Details

Time bar (total: 30.5s)

sample382.0ms

Algorithm
intervals
Results
224.0ms109×body1280valid
95.0ms71×body640valid
27.0ms39×body320valid
7.0ms15×body160valid
5.0ms22×body80valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01420
12020
22319
done2319

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.9b
(cos (- lambda1 lambda2))
4.0b
(sin (- lambda1 lambda2))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
33×sin-sum
32×add-sqr-sqrt
30×add-cube-cbrt *-un-lft-identity
11×distribute-rgt-in cos-sum distribute-lft-in
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u sub-neg log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×cos-diff pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 94
Calls
4 calls:
37.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
1.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
43.0ms
(cos (- lambda1 lambda2))
24.0ms
(sin (- lambda1 lambda2))

series315.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
181.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
30.0ms
(cos (- lambda1 lambda2))
32.0ms
(sin (- lambda1 lambda2))

simplify4.9s

Counts
106 → 106
Iterations

Useful iterations: 5 (3.6s)

IterNodesCost
02232679
13962016
27391591
312881421
422251060
54771825
done5000825

prune459.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.9b
(cos (- lambda1 lambda2))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×cos-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*
2×associate-*r/
1×distribute-rgt-in cos-diff sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ fma-udef unswap-sqr
Counts
4 → 64
Calls
4 calls:
67.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
14.0ms
(cos (- lambda1 lambda2))

series425.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
29.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
171.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
20.0ms
(cos (- lambda1 lambda2))

simplify3.7s

Counts
76 → 76
Iterations

Useful iterations: 3 (2.0s)

IterNodesCost
01831652
13671436
210441195
337441102
done50001102

prune719.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.5b
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite71.0ms

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×associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-+ flip-+ fma-udef sin-mult
Counts
4 → 64
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
56.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (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))

series667.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sin lambda1) (sin lambda2))
219.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
35.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
335.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify3.3s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01421455
13341370
211121196
340461194
done50001194

prune631.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (log1p (expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b
(expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2)))
0.2b
(log1p (expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2))))
0.5b
(fma (cos phi2) (+ (* (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
(atan2 (log1p (expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
1.0ms
(expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2)))
1.0ms
(log1p (expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2))))
1.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series998.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(atan2 (log1p (expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
297.0ms
(expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2)))
270.0ms
(log1p (expm1 (* (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))) (cos phi2))))
386.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify1.3s

Counts
53 → 53
Iterations

Useful iterations: 3 (266.0ms)

IterNodesCost
01071287
11861185
23961058
311471027
done50001027

prune466.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes643.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02335
12935
done2935

end0.0ms

sample11.0s

Algorithm
intervals
Results
6.3s3545×body1280valid
2.8s2386×body640valid
1.2s1003×body320valid
187.0ms362×body160valid
113.0ms704×body80valid