Details

sample503.0ms

Algorithm

intervals

Results

353.0ms	158×	body	1280	valid
109.0ms	57×	body	640	valid
8.0ms	11×	body	320	valid
5.0ms	9×	body	160	valid
4.0ms	21×	body	80	valid

simplify4.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite150.0ms

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:

48.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
38.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms	(cos (- lambda1 lambda2))
19.0ms	(sin (- lambda1 lambda2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
146.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
34.0ms	(sin (- lambda1 lambda2))

simplify75.0ms

Counts: 72 → 72

prune336.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))

rewrite141.0ms

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-cos-mult` `flip-+`

Counts

4 → 69

Calls

4 calls:

13.0ms	(* (cos phi1) (sin phi2))
61.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
50.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series397.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos phi1) (sin phi2))
196.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
108.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Counts: 81 → 81

prune586.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite199.0ms

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

Counts

4 → 89

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
47.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
21.0ms	(* (sin lambda1) (sin (- lambda2)))
117.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos phi1) (sin phi2))
164.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
72.0ms	(* (sin lambda1) (sin (- lambda2)))
290.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify85.0ms

Counts: 101 → 101

prune771.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
0.5b	(pow (* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))) 3)
18.1b	(cbrt (pow (* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))) 3))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*r/`
17×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cube-div` `cbrt-prod` `distribute-rgt-in` `distribute-lft-in`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
6×	`associate-l` `cos-mult`
4×	`sub-neg` `cbrt-div` `associate-r` `add-log-exp`
3×	`pow-unpow` `flip3--` `pow-pow` `pow-exp` `frac-sub` `flip--` `sub-div` `rem-cube-cbrt`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `sin-neg` `distribute-rgt-neg-out` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

16.0ms	(* (sin lambda1) (sin (- lambda2)))
123.0ms	(* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
90.0ms	(pow (* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))) 3)
90.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin lambda1) (sin (- lambda2)))
278.0ms	(* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
590.0ms	(pow (* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))) 3)
238.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))) 3))

simplify64.0ms

Counts: 112 → 112

prune904.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes493.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify44.0ms

end0.0ms

sample17.4s

Algorithm

intervals

Results

13.2s	4602×	body	1280	valid
2.9s	1994×	body	640	valid
516.0ms	511×	body	320	valid
161.0ms	225×	body	160	valid
148.0ms	668×	body	80	valid