Details

sample306.0ms

Algorithm

intervals

Results

149.0ms	100×	body	1280	valid
74.0ms	74×	body	640	valid
49.0ms	43×	body	320	valid
5.0ms	26×	body	80	valid
5.0ms	13×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune83.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize51.0ms

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))
4.0b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite33.0ms

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))
14.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
152.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
20.0ms	(cos (- lambda1 lambda2))
35.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

73 → 73

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	172	1599
1	290	1279
2	610	1016
3	1583	930
done	5000	821

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos 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))
4.0b	(cos (- lambda1 lambda2))

rewrite33.0ms

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` `sin-cos-mult` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

16.0ms	(* (sin lambda1) (cos 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))
15.0ms	(cos (- lambda1 lambda2))

series273.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda1) (cos lambda2))
17.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
174.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

73 → 73

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	176	1305
1	326	1140
2	916	948
3	4167	904
done	5001	902

prune596.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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×	`distribute-lft-neg-out` `sin-neg` `sin-cos-mult` `fma-udef` `sin-mult`

Counts

4 → 62

Calls

4 calls:

36.0ms	(* (sin lambda1) (cos lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (cos phi1)))
19.0ms	(* (sin (- lambda2)) (sin lambda1))
0.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (cos phi1))

series496.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin lambda1) (cos lambda2))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (cos phi1)))
97.0ms	(* (sin (- lambda2)) (sin lambda1))
307.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (cos phi1))

simplify829.0ms

Counts

74 → 74

Iterations

Useful iterations: done (825.0ms)

Iter	Nodes	Cost
0	142	1177
1	297	1162
2	1112	1020
done	5001	958

prune801.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
1×	`+-commutative` `sub-neg` `flip3--` `fma-def` `flip3-+` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `sin-cos-mult` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

19.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
23.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))
10.0ms	(+ (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

series523.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
84.0ms	(* (sin lambda1) (cos lambda2))
35.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))
251.0ms	(+ (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	138	1367
1	338	1304
2	1179	1178
done	5001	1161

prune535.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes501.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	34
1	26	34
done	26	34

end0.0ms

sample11.6s

Algorithm

intervals

Results

6.5s	3469×	body	1280	valid
3.1s	2407×	body	640	valid
715.0ms	965×	body	320	valid
550.0ms	430×	body	160	valid
179.0ms	729×	body	80	valid