Details

sample262.0ms

Algorithm

intervals

Results

191.0ms	145×	body	1280	valid
41.0ms	59×	body	640	valid
10.0ms	22×	body	320	valid
3.0ms	25×	body	80	valid
1.0ms	5×	body	160	valid

simplify36.0ms

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: 13.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.1b	(sin (- lambda1 lambda2))

rewrite33.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

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

series174.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify2.8s

Counts

98 → 98

Iterations

Useful iterations: 3 (555.0ms)

Iter	Nodes	Cost
0	208	1720
1	419	1383
2	1212	1069
3	4877	1020
done	5000	1020

prune430.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite30.0ms

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×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

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

series192.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos phi1) (sin phi2))
46.0ms	(* (sin phi1) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify573.0ms

Counts

97 → 97

Iterations

Useful iterations: done (571.0ms)

Iter	Nodes	Cost
0	210	1312
1	435	1135
2	1376	918
done	5000	917

prune507.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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` `sin-cos-mult` `cbrt-unprod`
5×	`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 → 98

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
26.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos phi1) (sin phi2))
42.0ms	(* (sin phi1) (cos phi2))
57.0ms	(* (sin lambda1) (sin (- lambda2)))
179.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify702.0ms

Counts

110 → 110

Iterations

Useful iterations: done (699.0ms)

Iter	Nodes	Cost
0	212	1595
1	528	1541
2	2147	1302
done	5000	1300

prune661.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin lambda1) (sin (- lambda2)))
20.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (cos phi1) (sin phi2))
42.0ms	(* (sin phi1) (cos phi2))
58.0ms	(* (sin lambda1) (sin (- lambda2)))
216.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))

simplify799.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (178.0ms)

Iter	Nodes	Cost
0	221	1933
1	540	1591
2	2151	1374
done	5000	1374

prune587.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes400.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	50
1	40	50
done	40	50

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.2s	4646×	body	1280	valid
1.4s	1891×	body	640	valid
270.0ms	572×	body	320	valid
93.0ms	695×	body	80	valid
57.0ms	196×	body	160	valid