Details

sample621.0ms

Algorithm

intervals

Results

410.0ms	145×	body	1280	valid
156.0ms	71×	body	640	valid
10.0ms	11×	body	320	valid
7.0ms	20×	body	80	valid
6.0ms	9×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	79
4	79
3	71
2	46
1	27
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(sin (- lambda1 lambda2))
3.6b	(cos (- lambda1 lambda2))

rewrite115.0ms

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` `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 → 60

Calls

4 calls:

26.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
55.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
148.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms	(sin (- lambda1 lambda2))
27.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1349
1	272
0	116

prune660.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize93.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.1b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(cos (- lambda1 lambda2))

rewrite125.0ms

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×	`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 → 69

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
63.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series465.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (cos phi1) (sin phi2))
225.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
148.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1919
1	378
0	150

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`sin-cos-mult`
3×	`*-commutative` `sin-mult`
2×	`frac-times` `diff-log` `associate-l/` `associate-r/` `cos-mult`
1×	`sum-log` `sub-neg` `flip3--` `flip--` `associate--r+` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

57.0ms	(- (* (cos phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))
18.0ms	(* (sin lambda1) (sin lambda2))
38.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
43.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series886.0ms

Counts

4 → 12

Calls

4 calls:

453.0ms	(- (* (cos phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))
93.0ms	(* (sin lambda1) (sin lambda2))
157.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
182.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify2.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	2183
1	459
0	161

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize198.0ms

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))

rewrite19.0ms

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` `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 → 73

Calls

4 calls:

12.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
1.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))

series606.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
124.0ms	(cbrt (sin lambda1))
145.0ms	(cbrt (sin lambda1))
113.0ms	(cbrt (sin lambda1))

simplify1.7s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	754
1	177
0	75

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes909.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample18.4s

Algorithm

intervals

Results

13.8s	4598×	body	1280	valid
3.2s	1953×	body	640	valid
511.0ms	562×	body	320	valid
206.0ms	661×	body	80	valid
170.0ms	226×	body	160	valid