Details

Time bar (total: 42.8s)

sample626.0ms

Algorithm
intervals
Results
463.0ms138×body1280valid
95.0ms65×body640valid
22.0ms22×body320valid
7.0ms23×body80valid
5.0ms8×body160valid

simplify99.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12724
24624
37124
47224
done7224

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b
(sin (- lambda1 lambda2))
3.4b
(cos (- lambda1 lambda2))

rewrite140.0ms

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:
48.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
55.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(sin (- lambda1 lambda2))
15.0ms
(cos (- lambda1 lambda2))

series324.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
157.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
40.0ms
(sin (- lambda1 lambda2))
30.0ms
(cos (- lambda1 lambda2))

simplify6.9s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0116760
1258748
2816644
32177642
43715642
done5000642

prune577.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))

rewrite157.0ms

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 flip3-- distribute-lft-in flip--
Counts
4 → 70
Calls
4 calls:
12.0ms
(* (sin lambda1) (cos lambda2))
85.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
41.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))

series451.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sin lambda1) (cos lambda2))
211.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
158.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))

simplify3.1s

Counts
82 → 82
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01481039
13471016
21155888
33732880
done5001880

prune759.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.3b
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

rewrite304.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×associate-*l/ *-commutative sin-cos-mult add-log-exp
3×sin-mult
2×frac-times associate-*r/ cos-mult unswap-sqr
1×flip3-- flip--
Counts
4 → 89
Calls
4 calls:
102.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
26.0ms
(* (sin lambda1) (sin lambda2))
86.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
85.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series665.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
87.0ms
(* (sin lambda1) (sin lambda2))
158.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
187.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.6s

Counts
101 → 101
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01671486
14411460
218341168
done50001164

prune878.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))) (cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))))
0.6b
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))
0.6b
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))
0.6b
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))

rewrite567.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-div
22×cos-mult sin-cos-mult
20×frac-times
14×associate-*r/ associate-*l/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 82
Calls
4 calls:
136.0ms
(* (cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))) (cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))))
43.0ms
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))
350.0ms
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))
33.0ms
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))

series1.4s

Counts
4 → 12
Calls
4 calls:
383.0ms
(* (cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))) (cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))))
334.0ms
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))
335.0ms
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))
327.0ms
(cbrt (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))))

simplify2.3s

Counts
94 → 94
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01222194
12722026
28651736
332301670
done50011654

prune789.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes463.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03562
14962
done4962

end0.0ms

sample20.4s

Algorithm
intervals
Results
14.4s4526×body1280valid
4.2s1971×body640valid
682.0ms599×body320valid
311.0ms701×body80valid
158.0ms203×body160valid