Details

Time bar (total: 22.0s)

sample406.0ms

Algorithm
intervals
Results
202.0ms119×body1280valid
87.0ms29×body320valid
79.0ms74×body640valid
4.0ms26×body80valid
3.0ms8×body160valid

simplify20.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01420
12020
22319
done2319

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.6b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
4.1b
(cos (- lambda1 lambda2))
4.2b
(sin (- lambda1 lambda2))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×sub-neg
1×cos-diff sin-diff fma-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
48.0ms
(cos (- lambda1 lambda2))
15.0ms
(sin (- lambda1 lambda2))

series219.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
157.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
27.0ms
(cos (- lambda1 lambda2))
24.0ms
(sin (- lambda1 lambda2))

simplify1.2s

Counts
73 → 73
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01721599
12901279
26101016
31583930
done5000821

prune438.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.6b
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
4.2b
(sin (- lambda1 lambda2))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
33×sin-sum
27×prod-diff
26×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
11×distribute-rgt-in distribute-lft-in
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sub-neg associate-*r* associate-*l*
1×pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 82
Calls
4 calls:
52.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
1.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
26.0ms
(sin (- lambda1 lambda2))

series431.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
15.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
303.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
40.0ms
(sin (- lambda1 lambda2))

simplify1.4s

Counts
94 → 94
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02112575
14802064
219391656
done50011583

prune587.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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×fma-udef sin-mult
Counts
4 → 60
Calls
4 calls:
20.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
1.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series446.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sin lambda1) (sin lambda2))
90.0ms
(* (cos lambda1) (sin lambda2))
35.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
259.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify803.0ms

Counts
72 → 72
Iterations

Useful iterations: done (800.0ms)

IterNodesCost
01261099
12701058
2912921
done5000920

prune605.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))
0.2b
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (log1p (expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
0.3b
(expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.6b
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 fma-udef expm1-udef
Counts
4 → 41
Calls
4 calls:
0.0ms
(log1p (expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))
0.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (log1p (expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
1.0ms
(expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
1.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

series1.6s

Counts
4 → 12
Calls
4 calls:
461.0ms
(log1p (expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))
18.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (log1p (expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
441.0ms
(expm1 (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
722.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify923.0ms

Counts
53 → 53
Iterations

Useful iterations: done (920.0ms)

IterNodesCost
0891325
11791247
23991069
312831067
done50011064

prune365.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes634.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02437
12937
done2937

end0.0ms

sample11.5s

Algorithm
intervals
Results
6.6s3552×body1280valid
3.3s2372×body640valid
649.0ms932×body320valid
166.0ms699×body80valid
164.0ms445×body160valid