Details

sample455.0ms

Algorithm

intervals

Results

325.0ms	138×	body	1280	valid
75.0ms	68×	body	640	valid
17.0ms	25×	body	320	valid
5.0ms	21×	body	80	valid
2.0ms	4×	body	160	valid

simplify81.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))
3.7b	(sin (- lambda1 lambda2))

rewrite106.0ms

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×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

25.0ms	(* (cos phi1) (sin phi2))
46.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
13.0ms	(sin (- lambda1 lambda2))

series270.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cos phi1) (sin phi2))
137.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))
38.0ms	(sin (- lambda1 lambda2))

simplify1.9s

Counts: 71 → 71

prune466.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

25.0ms	(* (sin lambda1) (cos lambda2))
24.0ms	(* (cos phi1) (sin phi2))
65.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
36.0ms	(cos (- lambda1 lambda2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin lambda1) (cos lambda2))
49.0ms	(* (cos phi1) (sin phi2))
104.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
36.0ms	(cos (- lambda1 lambda2))

simplify636.0ms

Counts: 80 → 80

prune805.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

14.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (cos phi1) (sin phi2))
69.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
73.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin lambda1) (sin lambda2))
61.0ms	(* (cos phi1) (sin phi2))
166.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
142.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify931.0ms

Counts: 99 → 99

prune812.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
2×	`sin-mult`
1×	`frac-times` `associate-*r/` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

26.0ms	(* (cos phi1) (sin phi2))
56.0ms	(* (* (sin phi1) (cos phi2)) (cos lambda1))
117.0ms	(* (* (* (sin phi1) (cos phi2)) (cos lambda1)) (cos lambda2))
80.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cos phi1) (sin phi2))
112.0ms	(* (* (sin phi1) (cos phi2)) (cos lambda1))
196.0ms	(* (* (* (sin phi1) (cos phi2)) (cos lambda1)) (cos lambda2))
153.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify1.2s

Counts: 96 → 96

prune603.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes649.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.2s

end0.0ms

sample18.7s

Algorithm

intervals

Results

13.3s	4580×	body	1280	valid
3.7s	1954×	body	640	valid
911.0ms	626×	body	320	valid
148.0ms	633×	body	80	valid
109.0ms	207×	body	160	valid