Details

Time bar (total: 48.7s)

sample1.4s

Algorithm
intervals
Results
612.0ms163×body1280valid
400.0ms24×body320valid
285.0ms55×body640valid
8.0ms9×body160valid
2.0ms5×body80valid

simplify82.0ms

Calls
1 calls:
Slowest
81.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize83.0ms

Local error

Found 4 expressions with local error:

2.3b
(cos (- lambda1 lambda2))
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Calls
4 calls:
Slowest
18.0ms
(cos (- lambda1 lambda2))
17.0ms
(* (sin phi1) (sin phi2))
14.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
6.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series170.0ms

Calls
4 calls:
Slowest
64.0ms
(* (sin phi1) (sin phi2))
60.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
35.0ms
(cos (- lambda1 lambda2))
10.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.7s

Calls
35 calls:
Slowest
446.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (* (* R R) R))
352.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
144.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
71.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (sqrt R))
62.0ms
(acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2))))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.2b

localize84.0ms

Local error

Found 4 expressions with local error:

1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (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 lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Calls
4 calls:
Slowest
14.0ms
(* (sin phi1) (sin phi2))
14.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
12.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)

series230.0ms

Calls
4 calls:
Slowest
87.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
64.0ms
(* (sin phi1) (sin phi2))
56.0ms
(* (sin lambda1) (sin lambda2))
23.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify3.8s

Calls
43 calls:
Slowest
347.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
292.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
288.0ms
(* (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))))))))
279.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))
264.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.1b

localize64.0ms

Local error

Found 4 expressions with local error:

1.4b
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
0.2b
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi2) (sin phi1))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Calls
4 calls:
Slowest
22.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(* (sin phi2) (sin phi1))
11.0ms
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
9.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))

series189.0ms

Calls
4 calls:
Slowest
72.0ms
(* (sin lambda1) (sin lambda2))
54.0ms
(* (sin phi2) (sin phi1))
43.0ms
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
19.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))

simplify5.3s

Calls
44 calls:
Slowest
484.0ms
(+ (log R) (log (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
458.0ms
(* (sqrt R) (sqrt (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
422.0ms
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
418.0ms
(cbrt (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
416.0ms
(* (sqrt R) (sqrt (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.1b

localize97.0ms

Local error

Found 4 expressions with local error:

1.4b
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cbrt (sin lambda1)) (sin lambda2)))) (cos phi2)))))
0.6b
(cbrt (sin lambda1))
0.6b
(cbrt (sin lambda1))
0.6b
(cbrt (sin lambda1))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
1×acos-asin
Calls
4 calls:
Slowest
11.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cbrt (sin lambda1)) (sin lambda2)))) (cos phi2)))))
3.0ms
(cbrt (sin lambda1))
2.0ms
(cbrt (sin lambda1))
2.0ms
(cbrt (sin lambda1))

series424.0ms

Calls
4 calls:
Slowest
157.0ms
(cbrt (sin lambda1))
122.0ms
(cbrt (sin lambda1))
117.0ms
(cbrt (sin lambda1))
28.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cbrt (sin lambda1)) (sin lambda2)))) (cos phi2)))))

simplify1.3s

Calls
21 calls:
Slowest
246.0ms
(- (pow lambda1 1/3) (+ (* 1/3240 (pow (pow lambda1 13) 1/3)) (* 1/18 (pow (pow lambda1 7) 1/3))))
219.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
218.0ms
(- (pow lambda1 1/3) (+ (* 1/3240 (pow (pow lambda1 13) 1/3)) (* 1/18 (pow (pow lambda1 7) 1/3))))
215.0ms
(- (pow lambda1 1/3) (+ (* 1/3240 (pow (pow lambda1 13) 1/3)) (* 1/18 (pow (pow lambda1 7) 1/3))))
178.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.1b

regimes2.7s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.2b and baseline of 3.7b

bsearch12.0ms

end0.0ms

sample24.2s

Algorithm
intervals
Results
16.6s4822×body1280valid
5.6s2070×body640valid
1.3s671×body320valid
311.0ms295×body160valid
70.0ms12×body2560valid
50.0ms130×body80valid