Details

Time bar (total: 1.0m)

sample1.1s

Algorithm
intervals
Results
690.0ms138×body1280valid
190.0ms81×body640valid
27.0ms19×body320valid
10.0ms13×body160valid
2.0ms5×body80valid

simplify80.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
79.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize51.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (- lambda1 lambda2))
1.7b
(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))

rewrite29.0ms

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
Counts
4 → 59
Calls
4 calls:
Slowest
10.0ms
(* (sin phi1) (sin phi2))
10.0ms
(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)))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(* (sin phi1) (sin phi2))
58.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
49.0ms
(cos (- lambda1 lambda2))
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.8s

Counts
35 → 71
Calls
35 calls:
Slowest
474.0ms
(* (* (* (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))
376.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
97.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
86.0ms
(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (log R))
76.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (sqrt R))

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.4b

localize72.0ms

Local error

Found 4 expressions with local error:

1.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b
(* (sin phi1) (sin phi2))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Counts
4 → 76
Calls
4 calls:
Slowest
70.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
10.0ms
(* (sin phi1) (sin phi2))
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series923.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
454.0ms
(* (sin phi1) (sin phi2))
328.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
119.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
22.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify8.2s

Counts
54 → 88
Calls
54 calls:
Slowest
639.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
548.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
516.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
465.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
340.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

prune2.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.3b

localize78.0ms

Local error

Found 4 expressions with local error:

1.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.2b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.3b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 62
Calls
4 calls:
Slowest
22.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
9.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
6.0ms
(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))))))

series226.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
75.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
35.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
29.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify7.5s

Counts
37 → 74
Calls
37 calls:
Slowest
442.0ms
(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)))))))))
297.0ms
(* (sqrt (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (sqrt R))
292.0ms
(* (* (* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (* (* R R) R))
272.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
271.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)

prune1.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.3b

localize72.0ms

Local error

Found 4 expressions with local error:

1.7b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.3b
(* (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)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-cbrt-cube add-exp-log
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×*-un-lft-identity cos-mult add-cube-cbrt
5×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×*-commutative
2×frac-times associate-*l/ associate-*r/ sin-mult
1×acos-asin unswap-sqr
Counts
4 → 80
Calls
4 calls:
Slowest
61.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
55.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
213.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
152.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
92.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
15.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify7.6s

Counts
55 → 92
Calls
55 calls:
Slowest
464.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (* (* R R) R))
277.0ms
(* (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))) (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))))
272.0ms
(* (* (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))))
267.0ms
(* (* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2))) (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))))
256.0ms
(* (* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2))) (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))))

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.2b

regimes1.8s

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch12.0ms

end0.0ms

sample24.7s

Algorithm
intervals
Results
17.7s4761×body1280valid
5.1s2165×body640valid
891.0ms658×body320valid
274.0ms284×body160valid
88.0ms7×body2560valid
48.0ms126×body80valid