Details

sample271.0ms

Algorithm

intervals

Results

159.0ms	96×	body	1280	valid
66.0ms	67×	body	640	valid
14.0ms	23×	body	320	valid
10.0ms	59×	body	80	valid
4.0ms	11×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	22	33
1	36	32
2	59	32
3	68	32
done	68	32

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

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)))

rewrite13.0ms

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:

4.0ms	(* (sin theta) (sin delta))
4.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin theta) (sin delta))
151.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
6.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
174.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify1.6s

Counts

84 → 84

Iterations

Useful iterations: 3 (350.0ms)

Iter	Nodes	Cost
0	158	1747
1	327	1677
2	889	1492
3	3165	1479
done	5001	1479

prune520.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

0.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms	(/ (- (* (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))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
9.0ms	(- (* (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)))
4.0ms	(* (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))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
622.0ms	(/ (- (* (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))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
346.0ms	(- (* (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)))
143.0ms	(* (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))))))

simplify810.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (181.0ms)

Iter	Nodes	Cost
0	223	6043
1	548	5595
2	2378	4962
done	5000	4962

prune814.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`unpow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow2` `sub-neg` `asin-acos` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqr-sin` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

0.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
19.0ms	(/ (- (pow (cos delta) 2) (* (pow (sin phi1) 2) (* (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)))))))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
10.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 2) (* (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))))))))
5.0ms	(* (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))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
631.0ms	(/ (- (pow (cos delta) 2) (* (pow (sin phi1) 2) (* (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)))))))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
351.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 2) (* (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))))))))
145.0ms	(* (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))))))

simplify924.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (188.0ms)

Iter	Nodes	Cost
0	224	6838
1	542	6525
2	2327	5672
done	5000	5672

prune906.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

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	(* (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))))))
0.5b	(- (/ (pow (cos delta) 2) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (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)) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

280×	`times-frac`
198×	`add-sqr-sqrt`
196×	`prod-diff`
186×	`*-un-lft-identity`
184×	`add-cube-cbrt`
73×	`unpow-prod-down`
38×	`div-inv`
28×	`fma-neg`
25×	`unpow2` `sqr-pow`
11×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`asin-acos`
1×	`pow2` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `flip--` `cbrt-unprod` `sqr-sin` `sin-mult` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 296

Calls

4 calls:

0.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(* (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))))))
38.0ms	(- (/ (pow (cos delta) 2) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (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)) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))

series1.2s

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
142.0ms	(* (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))))))
1.1s	(- (/ (pow (cos delta) 2) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (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)) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))

simplify2.0s

Counts

308 → 308

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	468	72240
1	1037	56550
2	3635	43724
done	5000	43710

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes466.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	231
1	46	231
2	57	231
3	59	231
done	59	231

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.2s	3184×	body	1280	valid
1.7s	1812×	body	640	valid
440.0ms	699×	body	320	valid
348.0ms	1993×	body	80	valid
123.0ms	312×	body	160	valid