Details

sample435.0ms

Algorithm

intervals

Results

340.0ms	149×	body	1280	valid
51.0ms	53×	body	640	valid
11.0ms	18×	body	320	valid
5.0ms	11×	body	160	valid
5.0ms	25×	body	80	valid

simplify58.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(sin (- lambda1 lambda2))
4.0b	(cos (- lambda1 lambda2))

rewrite151.0ms

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:

44.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
45.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
41.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

series268.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
125.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(sin (- lambda1 lambda2))
28.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts: 72 → 72

prune347.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))

rewrite77.0ms

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` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `diff-log` `associate-*l/` `flip--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

19.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
14.0ms	(* (sin lambda1) (cos lambda2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(cos (- lambda1 lambda2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
50.0ms	(* (sin lambda1) (cos lambda2))
104.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts: 74 → 74

prune562.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

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`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `associate-*l/` `flip--`

Counts

4 → 77

Calls

4 calls:

19.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
12.0ms	(* (sin lambda1) (cos lambda2))
12.0ms	(* (sin lambda1) (sin lambda2))
62.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
68.0ms	(* (sin lambda1) (cos lambda2))
75.0ms	(* (sin lambda1) (sin lambda2))
205.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify1.1s

Counts: 89 → 89

prune649.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

24.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
2.0ms	(cbrt (cos lambda2))
2.0ms	(cbrt (cos lambda2))
12.0ms	(cbrt (cos lambda2))

series502.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
115.0ms	(cbrt (cos lambda2))
102.0ms	(cbrt (cos lambda2))
113.0ms	(cbrt (cos lambda2))

simplify780.0ms

Counts: 85 → 85

prune625.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes745.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0s

end0.0ms

sample17.3s

Algorithm

intervals

Results

12.2s	4656×	body	1280	valid
3.0s	1919×	body	640	valid
882.0ms	544×	body	320	valid
552.0ms	622×	body	80	valid
151.0ms	259×	body	160	valid