Details

Time bar (total: 38.4s)

sample351.0ms

Algorithm
intervals
Results
213.0ms108×body1280valid
77.0ms79×body640valid
27.0ms41×body320valid
4.0ms10×body160valid
3.0ms18×body80valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01420
12020
22120
done2120

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.5b
(sin (- lambda1 lambda2))
6.0b
(cos (- lambda1 lambda2))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(sin (- lambda1 lambda2))
23.0ms
(cos (- lambda1 lambda2))

series642.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
148.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
457.0ms
(sin (- lambda1 lambda2))
24.0ms
(cos (- lambda1 lambda2))

simplify4.8s

Counts
52 → 52
Iterations

Useful iterations: 3 (287.0ms)

IterNodesCost
097702
1204687
2458615
3967613
42013613
54634613
done5000613

prune331.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.5b
(sin (- lambda1 lambda2))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×associate-+r+ sin-sum
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 49
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
35.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
11.0ms
(sin (- lambda1 lambda2))

series480.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
89.0ms
(* (sin lambda1) (sin lambda2))
317.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
38.0ms
(sin (- lambda1 lambda2))

simplify2.2s

Counts
61 → 61
Iterations

Useful iterations: 2 (149.0ms)

IterNodesCost
01211007
1265984
2729857
32744857
done5000857

prune439.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-cos-mult flip-+ sin-mult
Counts
4 → 58
Calls
4 calls:
12.0ms
(* (sin lambda1) (cos lambda2))
13.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
25.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sin lambda1) (cos lambda2))
73.0ms
(* (sin lambda1) (sin lambda2))
26.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
374.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.6s

Counts
70 → 70
Iterations

Useful iterations: 2 (204.0ms)

IterNodesCost
01341171
13111147
2884994
33078994
done5001994

prune618.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
0.4b
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
0.6b
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
1.2b
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite496.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt times-frac frac-add cos-mult
14×associate-*r/
13×associate-/r/
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×pow1 flip3-+ flip-+
6×frac-times
5×flip3-- sum-cubes flip-- distribute-lft-out associate-/l*
4×sin-mult
3×cube-div pow-unpow associate-*l/ associate-/r*
2×pow-pow pow-exp associate--l+ associate-/l/ rem-cube-cbrt
1×cbrt-undiv +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down frac-2neg distribute-lft-in diff-log unpow3 cube-prod div-exp pow-prod-down prod-exp clear-num sum-log cbrt-unprod div-inv sqr-pow
Counts
4 → 102
Calls
4 calls:
350.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
33.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
23.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
86.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series8.0s

Counts
4 → 12
Calls
4 calls:
5.7s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
1.9s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
227.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
297.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify2.3s

Counts
114 → 114
Iterations

Useful iterations: 2 (853.0ms)

IterNodesCost
03327034
110426636
246146111
done50016111

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes725.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
051132
177132
done77132

end0.0ms

sample12.2s

Algorithm
intervals
Results
7.0s3560×body1280valid
3.2s2369×body640valid
658.0ms980×body320valid
571.0ms407×body160valid
116.0ms684×body80valid