Details

sample339.0ms

Algorithm

intervals

Results

166.0ms	108×	body	1280	valid
114.0ms	80×	body	640	valid
18.0ms	30×	body	320	valid
6.0ms	24×	body	80	valid
6.0ms	14×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize94.0ms

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))))
2.6b	(sin (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))

rewrite60.0ms

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:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
15.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(sin (- lambda1 lambda2))
28.0ms	(cos (- lambda1 lambda2))

series248.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
158.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
48.0ms	(sin (- lambda1 lambda2))
29.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

81 → 81

Iterations

Useful iterations: done (2.9s)

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

prune443.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.6b	(sin (- lambda1 lambda2))

rewrite30.0ms

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:

13.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
15.0ms	(sin (- lambda1 lambda2))

series785.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sin lambda1) (sin lambda2))
24.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
636.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
31.0ms	(sin (- lambda1 lambda2))

simplify2.5s

Counts

73 → 73

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	179	1351
1	303	1165
2	569	973
3	1073	917
4	2174	819
done	5000	756

prune633.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

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

rewrite63.0ms

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:

23.0ms	(* (sin lambda1) (cos lambda2))
36.0ms	(* (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)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
1.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series373.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (cos lambda2))
65.0ms	(* (sin lambda1) (sin lambda2))
34.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
222.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify2.5s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	132	1073
1	255	1031
2	604	904
3	1236	890
4	2505	863
done	5001	863

prune677.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1))))
0.2b	(atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.3b	(log1p (expm1 (atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.5b	(fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1))

rewrite2.0ms

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	(expm1 (atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1))))
0.0ms	(atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.0ms	(log1p (expm1 (atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.0ms	(fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1))

series553.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(expm1 (atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1))))
30.0ms	(atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1)))
135.0ms	(log1p (expm1 (atan2 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
273.0ms	(fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify1.9s

Counts

53 → 53

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	87	1756
1	141	1715
2	263	1678
3	609	1493
4	2382	1493
done	5000	1493

prune460.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes650.0ms

Accuracy

0% (0.2b 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)

Iter	Nodes	Cost
0	22	34
1	26	34
done	26	34

end0.0ms

sample11.8s

Algorithm

intervals

Results

6.3s	3641×	body	1280	valid
3.8s	2245×	body	640	valid
734.0ms	955×	body	320	valid
211.0ms	426×	body	160	valid
180.0ms	733×	body	80	valid