Details

Time bar (total: 29.0s)

sample381.0ms

Algorithm
intervals
Results
239.0ms108×body1280valid
72.0ms79×body640valid
25.0ms41×body320valid
4.0ms10×body160valid
3.0ms18×body80valid

simplify19.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01420
12020
22319
done2319

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize51.0ms

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))

rewrite79.0ms

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)))))
15.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms
(sin (- lambda1 lambda2))
30.0ms
(cos (- lambda1 lambda2))

series218.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
128.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
40.0ms
(sin (- lambda1 lambda2))
30.0ms
(cos (- lambda1 lambda2))

simplify3.0s

Counts
81 → 81
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01911730
13531390
26691106
314121020
43099875
done5000874

prune410.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×sin-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×sub-neg pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
13.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
23.0ms
(sin (- lambda1 lambda2))

series312.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
66.0ms
(* (sin lambda1) (sin lambda2))
190.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
35.0ms
(sin (- lambda1 lambda2))

simplify2.4s

Counts
73 → 73
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01791351
13031165
2571973
31083917
42182819
done5000756

prune615.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

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

rewrite36.0ms

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*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-cos-mult fma-udef sin-mult
Counts
4 → 61
Calls
4 calls:
21.0ms
(* (sin lambda1) (cos lambda2))
13.0ms
(* (sin lambda1) (sin lambda2))
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))))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series367.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (sin lambda1) (cos lambda2))
75.0ms
(* (sin lambda1) (sin lambda2))
20.0ms
(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))))
213.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify2.9s

Counts
73 → 73
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
01321073
12551031
2604904
31236890
42505863
done5001863

prune806.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
3.1b
(log (exp (* (sin lambda1) (sin lambda2))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×log-prod associate-*r* associate-*l* log-pow
1×exp-prod exp-to-pow rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
26.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
9.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

series413.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (sin lambda1) (sin lambda2))
25.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
210.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
106.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

simplify2.5s

Counts
68 → 68
Iterations

Useful iterations: 4 (876.0ms)

IterNodesCost
01181084
12001001
2434866
3847852
41774826
done5000826

prune594.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes693.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02741
13641
done3641

end0.0ms

sample13.0s

Algorithm
intervals
Results
7.3s3560×body1280valid
3.9s2369×body640valid
689.0ms980×body320valid
317.0ms407×body160valid
134.0ms684×body80valid