Details

sample407.0ms

Algorithm

intervals

Results

254.0ms	108×	body	1280	valid
90.0ms	79×	body	640	valid
29.0ms	41×	body	320	valid
5.0ms	10×	body	160	valid
4.0ms	18×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	23	19
done	23	19

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.5b	(sin (- lambda1 lambda2))
6.0b	(cos (- lambda1 lambda2))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 69

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
22.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(sin (- lambda1 lambda2))
46.0ms	(cos (- lambda1 lambda2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
134.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
32.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

81 → 81

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	191	1730
1	353	1390
2	669	1106
3	1412	1020
4	3099	875
done	5000	874

prune473.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
5.5b	(sin (- lambda1 lambda2))

rewrite38.0ms

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-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 lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
14.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
21.0ms	(sin (- lambda1 lambda2))

series316.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
69.0ms	(* (sin lambda1) (sin lambda2))
195.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
30.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	179	1351
1	304	1177
2	582	973
3	1078	917
4	2199	819
done	5000	756

prune573.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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

Counts

4 → 61

Calls

4 calls:

13.0ms	(* (sin lambda1) (cos lambda2))
28.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series399.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin lambda1) (cos lambda2))
69.0ms	(* (sin lambda1) (sin lambda2))
30.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
228.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify2.8s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	132	1073
1	256	1043
2	614	904
3	1239	890
4	2504	863
done	5001	863

prune673.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2)))))))
0.5b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
3.1b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

38.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2)))))))
1.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
10.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin lambda1) (sin lambda2))
35.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2)))))))
211.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
75.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify2.0s

Counts

68 → 68

Iterations

Useful iterations: 4 (927.0ms)

Iter	Nodes	Cost
0	118	1084
1	200	1001
2	434	866
3	847	852
4	1774	826
done	5000	826

prune606.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes727.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	41
1	36	41
done	36	41

end0.0ms

sample12.8s

Algorithm

intervals

Results

8.1s	3560×	body	1280	valid
3.2s	2369×	body	640	valid
671.0ms	980×	body	320	valid
158.0ms	407×	body	160	valid
129.0ms	684×	body	80	valid