Details

Time bar (total: 19.5s)

sample181.0ms

Algorithm
intervals
Results
104.0ms117×body1280valid
47.0ms93×body640valid
7.0ms17×body80valid
6.0ms18×body320valid
2.0ms11×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01420
12020
22319
done2319

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

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)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(cos (- lambda1 lambda2))
3.5b
(sin (- lambda1 lambda2))

rewrite24.0ms

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)))))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(cos (- lambda1 lambda2))
7.0ms
(sin (- lambda1 lambda2))

series154.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
100.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
26.0ms
(sin (- lambda1 lambda2))

simplify1.8s

Counts
81 → 81
Iterations

Useful iterations: 4 (844.0ms)

IterNodesCost
01911730
13651390
26821124
314481020
43180875
done5000875

prune322.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(cos (- lambda1 lambda2))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
3×cos-diff sub-neg fma-def associate-*r* associate-*l*
2×associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 76
Calls
4 calls:
18.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(cos (- lambda1 lambda2))

series275.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
103.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify1.7s

Counts
88 → 88
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02061826
14241647
210831387
333181343
done50011341

prune440.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

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×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative sin-mult
1×associate-*l/ fma-udef unswap-sqr
Counts
4 → 61
Calls
4 calls:
10.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series267.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
47.0ms
(* (sin lambda1) (sin lambda2))
125.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify5.0s

Counts
73 → 73
Iterations

Useful iterations: 4 (3.7s)

IterNodesCost
01141133
12231106
2710951
32149937
44380911
done5000911

prune399.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(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)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod fma-udef sin-mult rem-cube-cbrt unswap-sqr
Counts
4 → 79
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
1.0ms
(cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3))
1.0ms
(pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)

series475.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin lambda1) (sin lambda2))
125.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
125.0ms
(cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3))
178.0ms
(pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)

simplify1.9s

Counts
91 → 91
Iterations

Useful iterations: 3 (477.0ms)

IterNodesCost
01161396
12271200
26031058
327691055
done50001055

prune397.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes421.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02439
13239
done3239

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.5s3570×body1280valid
1.3s2389×body640valid
316.0ms923×body320valid
100.0ms431×body160valid
71.0ms687×body80valid