Details

sample175.0ms

Algorithm

intervals

Results

104.0ms	110×	body	1280	valid
41.0ms	81×	body	640	valid
11.0ms	33×	body	320	valid
4.0ms	19×	body	160	valid
1.0ms	13×	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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize20.0ms

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))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite16.0ms

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	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series155.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
104.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify2.2s

Counts

73 → 73

Iterations

Useful iterations: 5 (1.2s)

Iter	Nodes	Cost
0	172	1599
1	282	1267
2	445	1016
3	804	930
4	1609	785
5	4329	749
done	5000	749

prune296.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 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))
5.0b	(sin (- lambda1 lambda2))

rewrite13.0ms

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:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
4.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
7.0ms	(sin (- lambda1 lambda2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
46.0ms	(* (sin lambda1) (sin lambda2))
197.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
21.0ms	(sin (- lambda1 lambda2))

simplify1.4s

Counts

73 → 73

Iterations

Useful iterations: 4 (724.0ms)

Iter	Nodes	Cost
0	182	1402
1	319	1201
2	600	1029
3	1241	986
4	2953	884
done	5000	884

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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 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))

rewrite10.0ms

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:

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

series303.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (cos 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)))
46.0ms	(* (sin lambda1) (sin lambda2))
197.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify1.6s

Counts

73 → 73

Iterations

Useful iterations: 4 (868.0ms)

Iter	Nodes	Cost
0	126	1108
1	256	1067
2	609	1020
3	1397	929
4	3692	928
done	5000	928

prune416.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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

rewrite13.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`associate-+l+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `distribute-lft-in` `flip3-+` `sum-log` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 67

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1)))
4.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(+ (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series312.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (cos lambda2))
16.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1)))
50.0ms	(* (sin lambda1) (sin lambda2))
203.0ms	(+ (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify1.1s

Counts

79 → 79

Iterations

Useful iterations: 3 (385.0ms)

Iter	Nodes	Cost
0	139	1253
1	321	1204
2	814	1067
3	2299	1055
done	5001	1055

prune348.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes450.0ms

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	21	36
1	29	36
done	29	36

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.3s	3554×	body	1280	valid
1.4s	2379×	body	640	valid
328.0ms	925×	body	320	valid
97.0ms	439×	body	160	valid
75.0ms	702×	body	80	valid
3.0ms	1×	body	2560	valid