Details

Time bar (total: 18.3s)

sample335.0ms

Algorithm
intervals
Results
200.0ms143×body1280valid
95.0ms67×body640valid
14.0ms28×body320valid
4.0ms12×body160valid
1.0ms6×body80valid

simplify3.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize28.0ms

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)
2.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.4b
(cos (- lambda1 lambda2))

rewrite83.0ms

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:
32.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms
(* (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)))))
38.0ms
(cos (- lambda1 lambda2))

series215.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
59.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
25.0ms
(cos (- lambda1 lambda2))

simplify97.0ms

Counts
69 → 69

prune308.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos 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
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity cos-mult
5×associate-*r* associate-*l*
4×add-log-exp
3×*-commutative
2×frac-times associate-*r/ associate-*l/ sin-mult
1×acos-asin unswap-sqr
Counts
4 → 76
Calls
4 calls:
45.0ms
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
10.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
48.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
80.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
124.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
22.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify48.0ms

Counts
88 → 88

prune433.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (* (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)))))))
1.3b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.0b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×add-exp-log add-cbrt-cube
8×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×add-log-exp
4×log-pow
3×acos-asin log-prod
2×exp-diff cos-mult sin-mult
1×frac-times log-div associate-*r/ rem-log-exp associate-*r* associate-*l* associate-*l/ *-commutative rem-exp-log
Counts
4 → 61
Calls
4 calls:
56.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
4.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
6.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series216.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
50.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
19.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify120.0ms

Counts
73 → 73

prune450.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.1b
(log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
2.0b
(acos (+ (* (sin phi1) (sin phi2)) (+ (log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
18×add-exp-log add-cbrt-cube
9×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
7×add-cube-cbrt *-un-lft-identity
5×add-log-exp
4×associate-*r* associate-*l*
3×log-prod log-pow
2×cos-mult *-commutative sin-mult
1×acos-asin frac-times exp-prod exp-to-pow associate-*r/ rem-log-exp associate-*l/ unswap-sqr
Counts
4 → 65
Calls
4 calls:
8.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
57.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
8.0ms
(log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
127.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
151.0ms
(log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (log (exp (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify42.0ms

Counts
77 → 77

prune401.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.1b

regimes615.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample13.7s

Algorithm
intervals
Results
10.3s4761×body1280valid
2.3s2122×body640valid
447.0ms693×body320valid
138.0ms296×body160valid
35.0ms7×body2560valid
23.0ms122×body80valid