Details

Time bar (total: 27.8s)

sample363.0ms

Algorithm
intervals
Results
180.0ms104×body1280valid
125.0ms86×body640valid
13.0ms19×body320valid
9.0ms19×body160valid
6.0ms28×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
014584
120584
223559
done23559

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.6b
(sin (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cos-sum sin-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log 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))
11.0ms
(sin (- lambda1 lambda2))
13.0ms
(cos (- lambda1 lambda2))

series223.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
155.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
27.0ms
(sin (- lambda1 lambda2))
30.0ms
(cos (- lambda1 lambda2))

simplify1.4s

Counts
73 → 73
Iterations

Useful iterations: done (1.4s)

IterNodesCost
017235963
129031831
261528232
3160027606
done500024267

prune961.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.7b

localize68.0ms

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))
3.8b
(cos (- lambda1 lambda2))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×cos-sum prod-diff
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in sub-neg distribute-lft-in associate-*r* associate-*l*
2×associate-*r/
1×cos-diff flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef flip-- unswap-sqr
Counts
4 → 68
Calls
4 calls:
47.0ms
(* (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))
11.0ms
(cos (- lambda1 lambda2))

series494.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
188.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
28.0ms
(cos (- lambda1 lambda2))

simplify1.7s

Counts
80 → 80
Iterations

Useful iterations: done (1.7s)

IterNodesCost
018943959
137441276
2135339334
done500139284

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize116.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
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 prod-diff pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×flip3-- fma-udef flip-- sin-mult
Counts
4 → 68
Calls
4 calls:
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)))
86.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
18.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series611.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
199.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
57.0ms
(* (sin lambda1) (sin lambda2))
323.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify1.9s

Counts
80 → 80
Iterations

Useful iterations: done (1.9s)

IterNodesCost
014840312
134438709
2156038554
done500038529

prune890.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
2×associate-+l+ sub-neg prod-diff pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod fma-udef unswap-sqr
1×+-commutative sum-log fma-def flip3-+ flip3-- flip-+ flip--
Counts
4 → 73
Calls
4 calls:
11.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
94.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms
(+ (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1))

series584.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (cos lambda1) (sin lambda2))
33.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
198.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
266.0ms
(+ (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1))

simplify2.2s

Counts
85 → 85
Iterations

Useful iterations: done (2.2s)

IterNodesCost
016544415
141542094
2176141779
done500241754

prune791.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
0271174
1361174
done361174

end0.0ms

sample12.9s

Algorithm
intervals
Results
7.7s3606×body1280valid
3.6s2359×body640valid
676.0ms900×body320valid
337.0ms429×body160valid
183.0ms706×body80valid