Details

sample390.0ms

Algorithm

intervals

Results

193.0ms	118×	body	1280	valid
136.0ms	71×	body	640	valid
29.0ms	37×	body	320	valid
5.0ms	12×	body	160	valid
4.0ms	18×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.7b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`sin-sum`
32×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
11×	`distribute-rgt-in` `cos-sum` `distribute-lft-in`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`cos-diff` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

68.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
1.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
31.0ms	(sin (- lambda1 lambda2))
57.0ms	(cos (- lambda1 lambda2))

series294.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
153.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
29.0ms	(sin (- lambda1 lambda2))
36.0ms	(cos (- lambda1 lambda2))

simplify5.0s

Counts

106 → 106

Iterations

Useful iterations: 5 (3.7s)

Iter	Nodes	Cost
0	223	2679
1	396	2016
2	739	1591
3	1279	1421
4	2214	1060
5	4741	825
done	5000	825

prune533.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.2b	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.8b	(cos (- lambda1 lambda2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `cos-sum` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `prod-diff` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`distribute-lft-neg-out` `cos-diff` `sub-neg` `associate-l` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `fma-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
39.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
14.0ms	(cos (- lambda1 lambda2))

series325.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
144.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
127.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
33.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

73 → 73

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	185	1467
1	335	1246
2	808	993
3	2614	913
done	5000	831

prune546.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
0.2b	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.6b	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`sin-neg` `*-commutative` `distribute-rgt-neg-out`
1×	`distribute-lft-neg-out` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

0.0ms	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
40.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
17.0ms	(* (sin lambda1) (sin (- lambda2)))
0.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series566.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
124.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
108.0ms	(* (sin lambda1) (sin (- lambda2)))
311.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify2.7s

Counts

74 → 74

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	141	1339
1	296	1274
2	910	1081
3	2994	1022
done	5000	1022

prune846.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (+ (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
0.2b	(fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))
0.2b	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.6b	(+ (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`associate-+l+`
1×	`+-commutative` `distribute-lft-neg-out` `distribute-rgt-in` `fma-def` `distribute-lft-in` `flip3-+` `associate-l` `sin-neg` `sum-log` `*-commutative` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 56

Calls

4 calls:

0.0ms	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (+ (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
0.0ms	(fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))
47.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
24.0ms	(+ (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1))

series575.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(atan2 (+ (* (* (sin lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (sin (- lambda2))) (cos phi2))) (+ (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
111.0ms	(fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))
122.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
314.0ms	(+ (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1))

simplify2.8s

Counts

68 → 68

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	139	1411
1	321	1314
2	956	1127
3	3746	1115
done	5000	1114

prune377.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes709.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	37
1	32	37
done	32	37

end0.0ms

sample11.3s

Algorithm

intervals

Results

6.1s	3555×	body	1280	valid
3.8s	2408×	body	640	valid
704.0ms	975×	body	320	valid
180.0ms	375×	body	160	valid
152.0ms	687×	body	80	valid