Details

sample318.0ms

Algorithm

intervals

Results

202.0ms	115×	body	1280	valid
59.0ms	61×	body	640	valid
21.0ms	35×	body	320	valid
6.0ms	30×	body	80	valid
5.0ms	15×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune87.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.7b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

54.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms	(sin (- lambda1 lambda2))
15.0ms	(cos (- lambda1 lambda2))

series324.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
141.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
37.0ms	(sin (- lambda1 lambda2))
39.0ms	(cos (- lambda1 lambda2))

simplify610.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	998
1	265
0	112

prune483.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda2)) (sin lambda1))
0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))
3.7b	(sin (- lambda1 lambda2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`sin-sum` `associate-r` `associate-l` `add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-lft-neg-out` `+-commutative` `sum-log` `flip3-+` `sin-neg` `sin-diff` `flip-+` `sin-mult`

Counts

4 → 67

Calls

4 calls:

23.0ms	(* (sin (- lambda2)) (sin lambda1))
27.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
7.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))
8.0ms	(sin (- lambda1 lambda2))

series530.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin (- lambda2)) (sin lambda1))
70.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
361.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))
40.0ms	(sin (- lambda1 lambda2))

simplify681.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1223
1	330
0	139

prune951.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda2)) (sin lambda1))
0.2b	(* (sin lambda2) (* (cos lambda1) (cos phi2)))
0.2b	(* (* (cos lambda2) (cos phi2)) (sin lambda1))
0.6b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`associate-+r+`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `cos-mult`
1×	`distribute-lft-neg-out` `+-commutative` `sum-log` `flip3-+` `associate-l/` `sin-neg` `associate-r/` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

24.0ms	(* (sin (- lambda2)) (sin lambda1))
45.0ms	(* (sin lambda2) (* (cos lambda1) (cos phi2)))
40.0ms	(* (* (cos lambda2) (cos phi2)) (sin lambda1))
15.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))

series651.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin (- lambda2)) (sin lambda1))
114.0ms	(* (sin lambda2) (* (cos lambda1) (cos phi2)))
117.0ms	(* (* (cos lambda2) (cos phi2)) (sin lambda1))
357.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))

simplify843.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	1855
1	418
0	166

prune839.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos lambda2) (cos phi2)) (sin lambda1))
0.6b	(cbrt (pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3))
0.6b	(+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))
0.6b	(pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3)

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
4×	`cube-div`
3×	`pow-unpow` `flip3-+` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `pow1/3` `associate-l` `associate-l/` `pow-exp` `cos-mult` `-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 78

Calls

4 calls:

39.0ms	(* (* (cos lambda2) (cos phi2)) (sin lambda1))
48.0ms	(cbrt (pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3))
40.0ms	(+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))
42.0ms	(pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3)

series1.3s

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* (cos lambda2) (cos phi2)) (sin lambda1))
316.0ms	(cbrt (pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3))
341.0ms	(+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))
490.0ms	(pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3)

simplify2.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	2682
1	438
0	148

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes781.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	56
2	56
1	48
0	31

end0.0ms

sample13.2s

Algorithm

intervals

Results

7.2s	3510×	body	1280	valid
4.1s	2346×	body	640	valid
947.0ms	959×	body	320	valid
327.0ms	475×	body	160	valid
134.0ms	710×	body	80	valid