Details

sample473.0ms

Algorithm

intervals

Results

359.0ms	144×	body	1280	valid
65.0ms	61×	body	640	valid
13.0ms	19×	body	320	valid
4.0ms	23×	body	80	valid
4.0ms	9×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	46	24
3	71	24
4	83	24
5	84	24
done	84	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite95.0ms

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:

12.0ms	(* (cos phi1) (sin phi2))
56.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series265.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos phi1) (sin phi2))
142.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
38.0ms	(cos (- lambda1 lambda2))
36.0ms	(sin (- lambda1 lambda2))

simplify987.0ms

Counts

71 → 71

Iterations

Useful iterations: done (984.0ms)

Iter	Nodes	Cost
0	128	709
1	299	697
2	1433	601
done	5000	599

prune516.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

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:

14.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (sin lambda1) (cos lambda2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cos phi1) (sin phi2))
59.0ms	(* (sin lambda1) (cos lambda2))
115.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

simplify879.0ms

Counts

80 → 80

Iterations

Useful iterations: done (876.0ms)

Iter	Nodes	Cost
0	150	782
1	363	770
2	1742	668
done	5000	664

prune678.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite211.0ms

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

Counts

4 → 88

Calls

4 calls:

15.0ms	(* (cos phi1) (sin phi2))
11.0ms	(* (sin lambda1) (cos lambda2))
24.0ms	(* (sin (- lambda2)) (sin lambda1))
157.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos phi1) (sin phi2))
46.0ms	(* (sin lambda1) (cos lambda2))
56.0ms	(* (sin (- lambda2)) (sin lambda1))
207.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin (- lambda2)) (sin lambda1))))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	211	1445
1	537	1403
2	2735	1207
done	5001	1200

prune866.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize124.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin (- lambda2)) (sin lambda1)) (* (sin (- lambda2)) (sin lambda1)))
0.3b	(pow (* (sin (- lambda2)) (sin lambda1)) 3)
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
0.5b	(pow (* (cos lambda2) (cos lambda1)) 3)

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`distribute-lft-neg-out` `add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
5×	`sin-neg` `cos-mult` `sin-mult`
4×	`pow-pow` `pow-plus` `pow-exp` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`
1×	`cube-neg` `sqr-neg` `distribute-rgt-neg-out`

Counts

4 → 124

Calls

4 calls:

85.0ms	(* (* (sin (- lambda2)) (sin lambda1)) (* (sin (- lambda2)) (sin lambda1)))
10.0ms	(pow (* (sin (- lambda2)) (sin lambda1)) 3)
60.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
9.0ms	(pow (* (cos lambda2) (cos lambda1)) 3)

series362.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (* (sin (- lambda2)) (sin lambda1)) (* (sin (- lambda2)) (sin lambda1)))
98.0ms	(pow (* (sin (- lambda2)) (sin lambda1)) 3)
70.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
96.0ms	(pow (* (cos lambda2) (cos lambda1)) 3)

simplify4.0s

Counts

136 → 136

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	180	1636
1	621	1114
2	4383	993
done	5001	988

prune903.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes588.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	79
1	48	79
done	48	79

end0.0ms

sample20.8s

Algorithm

intervals

Results

14.8s	4617×	body	1280	valid
4.3s	1946×	body	640	valid
590.0ms	553×	body	320	valid
236.0ms	218×	body	160	valid
226.0ms	666×	body	80	valid