Details

sample707.0ms

Algorithm

intervals

Results

482.0ms	149×	body	1280	valid
116.0ms	60×	body	640	valid
59.0ms	28×	body	80	valid
12.0ms	10×	body	160	valid
10.0ms	9×	body	320	valid

simplify108.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	80
4	80
3	77
2	47
1	28
0	17

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize93.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(sin (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(sin (- lambda1 lambda2))
30.0ms	(cos (- lambda1 lambda2))

series240.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos phi1) (sin phi2))
140.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(sin (- lambda1 lambda2))
25.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

101 → 101

Iterations

Iter	Nodes
3	3162
2	1024
1	452
0	226

prune2.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

localize128.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 89

Calls

4 calls:

13.0ms	(* (cos lambda1) (sin lambda2))
23.0ms	(* (sin lambda1) (cos lambda2))
66.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos lambda1) (sin lambda2))
58.0ms	(* (sin lambda1) (cos lambda2))
149.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

101 → 101

Iterations

Iter	Nodes
3	3736
2	1198
1	478
0	228

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

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`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

12.0ms	(* (sin lambda1) (cos lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
82.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
83.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (cos lambda2))
70.0ms	(* (sin lambda1) (sin lambda2))
131.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
182.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify3.0s

Counts

112 → 112

Iterations

Iter	Nodes
3	7352
2	1516
1	434
0	169

prune2.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
0.3b	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
0.3b	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
25.6b	(cbrt (* (* (* (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2)) (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2))) (* (sin lambda1) (* (sin lambda2) (sin phi1)))) (cos phi2)))

rewrite5.3s

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
19×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`associate-*r/`
15×	`sin-mult`
9×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
5×	`frac-times`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 85

Calls

4 calls:

46.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
41.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
41.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
5.2s	(cbrt (* (* (* (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2)) (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2))) (* (sin lambda1) (* (sin lambda2) (sin phi1)))) (cos phi2)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
99.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
100.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))
149.0ms	(cbrt (* (* (* (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2)) (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2))) (* (sin lambda1) (* (sin lambda2) (sin phi1)))) (cos phi2)))

simplify1.9s

Counts

97 → 97

Iterations

Iter	Nodes
3	4375
2	870
1	241
0	105

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes834.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	43
1	43
0	30

end0.0ms

sample24.6s

Algorithm

intervals

Results

17.0s	4634×	body	1280	valid
5.4s	1941×	body	640	valid
1.3s	577×	body	320	valid
271.0ms	627×	body	80	valid
186.0ms	221×	body	160	valid