Details

Time bar (total: 43.8s)

sample609.0ms

Algorithm
intervals
Results
447.0ms150×body1280valid
93.0ms67×body640valid
20.0ms20×body320valid
4.0ms13×body80valid
3.0ms6×body160valid

simplify149.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12724
24624
37124
48324
58424
done8424

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b
(sin (- lambda1 lambda2))
3.1b
(cos (- lambda1 lambda2))

rewrite159.0ms

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×sub-neg cos-sum sin-sum *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
57.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
62.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

series347.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
166.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
38.0ms
(sin (- lambda1 lambda2))
33.0ms
(cos (- lambda1 lambda2))

simplify1.3s

Counts
72 → 72
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0116760
1272748
21318644
done5001642

prune831.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.4b

localize102.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b
(cos (- lambda1 lambda2))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cos-diff associate-*l/ *-commutative
2×cos-sum sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ flip-+
Counts
4 → 70
Calls
4 calls:
73.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
24.0ms
(* (sin lambda1) (cos lambda2))
64.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms
(cos (- lambda1 lambda2))

series505.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
71.0ms
(* (sin lambda1) (cos lambda2))
157.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms
(cos (- lambda1 lambda2))

simplify1.7s

Counts
82 → 82
Iterations

Useful iterations: 2 (366.0ms)

IterNodesCost
01541068
13961045
22059905
done5002905

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.1b
(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))))
0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (sin (- lambda2)) (sin lambda1))
0.2b
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×sin-cos-mult
5×pow-prod-down prod-exp cbrt-unprod sin-mult
4×frac-times associate-*r/ cos-mult add-log-exp
3×*-commutative
2×distribute-rgt-in sub-neg flip3-- distribute-lft-in frac-sub flip-- sub-div unswap-sqr
1×distribute-lft-neg-out associate-*l/ sin-neg
Counts
4 → 77
Calls
4 calls:
0.0ms
(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))))
23.0ms
(* (sin lambda1) (cos lambda2))
29.0ms
(* (sin (- lambda2)) (sin lambda1))
157.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))))
94.0ms
(* (sin lambda1) (cos lambda2))
97.0ms
(* (sin (- lambda2)) (sin lambda1))
370.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))

simplify2.3s

Counts
89 → 89
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02121830
15241789
225751525
done50001518

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (sin (- lambda2)) (sin lambda1))
0.2b
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin (- lambda2)) (sin lambda1))))))
2.7b
(log (exp (* (sin (- lambda2)) (sin lambda1))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
9×associate-*r*
7×associate-*l*
5×distribute-lft-neg-out pow-prod-down prod-exp sin-neg cbrt-unprod add-log-exp
4×exp-neg sin-cos-mult
3×distribute-rgt-in log-div log-prod distribute-lft-in log-pow *-commutative
2×frac-times sub-neg flip3-- associate-*r/ flip-- associate--r- unswap-sqr
1×exp-prod exp-to-pow rem-log-exp log-rec associate-*l/ sin-mult
Counts
4 → 84
Calls
4 calls:
21.0ms
(* (sin lambda1) (cos lambda2))
29.0ms
(* (sin (- lambda2)) (sin lambda1))
139.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin (- lambda2)) (sin lambda1))))))
8.0ms
(log (exp (* (sin (- lambda2)) (sin lambda1))))

series1.1s

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sin lambda1) (cos lambda2))
89.0ms
(* (sin (- lambda2)) (sin lambda1))
367.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin (- lambda2)) (sin lambda1))))))
571.0ms
(log (exp (* (sin (- lambda2)) (sin lambda1))))

simplify2.0s

Counts
96 → 96
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01841477
14501312
223571160
done50001126

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03689
14889
done4889

end0.0ms

sample26.4s

Algorithm
intervals
Results
18.4s4639×body1280valid
4.9s1928×body640valid
1.4s576×body320valid
592.0ms665×body80valid
134.0ms192×body160valid