Details

Time bar (total: 32.2s)

sample801.0ms

Algorithm
intervals
Results
458.0ms70×body640valid
287.0ms128×body1280valid
28.0ms28×body320valid
5.0ms9×body160valid
5.0ms21×body80valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.4b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
2.0b
(sin (- lambda1 lambda2))
2.0b
(cos (- lambda1 lambda2))

rewrite41.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg
1×cos-diff sin-diff fma-udef
Counts
4 → 65
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
1.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms
(sin (- lambda1 lambda2))
20.0ms
(cos (- lambda1 lambda2))

series201.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
147.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
24.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify2.5s

Counts
77 → 77
Iterations
IterNodes
done5000
42323
31027
2478
1294
0176

prune846.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize53.0ms

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)))
0.4b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
2.0b
(cos (- lambda1 lambda2))

rewrite84.0ms

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 insert-posit16 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 → 72
Calls
4 calls:
64.0ms
(* (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))
18.0ms
(cos (- lambda1 lambda2))

series394.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
156.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
20.0ms
(cos (- lambda1 lambda2))

simplify2.3s

Counts
84 → 84
Iterations
IterNodes
done5007
33015
2955
1375
0193

prune965.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

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) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b
(* (sin lambda1) (sin lambda2))
0.4b
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite106.0ms

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 insert-posit16 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 → 72
Calls
4 calls:
85.0ms
(* (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)))
19.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series584.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
25.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
79.0ms
(* (sin lambda1) (sin lambda2))
286.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.4s

Counts
84 → 84
Iterations
IterNodes
done5000
34283
21150
1352
0152

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
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×+-commutative sum-log fma-def flip3-+ flip3-- flip-+ sin-cos-mult flip--
Counts
4 → 76
Calls
4 calls:
21.0ms
(* (sin lambda1) (cos lambda2))
119.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))
9.0ms
(+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

series554.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin lambda1) (cos lambda2))
219.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
21.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))
251.0ms
(+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

simplify1.8s

Counts
88 → 88
Iterations
IterNodes
done5001
21437
1408
0166

prune817.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes880.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations
IterNodes
done33
133
026

end0.0ms

sample15.4s

Algorithm
intervals
Results
9.1s3647×body1280valid
4.0s2303×body640valid
1.5s976×body320valid
293.0ms398×body160valid
212.0ms676×body80valid