Details

Time bar (total: 18.6s)

sample179.0ms

Algorithm
intervals
Results
109.0ms119×body1280valid
39.0ms81×body640valid
10.0ms31×body320valid
2.0ms11×body160valid
1.0ms14×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01420
12020
22120
done2120

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.1b
(cos (- lambda1 lambda2))
2.1b
(sin (- lambda1 lambda2))

rewrite31.0ms

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)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms
(cos (- lambda1 lambda2))
10.0ms
(sin (- lambda1 lambda2))

series169.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
111.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))
27.0ms
(sin (- lambda1 lambda2))

simplify2.8s

Counts
52 → 52
Iterations

Useful iterations: 3 (191.0ms)

IterNodesCost
097702
1204687
2458615
3970613
42017613
54604613
done5000613

prune249.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.1b
(cos (- lambda1 lambda2))

rewrite33.0ms

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×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 48
Calls
4 calls:
11.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms
(cos (- lambda1 lambda2))

series403.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (cos lambda1) (sin lambda2))
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
321.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify2.0s

Counts
60 → 60
Iterations

Useful iterations: 3 (302.0ms)

IterNodesCost
0115857
1255841
2640743
31357741
42836741
done5000741

prune319.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
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)) (cos phi2))))
0.4b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite53.0ms

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* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative sin-mult
1×+-commutative flip3-+ associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 56
Calls
4 calls:
28.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
12.0ms
(* (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)) (cos phi2))))
12.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series286.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
47.0ms
(* (sin lambda1) (sin lambda2))
19.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
135.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.9s

Counts
68 → 68
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
01231123
12881103
2945910
33126910
done5000910

prune345.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.4b
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.6b
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
0.9b
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
21×add-exp-log add-cbrt-cube
19×pow1
16×add-sqr-sqrt add-cube-cbrt
15×times-frac
12×cos-mult
11×associate-*r/
9×pow-prod-down prod-exp cbrt-unprod
7×associate-/r/
6×add-log-exp
5×flip3-- frac-add flip-- associate-/l*
4×frac-times sum-cubes distribute-lft-out
3×sub-neg pow-unpow pow-pow associate-*r* pow-exp associate-/r* rem-cube-cbrt
2×distribute-rgt-in distribute-lft-in flip3-+ associate-*l/ flip-+ associate-/l/
1×cbrt-undiv cube-div cube-mult pow-to-exp unpow-prod-down frac-2neg diff-log unpow3 cube-prod div-exp associate-*l* clear-num *-commutative div-inv sqr-pow
Counts
4 → 112
Calls
4 calls:
152.0ms
(* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
141.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
19.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
28.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

series1.3s

Counts
4 → 12
Calls
4 calls:
255.0ms
(* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
753.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
123.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
145.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify1.6s

Counts
124 → 124
Iterations

Useful iterations: 2 (430.0ms)

IterNodesCost
02534685
16554337
232133965
done50013965

prune782.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes518.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03784
15084
done5084

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3591×body1280valid
1.2s2364×body640valid
294.0ms899×body320valid
88.0ms423×body160valid
74.0ms723×body80valid