Details

sample797.0ms

Algorithm

intervals

Results

567.0ms	149×	body	1280	valid
168.0ms	60×	body	640	valid
12.0ms	28×	body	80	valid
11.0ms	9×	body	320	valid
10.0ms	10×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize75.0ms

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))

rewrite93.0ms

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))
49.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(sin (- lambda1 lambda2))
23.0ms	(cos (- lambda1 lambda2))

series260.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (cos phi1) (sin phi2))
122.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
37.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

75 → 75

Iterations

Iter	Nodes
3	2651
2	814
1	300
0	132

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

localize100.0ms

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))

rewrite113.0ms

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

Counts

4 → 72

Calls

4 calls:

22.0ms	(* (cos lambda1) (sin lambda2))
21.0ms	(* (sin lambda1) (cos lambda2))
55.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series306.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos lambda1) (sin lambda2))
78.0ms	(* (sin lambda1) (cos lambda2))
131.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

84 → 84

Iterations

Iter	Nodes
3	3375
2	1023
1	362
0	152

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize97.0ms

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)))

rewrite145.0ms

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

Counts

4 → 92

Calls

4 calls:

13.0ms	(* (sin lambda1) (cos lambda2))
20.0ms	(* (sin lambda1) (sin lambda2))
53.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
57.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (cos lambda2))
73.0ms	(* (sin lambda1) (sin lambda2))
141.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
161.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify3.2s

Counts

104 → 104

Iterations

Iter	Nodes
3	7357
2	1507
1	421
0	161

prune2.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2))) (* (sin phi1) (cos phi2)))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2)))
25.6b	(cbrt (* (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))) (* (* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2))) (* (sin phi1) (cos phi2)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

237×	`pow1`
136×	`frac-times`
112×	`sin-cos-mult`
104×	`pow-prod-down`
100×	`sin-mult`
94×	`associate-*l/`
69×	`add-cbrt-cube` `add-exp-log`
63×	`cbrt-div`
60×	`associate-*r/`
47×	`prod-exp` `cbrt-unprod`
42×	`pow-prod-up`
21×	`pow-plus`
20×	`pow-sqr`
5×	`pow2`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l` `pow3` `*-commutative`
2×	`swap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 232

Calls

4 calls:

190.0ms	(* (* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2))) (* (sin phi1) (cos phi2)))
64.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
56.0ms	(* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2)))
915.0ms	(cbrt (* (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))) (* (* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2))) (* (sin phi1) (cos phi2)))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2))) (* (sin phi1) (cos phi2)))
84.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
103.0ms	(* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2)))
157.0ms	(cbrt (* (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))) (* (* (* (sin phi1) (cos phi2)) (* (sin phi1) (cos phi2))) (* (sin phi1) (cos phi2)))))

simplify1.3s

Counts

244 → 244

Iterations

Iter	Nodes
2	3399
1	879
0	335

prune7.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes917.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations

Iter	Nodes
2	46
1	46
0	33

end0.0ms

sample27.5s

Algorithm

intervals

Results

20.2s	4634×	body	1280	valid
5.1s	1941×	body	640	valid
1.3s	577×	body	320	valid
304.0ms	627×	body	80	valid
224.0ms	221×	body	160	valid