Details

sample291.0ms

Algorithm

intervals

Results

155.0ms	116×	body	1280	valid
91.0ms	71×	body	640	valid
19.0ms	37×	body	320	valid
4.0ms	15×	body	160	valid
3.0ms	17×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize96.0ms

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))
1.8b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite35.0ms

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))
20.0ms	(cos (- lambda1 lambda2))
11.0ms	(sin (- lambda1 lambda2))

series242.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
157.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
32.0ms	(cos (- lambda1 lambda2))
34.0ms	(sin (- lambda1 lambda2))

simplify2.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	2153
3	904
2	441
1	290
0	172

prune860.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize64.0ms

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))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
1.9b	(sin (- lambda1 lambda2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`sin-sum`
9×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`sub-neg` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 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))
15.0ms	(sin (- lambda1 lambda2))

series509.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
91.0ms	(* (sin lambda1) (sin lambda2))
352.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
38.0ms	(sin (- lambda1 lambda2))

simplify2.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1779
2	647
1	341
0	184

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize112.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef` `sin-mult`

Counts

4 → 60

Calls

4 calls:

18.0ms	(* (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)))
29.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series492.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos lambda1) (sin lambda2))
32.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
83.0ms	(* (sin lambda1) (sin lambda2))
313.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	1776
2	630
1	275
0	128

prune750.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize126.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.2b	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.5b	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
0.6b	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `add-exp-log` `log-pow` `log1p-expm1-u`
3×	`fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 51

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
3.0ms	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.0ms	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
4.0ms	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

30.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
396.0ms	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
309.0ms	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
326.0ms	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

simplify3.4s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
4	4444
3	1150
2	380
1	188
0	100

prune722.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes1.2s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample11.2s

Algorithm

intervals

Results

6.7s	3491×	body	1280	valid
2.8s	2417×	body	640	valid
699.0ms	954×	body	320	valid
413.0ms	702×	body	80	valid
195.0ms	436×	body	160	valid