Details

sample693.0ms

Algorithm

intervals

Results

401.0ms	89×	body	1280	valid
171.0ms	60×	body	640	valid
43.0ms	25×	body	320	valid
38.0ms	75×	body	80	valid
7.0ms	7×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite40.0ms

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:

17.0ms	(* (sin theta) (sin delta))
13.0ms	(* (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)))))))

series959.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin theta) (sin delta))
610.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
271.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	2002
3	2002
2	896
1	355
0	166

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1))
0.4b	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
0.6b	(- (cos delta) (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`asin-acos` `log1p-udef` `sub-neg` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

11.0ms	(* (sin theta) (sin delta))
13.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1))
1.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
19.0ms	(- (cos delta) (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))))

series698.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin theta) (sin delta))
238.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1))
10.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
376.0ms	(- (cos delta) (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	2001
3	2001
2	890
1	388
0	189

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize138.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
0.4b	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
0.4b	(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
0.5b	(pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
106×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
82×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`fma-neg`
6×	`add-log-exp`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`asin-acos`
1×	`pow-to-exp` `difference-cubes` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `flip--` `rem-cube-cbrt`

Counts

4 → 241

Calls

4 calls:

1.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
1.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
28.0ms	(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
4.0ms	(pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3)

series1.3s

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
11.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
937.0ms	(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
376.0ms	(pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3)

simplify1.7s

Counts

253 → 253

Iterations

Iter	Nodes
done	2000
2	2000
1	836
0	327

prune9.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize190.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
0.4b	(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
0.5b	(pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3)
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
108×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
84×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`fma-neg`
6×	`pow1` `add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `log-prod` `exp-prod`
2×	`asin-acos`
1×	`pow-to-exp` `difference-cubes` `log-div` `sub-neg` `pow-pow` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-exp` `flip--` `rem-cube-cbrt`

Counts

4 → 249

Calls

4 calls:

1.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
19.0ms	(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
4.0ms	(pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3)
6.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

11.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
1.1s	(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
442.0ms	(pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3)
6.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

simplify1.8s

Counts

261 → 261

Iterations

Iter	Nodes
done	2002
2	2002
1	871
0	355

prune11.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes681.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	48
1	48
0	38

end0.0ms

sample25.6s

Algorithm

intervals

Results

14.7s	3154×	body	1280	valid
6.5s	1833×	body	640	valid
1.7s	679×	body	320	valid
1.4s	2026×	body	80	valid
788.0ms	308×	body	160	valid