Details

sample472.0ms

Algorithm

intervals

Results

359.0ms	145×	body	1280	valid
67.0ms	61×	body	640	valid
12.0ms	18×	body	320	valid
5.0ms	26×	body	80	valid
3.0ms	6×	body	160	valid

simplify5.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite159.0ms

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

Counts

4 → 60

Calls

4 calls:

47.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
52.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
40.0ms	(cos (- lambda1 lambda2))
18.0ms	(sin (- lambda1 lambda2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
112.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
33.0ms	(sin (- lambda1 lambda2))

simplify89.0ms

Counts: 72 → 72

prune472.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(cos (- lambda1 lambda2))

rewrite153.0ms

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` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-neg` `distribute-rgt-neg-out` `sin-cos-mult` `flip-+`

Counts

4 → 70

Calls

4 calls:

28.0ms	(* (cos lambda1) (sin (- lambda2)))
66.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(cos (- lambda1 lambda2))

series435.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (cos lambda1) (sin (- lambda2)))
181.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
147.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Counts: 82 → 82

prune738.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

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`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `flip3-+` `associate-r/` `associate-l/` `flip-+` `sin-mult` `unswap-sqr`
2×	`frac-add` `cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 85

Calls

4 calls:

18.0ms	(* (cos lambda1) (sin (- lambda2)))
64.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
75.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
32.0ms	(* (sin lambda1) (sin lambda2))

series523.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos lambda1) (sin (- lambda2)))
175.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
240.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
50.0ms	(* (sin lambda1) (sin lambda2))

simplify70.0ms

Counts: 97 → 97

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
3.0b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `flip3-+` `associate-l/` `log-pow` `-commutative` `sin-cos-mult` `flip-+`
2×	`frac-times` `associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `exp-prod` `exp-to-pow` `distribute-lft-in` `rem-log-exp` `sin-mult`

Counts

4 → 78

Calls

4 calls:

48.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
77.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
19.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
225.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
66.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify72.0ms

Counts: 90 → 90

prune694.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes826.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify38.0ms

end0.0ms

sample17.1s

Algorithm

intervals

Results

12.6s	4671×	body	1280	valid
3.2s	1908×	body	640	valid
513.0ms	560×	body	320	valid
183.0ms	649×	body	80	valid
95.0ms	212×	body	160	valid