Details

sample848.0ms

Algorithm

intervals

Results

699.0ms	144×	body	1280	valid
108.0ms	66×	body	640	valid
7.0ms	9×	body	320	valid
7.0ms	30×	body	80	valid
4.0ms	7×	body	160	valid

simplify102.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.4b	(cos (- lambda1 lambda2))
1.5b	(sin (- lambda1 lambda2))

rewrite130.0ms

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

Counts

4 → 64

Calls

4 calls:

34.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

series268.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
110.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify2.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2896
2	805
1	276
0	120

prune749.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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)))
1.4b	(cos (- lambda1 lambda2))

rewrite188.0ms

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:

25.0ms	(* (cos phi1) (sin phi2))
104.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
40.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

series409.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos phi1) (sin phi2))
189.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
129.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
32.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4780
2	1197
1	382
0	154

prune954.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

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

rewrite291.0ms

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:

23.0ms	(* (sin lambda1) (sin lambda2))
116.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
60.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (sin lambda2))
161.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
127.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
117.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify1.7s

Counts

105 → 105

Iterations

Iter	Nodes
done	5008
2	1668
1	434
0	167

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

17.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
1.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))

series607.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
127.0ms	(cbrt (sin lambda1))
137.0ms	(cbrt (sin lambda1))
139.0ms	(cbrt (sin lambda1))

simplify3.5s

Counts

89 → 89

Iterations

Iter	Nodes
done	5027
4	4827
3	1395
2	456
1	176
0	77

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes826.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample20.8s

Algorithm

intervals

Results

15.6s	4668×	body	1280	valid
3.8s	1963×	body	640	valid
679.0ms	550×	body	320	valid
182.0ms	613×	body	80	valid
124.0ms	206×	body	160	valid