Details

sample569.0ms

Algorithm

intervals

Results

350.0ms	97×	body	1280	valid
124.0ms	64×	body	640	valid
36.0ms	31×	body	320	valid
17.0ms	54×	body	80	valid
7.0ms	10×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	22	33
1	36	32
2	60	32
3	70	32
done	70	32

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.3b	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

26.0ms	(* (sin theta) (sin delta))
42.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
1.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin theta) (sin delta))
216.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
8.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
285.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify2.4s

Counts

84 → 84

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	158	1747
1	322	1677
2	762	1492
3	1915	1479
done	5000	1418

prune834.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
0.4b	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l` `sin-mult`
2×	`asin-acos` `associate-*l/` `cos-mult`
1×	`pow2` `sub-neg` `sqr-cos` `flip3--` `pow-plus` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `associate--l+` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `flip--` `cbrt-unprod` `sqr-sin` `sub-div` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

1.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
44.0ms	(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
14.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

series803.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
15.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
556.0ms	(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
217.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify1.3s

Counts

80 → 80

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	158	3029
1	386	2680
2	1215	2280
done	5000	1843

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize129.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(pow (sin phi1) 3)
0.4b	(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))
0.5b	(pow (sin phi1) 4)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`prod-diff`
19×	`unpow-prod-down`
8×	`fma-neg`
7×	`sqr-pow`
6×	`pow1` `add-exp-log` `pow-unpow` `add-log-exp`
5×	`add-cbrt-cube` `unpow2`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`cube-prod`
2×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`cube-mult` `sub-neg` `asin-acos` `flip3--` `diff-log` `unpow3` `flip--` `fma-udef` `associate--r+` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 106

Calls

4 calls:

1.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(pow (sin phi1) 3)
30.0ms	(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))
4.0ms	(pow (sin phi1) 4)

series812.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
33.0ms	(pow (sin phi1) 3)
717.0ms	(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))
54.0ms	(pow (sin phi1) 4)

simplify1.1s

Counts

118 → 118

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	224	9686
1	517	6026
2	1442	4679
done	5000	3438

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize162.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))
0.4b	(pow (pow (sin phi1) 3) 3)
0.5b	(pow (sin phi1) 4)
6.0b	(cbrt (pow (pow (sin phi1) 3) 3))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

52×	`unpow-prod-down`
42×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt` `cube-prod`
30×	`cbrt-prod`
24×	`prod-diff`
12×	`sqr-pow`
8×	`fma-neg`
7×	`add-exp-log`
6×	`cube-mult` `pow-unpow` `unpow3` `add-log-exp`
5×	`pow1` `pow-exp` `add-cbrt-cube` `unpow2`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`pow-to-exp`
2×	`pow-pow`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `rem-cbrt-cube` `fma-udef` `associate--r+` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

38.0ms	(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))
7.0ms	(pow (pow (sin phi1) 3) 3)
4.0ms	(pow (sin phi1) 4)
26.0ms	(cbrt (pow (pow (sin phi1) 3) 3))

series921.0ms

Counts

4 → 12

Calls

4 calls:

717.0ms	(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))
107.0ms	(pow (pow (sin phi1) 3) 3)
34.0ms	(pow (sin phi1) 4)
63.0ms	(cbrt (pow (pow (sin phi1) 3) 3))

simplify1.9s

Counts

169 → 169

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	261	10926
1	607	6294
2	1759	4973
done	5000	3846

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes797.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	85
1	57	85
done	57	85

end0.0ms

sample20.3s

Algorithm

intervals

Results

12.8s	3122×	body	1280	valid
4.6s	1847×	body	640	valid
1.2s	749×	body	320	valid
792.0ms	1973×	body	80	valid
287.0ms	309×	body	160	valid