Details

sample607.0ms

Algorithm

intervals

Results

415.0ms	159×	body	1280	valid
140.0ms	46×	body	640	valid
19.0ms	21×	body	320	valid
7.0ms	26×	body	80	valid
2.0ms	4×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite73.0ms

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:

11.0ms	(* (sin phi1) (cos phi2))
29.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

series292.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (sin phi1) (cos phi2))
143.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	3276
2	794
1	268
0	114

prune827.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(cos (- lambda1 lambda2))

rewrite107.0ms

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` `add-log-exp`
5×	`cos-diff`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `cos-sum` `sub-neg` `distribute-lft-in` `*-commutative` `sin-cos-mult` `associate--r+`
1×	`flip3--` `diff-log` `associate-*l/` `flip--` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

19.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
17.0ms	(* (sin phi1) (cos phi2))
52.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

series766.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
84.0ms	(* (sin phi1) (cos phi2))
455.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	3962
2	1007
1	314
0	125

prune797.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite159.0ms

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

Counts

4 → 88

Calls

4 calls:

19.0ms	(* (sin phi1) (cos phi2))
19.0ms	(* (sin lambda1) (sin lambda2))
65.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
50.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sin phi1) (cos phi2))
74.0ms	(* (sin lambda1) (sin lambda2))
185.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
150.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1532
1	410
0	151

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
0.7b	(cbrt (sin lambda1))
0.7b	(cbrt (sin lambda1))
0.7b	(cbrt (sin lambda1))

rewrite33.0ms

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:

23.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
2.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))

series652.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
134.0ms	(cbrt (sin lambda1))
181.0ms	(cbrt (sin lambda1))
161.0ms	(cbrt (sin lambda1))

simplify3.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5006
4	4614
3	1307
2	472
1	175
0	75

prune966.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes963.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample19.0s

Algorithm

intervals

Results

13.8s	4641×	body	1280	valid
3.8s	1929×	body	640	valid
602.0ms	554×	body	320	valid
210.0ms	661×	body	80	valid
170.0ms	215×	body	160	valid