Details

sample551.0ms

Algorithm

intervals

Results

371.0ms	155×	body	1280	valid
128.0ms	56×	body	640	valid
15.0ms	22×	body	320	valid
4.0ms	18×	body	80	valid
3.0ms	5×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	73
4	73
3	69
2	45
1	27
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize419.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.8b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `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))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))
9.0ms	(sin (- lambda1 lambda2))

series266.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos phi1) (sin phi2))
135.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify2.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	3123
2	840
1	299
0	128

prune733.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.8b	(cos (- lambda1 lambda2))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

18.0ms	(* (cos lambda1) (sin lambda2))
18.0ms	(* (cos phi1) (sin phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))

series359.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cos lambda1) (sin lambda2))
88.0ms	(* (cos phi1) (sin phi2))
156.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
36.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	3545
2	981
1	349
0	146

prune959.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 82

Calls

4 calls:

21.0ms	(* (cos lambda1) (sin lambda2))
18.0ms	(* (cos phi1) (sin phi2))
19.0ms	(* (sin lambda1) (sin lambda2))
81.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos lambda1) (sin lambda2))
61.0ms	(* (cos phi1) (sin phi2))
61.0ms	(* (sin lambda1) (sin lambda2))
275.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5029
2	2069
1	545
0	189

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(cbrt (cos lambda1))
0.3b	(cbrt (cos lambda1))
0.3b	(cbrt (cos lambda1))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`sin-cos-mult` `add-log-exp`
3×	`frac-times` `pow1/3` `associate-r` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+` `sin-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate-l/` `-commutative`

Counts

4 → 60

Calls

4 calls:

51.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
2.0ms	(cbrt (cos lambda1))
2.0ms	(cbrt (cos lambda1))
3.0ms	(cbrt (cos lambda1))

series658.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
139.0ms	(cbrt (cos lambda1))
127.0ms	(cbrt (cos lambda1))
142.0ms	(cbrt (cos lambda1))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
2	1591
1	374
0	119

prune791.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes799.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	51
1	51
0	38

end0.0ms

sample19.6s

Algorithm

intervals

Results

13.8s	4598×	body	1280	valid
4.2s	1974×	body	640	valid
717.0ms	550×	body	320	valid
248.0ms	686×	body	80	valid
166.0ms	192×	body	160	valid