Details

Time bar (total: 33.7s)

sample749.0ms

Algorithm
intervals
Results
392.0ms148×body1280valid
189.0ms65×body640valid
20.0ms29×body320valid
3.0ms7×body160valid
2.0ms7×body80valid

simplify61.0ms

Counts
1 → 1
Iterations
IterNodes
done36
336
233
126
017

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize102.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.2b
(cos (- lambda1 lambda2))

rewrite34.0ms

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×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 → 55
Calls
4 calls:
12.0ms
(* (sin phi1) (sin phi2))
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)))))
12.0ms
(cos (- lambda1 lambda2))

series202.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (sin phi1) (sin phi2))
75.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
38.0ms
(cos (- lambda1 lambda2))

simplify1.3s

Counts
67 → 67
Iterations
IterNodes
done5000
2721
1208
0111

prune714.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 64
Calls
4 calls:
19.0ms
(* (sin lambda1) (sin lambda2))
20.0ms
(* (sin phi1) (sin phi2))
12.0ms
(* (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))))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (sin lambda1) (sin lambda2))
68.0ms
(* (sin phi1) (sin phi2))
148.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
36.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
done5000
2999
1277
0134

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

localize128.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))))))
26.9b
(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
16×sin-mult
9×prod-exp cbrt-unprod
8×add-sqr-sqrt
7×cbrt-div
6×frac-times *-un-lft-identity associate-*r/ add-cube-cbrt
4×associate-*r* associate-*l* associate-*l/ pow-sqr pow-prod-up add-log-exp
2×pow-plus *-commutative
1×cbrt-prod pow2 acos-asin pow1/3 cube-unmult swap-sqr rem-cbrt-cube unswap-sqr
Counts
4 → 80
Calls
4 calls:
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
60.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))))))
122.0ms
(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

series263.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
85.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))))))
66.0ms
(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.9s

Counts
92 → 92
Iterations
IterNodes
done5001
21769
1370
0155

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 2.8b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b
(* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))
0.5b
(acos (+ (cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
27.9b
(cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
16×sin-mult
9×prod-exp cbrt-unprod
8×add-sqr-sqrt
7×cbrt-div
6×frac-times *-un-lft-identity associate-*r/ add-cube-cbrt
4×associate-*r* associate-*l* associate-*l/ pow-sqr pow-prod-up add-log-exp
2×pow-plus *-commutative
1×cbrt-prod pow2 acos-asin pow1/3 cube-unmult swap-sqr rem-cbrt-cube unswap-sqr
Counts
4 → 80
Calls
4 calls:
6.0ms
(* (acos (+ (cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
66.0ms
(* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))
2.0ms
(acos (+ (cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
124.0ms
(cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (acos (+ (cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
76.0ms
(* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))
25.0ms
(acos (+ (cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
62.0ms
(cbrt (* (* (sin phi2) (sin phi1)) (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))))

simplify1.6s

Counts
92 → 92
Iterations
IterNodes
done5001
21807
1369
0155

prune892.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.8b

regimes1.3s

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done34
134
025

end0.0ms

sample19.6s

Algorithm
intervals
Results
14.5s4762×body1280valid
3.4s2104×body640valid
640.0ms672×body320valid
218.0ms302×body160valid
84.0ms14×body2560valid
39.0ms147×body80valid