Details

Time bar (total: 24.1s)

sample336.0ms

Algorithm
intervals
Results
177.0ms114×body1280valid
104.0ms79×body640valid
22.0ms33×body320valid
5.0ms25×body80valid
2.0ms5×body160valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01420
12020
22319
done2319

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

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))
2.5b
(sin (- lambda1 lambda2))
2.6b
(cos (- lambda1 lambda2))

rewrite31.0ms

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))
14.0ms
(sin (- lambda1 lambda2))
14.0ms
(cos (- lambda1 lambda2))

series232.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
164.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
22.0ms
(sin (- lambda1 lambda2))
29.0ms
(cos (- lambda1 lambda2))

simplify1.1s

Counts
73 → 73
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01721599
12901279
26101016
31574930
done5001821

prune405.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.7b
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))
2.5b
(sin (- lambda1 lambda2))

rewrite45.0ms

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-neg sin-diff *-commutative distribute-rgt-neg-out cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
17.0ms
(* (sin lambda1) (sin (- lambda2)))
0.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))
26.0ms
(sin (- lambda1 lambda2))

series481.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
67.0ms
(* (sin lambda1) (sin (- lambda2)))
361.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))
37.0ms
(sin (- lambda1 lambda2))

simplify2.7s

Counts
74 → 74
Iterations

Useful iterations: 3 (827.0ms)

IterNodesCost
01901471
13571301
29901088
34646985
done5000985

prune709.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (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)))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.7b
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

rewrite93.0ms

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
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-*r/ prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- sin-neg distribute-rgt-neg-out flip-- fma-udef sin-mult
Counts
4 → 69
Calls
4 calls:
45.0ms
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (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)))
42.0ms
(* (sin lambda1) (sin (- lambda2)))
1.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series649.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
36.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
67.0ms
(* (sin lambda1) (sin (- lambda2)))
326.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify1.0s

Counts
81 → 81
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01571567
13601552
217191367
done50001308

prune866.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(expm1 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))))
0.3b
(log1p (expm1 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))))
0.7b
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p log1p-expm1 pow-prod-down prod-exp sin-neg *-commutative distribute-rgt-neg-out cbrt-unprod fma-udef sin-mult expm1-udef unswap-sqr
Counts
4 → 54
Calls
4 calls:
17.0ms
(* (sin lambda1) (sin (- lambda2)))
8.0ms
(expm1 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))))
0.0ms
(log1p (expm1 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))))
0.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series903.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (sin lambda1) (sin (- lambda2)))
262.0ms
(expm1 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))))
285.0ms
(log1p (expm1 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))))
287.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify758.0ms

Counts
66 → 66
Iterations

Useful iterations: done (755.0ms)

IterNodesCost
01191000
1236958
2839842
done5000807

prune629.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes881.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02336
12836
done2836

end0.0ms

sample11.9s

Algorithm
intervals
Results
7.2s3557×body1280valid
2.7s2375×body640valid
1.0s899×body320valid
251.0ms427×body160valid
248.0ms742×body80valid