify3.6s

Calls
40 calls:
Slowest
311.0ms
(* (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))) (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))))
228.0ms
(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
210.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
206.0ms
(* (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))) R)
195.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
0.4b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
0.2b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt exp-prod *-un-lft-identity add-cube-cbrt
8×log-pow
7×associate-*l*
6×pow1
5×add-log-exp
4×add-cbrt-cube add-exp-log insert-posit16
3×acos-asin log-prod
2×exp-diff
1×log-div rem-log-exp *-commutative rem-exp-log
Calls
4 calls:
Slowest
13.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
7.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
5.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series209.0ms

Calls
4 calls:
Slowest
87.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
64.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
31.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
27.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify5.7s

Calls
30 calls:
Slowest
594.0ms
(exp (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
262.0ms
(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))))
255.0ms
(log (* (cbrt (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) (cbrt (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))))
246.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
235.0ms
(exp (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
0.6b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
0.4b
(exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))))
0.4b
(log (exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod exp-prod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×log-pow
6×pow1 exp-sum
5×add-exp-log add-log-exp
4×add-cbrt-cube insert-posit16
2×rem-log-exp
1×acos-asin rem-exp-log
Calls
4 calls:
Slowest
8.0ms
(exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))))
5.0ms
(log (exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
2.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))

series178.0ms

Calls
4 calls:
Slowest
69.0ms
(exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))))
55.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
30.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
23.0ms
(log (exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))))

simplify5.5s

Calls
33 calls:
Slowest
242.0ms
(exp (exp (log (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))))))
242.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
241.0ms
(log (sqrt (exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))))))
237.0ms
(exp (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
224.0ms
(exp (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))))

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.1b

regimes3.0s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch5.0ms

end0.0ms

sample23.5s

Algorithm
intervals
Results
17.2s4717×body1280valid
4.8s2136×body640valid
854.0ms701×body320valid
229.0ms294×body160valid
62.0ms11×body2560valid
58.0ms141×body80valid