Details

sample174.0ms

Algorithm

intervals

Results

103.0ms	111×	body	1280	valid
43.0ms	86×	body	640	valid
9.0ms	27×	body	320	valid
2.0ms	23×	body	80	valid
2.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize26.0ms

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))
3.3b	(sin (- lambda1 lambda2))
3.3b	(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `sin-sum`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series156.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
108.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

73 → 73

Iterations

Useful iterations: 3 (236.0ms)

Iter	Nodes	Cost
0	172	1599
1	288	1267
2	538	980
3	1546	822
done	5000	822

prune292.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

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))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.4b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.3b	(cos (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-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×	`cos-diff` `sub-neg` `pow-prod-down` `prod-exp` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

8.0ms	(* (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))
7.0ms	(cos (- lambda1 lambda2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos lambda1) (sin (- lambda2)))
13.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
108.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))

simplify2.0s

Counts

73 → 73

Iterations

Useful iterations: 3 (381.0ms)

Iter	Nodes	Cost
0	179	1345
1	327	1156
2	832	948
3	3032	922
done	5001	922

prune400.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef` `sin-mult`

Counts

4 → 62

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin (- lambda2)))
6.0ms	(* (sin 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)))
0.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series340.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos lambda1) (sin (- lambda2)))
56.0ms	(* (sin lambda1) (sin (- lambda2)))
16.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
214.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify1.6s

Counts

74 → 74

Iterations

Useful iterations: 3 (359.0ms)

Iter	Nodes	Cost
0	135	1217
1	295	1184
2	854	1036
3	3250	977
done	5000	977

prune462.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

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 (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
0.2b	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.4b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
0.5b	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `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 (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
1.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
1.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
262.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
202.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
207.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

simplify532.0ms

Counts

63 → 63

Iterations

Useful iterations: 3 (147.0ms)

Iter	Nodes	Cost
0	105	1566
1	195	1465
2	405	1274
3	1279	1271
done	5000	1271

prune361.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes495.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.2s	3551×	body	1280	valid
1.3s	2449×	body	640	valid
322.0ms	943×	body	320	valid
87.0ms	372×	body	160	valid
70.0ms	685×	body	80	valid