Details

Time bar (total: 44.2s)

sample578.0ms

Algorithm
intervals
Results
338.0ms146×body1280valid
126.0ms74×body640valid
23.0ms28×body320valid
4.0ms8×body160valid

simplify49.0ms

Calls
1 calls:
Slowest
48.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize40.0ms

Local error

Found 4 expressions with local error:

5.1b
(cos (- lambda1 lambda2))
0.8b
(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)))

rewrite25.0ms

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
15.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series216.0ms

Calls
4 calls:
Slowest
137.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
39.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
28.0ms
(cos (- lambda1 lambda2))
11.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.8s

Calls
30 calls:
Slowest
424.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
283.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
141.0ms
(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
111.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
85.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r*
4×insert-posit16 add-log-exp
3×*-commutative
2×pow-prod-down prod-exp cbrt-unprod sin-mult
1×acos-asin
Calls
4 calls:
Slowest
4.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(* (sin phi1) (sin phi2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series239.0ms

Calls
4 calls:
Slowest
72.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
72.0ms
(* (sin lambda1) (sin lambda2))
65.0ms
(* (sin phi1) (sin phi2))
30.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.0s

Calls
32 calls:
Slowest
238.0ms
(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
224.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
202.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
197.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
196.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.9b

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b
(log (exp (* (sin lambda1) (sin lambda2))))
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×add-cbrt-cube associate-*l* add-exp-log
5×add-log-exp
4×insert-posit16
3×log-prod associate-*r* log-pow
2×*-commutative
1×acos-asin exp-prod exp-to-pow rem-log-exp pow-prod-down prod-exp cbrt-unprod sin-mult
Calls
4 calls:
Slowest
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

series205.0ms

Calls
4 calls:
Slowest
94.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
46.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
45.0ms
(* (sin lambda1) (sin lambda2))
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

simplify1.7s

Calls
29 calls:
Slowest
232.0ms
(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
214.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))))
199.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
176.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
172.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.3b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×exp-prod add-cbrt-cube add-exp-log
5×add-log-exp
4×log-pow insert-posit16
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 sin-mult rem-exp-log
Calls
4 calls:
Slowest
9.0ms
(* (sin lambda1) (sin lambda2))
7.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
5.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series151.0ms

Calls
4 calls:
Slowest
59.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
56.0ms
(* (sin lambda1) (sin lambda2))
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
15.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify3.9s

Calls
34 calls:
Slowest
282.0ms
(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
252.0ms
(log (* (cbrt (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) (cbrt (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))))
245.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
235.0ms
(log (sqrt (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
230.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.9b

regimes2.1s

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample24.3s

Algorithm
intervals
Results
17.5s4789×body1280valid
4.4s2131×body640valid
1.5s671×body320valid
363.0ms278×body160valid
66.0ms10×body2560valid
50.0ms127×body80valid