Details

sample885.0ms

Algorithm

intervals

Results

691.0ms	159×	body	1280	valid
134.0ms	50×	body	640	valid
33.0ms	24×	body	320	valid
4.0ms	17×	body	80	valid
4.0ms	6×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	73
4	73
3	69
2	45
1	27
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize53.0ms

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))

rewrite76.0ms

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` `insert-posit16` `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 → 63

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
48.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

series215.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos phi1) (sin phi2))
111.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

75 → 75

Iterations

Iter	Nodes
3	2688
2	822
1	300
0	132

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.4b

localize72.0ms

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)))
4.0b	(cos (- lambda1 lambda2))

rewrite149.0ms

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×	`insert-posit16` `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 → 73

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
86.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
43.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series380.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos phi1) (sin phi2))
180.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
117.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

85 → 85

Iterations

Iter	Nodes
3	4181
2	1204
1	380
0	154

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`associate-l/` `-commutative` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 93

Calls

4 calls:

96.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (sin lambda1) (sin lambda2))
71.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
50.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
86.0ms	(* (sin lambda1) (sin lambda2))
157.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
148.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify4.2s

Counts

105 → 105

Iterations

Iter	Nodes
3	9023
2	1673
1	434
0	167

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

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) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))

rewrite232.0ms

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` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-l/` `associate-r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 88

Calls

4 calls:

13.0ms	(* (cos phi1) (sin phi2))
83.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
102.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
32.0ms	(* (sin lambda1) (sin lambda2))

series553.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos phi1) (sin phi2))
160.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
255.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
81.0ms	(* (sin lambda1) (sin lambda2))

simplify770.0ms

Counts

100 → 100

Iterations

Iter	Nodes
2	2217
1	571
0	202

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes676.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	47
1	47
0	34

end0.0ms

sample26.4s

Algorithm

intervals

Results

19.6s	4624×	body	1280	valid
5.1s	1925×	body	640	valid
801.0ms	573×	body	320	valid
333.0ms	667×	body	80	valid
173.0ms	211×	body	160	valid