Details

Time bar (total: 20.4s)

sample177.0ms

Algorithm
intervals
Results
108.0ms119×body1280valid
39.0ms81×body640valid
10.0ms31×body320valid
2.0ms11×body160valid
1.0ms14×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01420
12020
22319
done2319

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize20.0ms

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))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
13.0ms
(sin (- lambda1 lambda2))

series160.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
109.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify1.9s

Counts
81 → 81
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01911730
13531390
26691106
314031020
43090875
done5000874

prune302.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.0b

localize34.0ms

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))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sin-neg sum-log *-commutative distribute-rgt-neg-out cbrt-unprod flip-+ unswap-sqr
Counts
4 → 69
Calls
4 calls:
14.0ms
(* (cos lambda1) (sin (- lambda2)))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))

series194.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (cos lambda1) (sin (- lambda2)))
14.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
107.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(cos (- lambda1 lambda2))

simplify3.0s

Counts
81 → 81
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
01991476
13901279
28881038
32036958
44531875
done5000875

prune432.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative sin-mult
1×associate-*r/ fma-udef unswap-sqr
Counts
4 → 61
Calls
4 calls:
24.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
11.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.0ms
(fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))

series276.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
46.0ms
(* (sin lambda1) (sin lambda2))
18.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
137.0ms
(fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))

simplify4.3s

Counts
73 → 73
Iterations

Useful iterations: 4 (3.4s)

IterNodesCost
01231144
12391103
2668948
32000934
44326908
done5000908

prune444.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cbrt (pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.4b
(fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1))
0.5b
(cbrt (pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3))
0.7b
(pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
4 → 67
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cbrt (pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.0ms
(fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1))
2.0ms
(cbrt (pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3))
3.0ms
(pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3)

series480.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cbrt (pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
133.0ms
(fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1))
138.0ms
(cbrt (pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3))
191.0ms
(pow (fma (* (cos lambda1) (cos phi2)) (cos lambda2) (cos phi1)) 3)

simplify2.2s

Counts
79 → 79
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01131796
12201548
25281348
329071324
done50001298

prune397.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes599.0ms

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
02843
13743
done3743

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3591×body1280valid
1.2s2364×body640valid
300.0ms899×body320valid
88.0ms423×body160valid
69.0ms723×body80valid