Details

sample806.0ms

Algorithm

intervals

Results

469.0ms	94×	body	1280	valid
153.0ms	52×	body	640	valid
104.0ms	29×	body	320	valid
33.0ms	68×	body	80	valid
14.0ms	13×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	64
3	64
2	59
1	36
0	22

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize108.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 76

Calls

4 calls:

12.0ms	(* (sin theta) (sin delta))
34.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin theta) (sin delta))
221.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
270.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify932.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
2	896
1	355
0	166

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

31.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
12.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
12.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
225.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
6.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
271.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify826.0ms

Counts

87 → 87

Iterations

Iter	Nodes
done	2003
2	1021
1	377
0	170

prune943.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

40.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
12.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
12.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series987.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
242.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
7.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
632.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	2002
2	1135
1	388
0	171

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize156.0ms

Local error

Found 4 expressions with local error:

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

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
19×	`sin-mult`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `associate-*r/` `add-exp-log`
10×	`cos-mult`
9×	`associate-*l/`
8×	`prod-exp` `cbrt-unprod`
7×	`frac-sub`
6×	`frac-times` `add-log-exp`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `pow-sqr` `pow-prod-up` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u`
3×	`sub-div`
2×	`asin-acos` `sqr-cos` `pow-plus` `associate--l+`
1×	`pow2` `distribute-rgt-in` `difference-cubes` `sub-neg` `distribute-lft-in` `flip3--` `fma-neg` `diff-log` `cube-unmult` `swap-sqr` `associate-r` `associate-l` `prod-diff` `pow3` `*-commutative` `flip--`

Counts

4 → 92

Calls

4 calls:

1.0ms	(asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))
1.0ms	(asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))
59.0ms	(* (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)))
299.0ms	(- (* (cos delta) (* (cos delta) (cos delta))) (* (* (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))))

series1.2s

Counts

4 → 12

Calls

4 calls:

10.0ms	(asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))
6.0ms	(asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))
257.0ms	(* (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)))
924.0ms	(- (* (cos delta) (* (cos delta) (cos delta))) (* (* (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))))

simplify1.0s

Counts

104 → 104

Iterations

Iter	Nodes
done	2001
1	706
0	235

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes908.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify28.0ms

Iterations

Iter	Nodes
done	43
1	43
0	32

end0.0ms

sample26.7s

Algorithm

intervals

Results

16.0s	3095×	body	1280	valid
6.4s	1875×	body	640	valid
1.7s	2003×	body	80	valid
1.6s	723×	body	320	valid
540.0ms	304×	body	160	valid