Details

sample249.0ms

Algorithm

intervals

Results

178.0ms	145×	body	1280	valid
42.0ms	58×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	26×	body	80	valid
2.0ms	6×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	79	24
4	88	24
done	88	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.6b	(sin (- lambda1 lambda2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos phi1) (sin phi2))
84.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify2.7s

Counts

97 → 97

Iterations

Useful iterations: 3 (530.0ms)

Iter	Nodes	Cost
0	222	1711
1	450	1374
2	1271	1060
3	4994	1011
done	5000	1011

prune407.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series194.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos lambda1) (sin lambda2))
42.0ms	(* (cos phi1) (sin phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify547.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (127.0ms)

Iter	Nodes	Cost
0	221	1303
1	463	1126
2	1504	909
done	5001	909

prune483.0ms

Pruning

12 alts after pruning (12 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	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult` `sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `cos-mult` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div`
1×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 97

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
29.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
48.0ms	(* (cos phi1) (sin phi2))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
178.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify881.0ms

Counts

109 → 109

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	224	1586
1	561	1532
2	2202	1293
done	5001	1291

prune627.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (sin phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `*-commutative` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
1×	`sin-mult`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (sin phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
46.0ms	(* (cos phi1) (sin phi2))
45.0ms	(* (sin lambda1) (sin lambda2))
175.0ms	(* (sin phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))

simplify485.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	173	1079
1	394	1063
2	1312	907
done	5000	907

prune421.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes419.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	25	39
1	32	39
done	32	39

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.8s	4553×	body	1280	valid
1.4s	1976×	body	640	valid
263.0ms	583×	body	320	valid
94.0ms	674×	body	80	valid
59.0ms	214×	body	160	valid