Details

sample171.0ms

Algorithm

intervals

Results

105.0ms	121×	body	1280	valid
32.0ms	62×	body	640	valid
10.0ms	31×	body	320	valid
7.0ms	15×	body	160	valid
3.0ms	27×	body	80	valid

simplify7.0ms

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)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
1.6b	(cos (- lambda1 lambda2))
1.6b	(sin (- 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))
8.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series346.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
297.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
16.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify1.0s

Counts

73 → 73

Iterations

Useful iterations: 3 (223.0ms)

Iter	Nodes	Cost
0	172	1599
1	288	1267
2	538	980
3	1549	822
done	5000	822

prune295.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

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)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
1.6b	(cos (- lambda1 lambda2))

rewrite13.0ms

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` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (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))

series179.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
16.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
104.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (330.0ms)

Iter	Nodes	Cost
0	171	1296
1	305	1124
2	775	920
3	2803	840
done	5000	840

prune375.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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) (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))

rewrite15.0ms

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-neg` `distribute-rgt-neg-out` `fma-udef` `sin-mult`

Counts

4 → 61

Calls

4 calls:

4.0ms	(* (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)))
9.0ms	(* (sin lambda1) (sin (- lambda2)))
0.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series317.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
206.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify1.6s

Counts

73 → 73

Iterations

Useful iterations: 3 (328.0ms)

Iter	Nodes	Cost
0	137	1168
1	285	1152
2	814	1008
3	3322	949
done	5000	949

prune428.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (log1p (expm1 (* (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))

rewrite11.0ms

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-neg` `distribute-rgt-neg-out` `fma-udef` `sin-mult`

Counts

4 → 61

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (log1p (expm1 (* (cos lambda1) (sin lambda2)))))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
0.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series320.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos lambda1) (sin lambda2))
16.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (log1p (expm1 (* (cos lambda1) (sin lambda2)))))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
50.0ms	(* (sin lambda1) (sin (- lambda2)))
209.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify1.6s

Counts

73 → 73

Iterations

Useful iterations: 3 (328.0ms)

Iter	Nodes	Cost
0	138	1198
1	286	1152
2	818	1008
3	3318	949
done	5000	949

prune401.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes495.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	29	35
done	29	35

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.2s	3520×	body	1280	valid
1.4s	2367×	body	640	valid
328.0ms	960×	body	320	valid
101.0ms	435×	body	160	valid
80.0ms	718×	body	80	valid