Details

sample733.0ms

Algorithm

intervals

Results

465.0ms	140×	body	1280	valid
181.0ms	71×	body	640	valid
35.0ms	23×	body	80	valid
20.0ms	17×	body	320	valid
4.0ms	5×	body	160	valid

simplify72.0ms

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: 11.8b

localize110.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite114.0ms

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:

15.0ms	(* (cos phi1) (sin phi2))
63.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
17.0ms	(sin (- lambda1 lambda2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos phi1) (sin phi2))
133.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify2.3s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	3145
2	833
1	302
0	132

prune619.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(cos (- lambda1 lambda2))

rewrite67.0ms

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` `*-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 71

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
14.0ms	(* (cos lambda1) (sin lambda2))
29.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))

series234.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos phi1) (sin phi2))
49.0ms	(* (cos lambda1) (sin lambda2))
118.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

83 → 83

Iterations

Iter	Nodes
done	5006
3	3588
2	987
1	356
0	150

prune883.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 86

Calls

4 calls:

15.0ms	(* (cos phi1) (sin phi2))
17.0ms	(* (cos lambda1) (sin lambda2))
14.0ms	(* (sin lambda1) (sin lambda2))
78.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos phi1) (sin phi2))
46.0ms	(* (cos lambda1) (sin lambda2))
53.0ms	(* (sin lambda1) (sin lambda2))
204.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	2068
1	549
0	193

prune996.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
6.0b	(cbrt (* (sin lambda1) (sin lambda2)))
6.0b	(cbrt (* (sin lambda1) (sin lambda2)))
6.0b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod` `cbrt-div` `sin-mult`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

35.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
6.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
125.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
120.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
116.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify1.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	2061
2	651
1	231
0	91

prune656.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes840.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample24.5s

Algorithm

intervals

Results

16.6s	4534×	body	1280	valid
5.4s	1950×	body	640	valid
1.3s	618×	body	320	valid
629.0ms	682×	body	80	valid
170.0ms	216×	body	160	valid