Details

sample642.0ms

Algorithm

intervals

Results

350.0ms	106×	body	1280	valid
152.0ms	56×	body	640	valid
27.0ms	23×	body	320	valid
24.0ms	56×	body	80	valid
12.0ms	15×	body	160	valid

simplify66.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

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))
0.4b	(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)))

rewrite70.0ms

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:

23.0ms	(* (sin theta) (sin delta))
26.0ms	(* (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))))
18.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin theta) (sin delta))
227.0ms	(* (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))))
301.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify2.8s

Counts

84 → 84

Iterations

Useful iterations: done (2.8s)

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

prune797.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `prod-diff` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `asin-acos` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 82

Calls

4 calls:

1.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
8.0ms	(cbrt (pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3))
31.0ms	(pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3)

series1.0s

Counts

4 → 12

Calls

4 calls:

15.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
281.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
323.0ms	(cbrt (pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3))
423.0ms	(pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3)

simplify1.4s

Counts

94 → 94

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	141	3240
1	319	2919
2	857	2599
done	5000	2550

prune877.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin (cbrt (pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))) (sin phi1)))
0.6b	(pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3)
6.6b	(cbrt (pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `prod-diff`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `asin-acos` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 78

Calls

4 calls:

1.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms	(- (cos delta) (* (sin (cbrt (pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))) (sin phi1)))
3.0ms	(pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3)
3.0ms	(cbrt (pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))

series371.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
306.0ms	(- (cos delta) (* (sin (cbrt (pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))) (sin phi1)))
36.0ms	(pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3)
15.0ms	(cbrt (pow (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))

simplify3.8s

Counts

90 → 90

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	127	2477
1	271	2149
2	663	1882
3	3184	1863
done	5001	1796

prune853.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`fma-neg` `prod-diff`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`cbrt-prod` `sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 75

Calls

4 calls:

8.0ms	(cbrt (- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))
23.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
16.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
18.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

444.0ms	(cbrt (- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))
314.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
282.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
331.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify4.8s

Counts

87 → 87

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	92	2977
1	208	2875
2	473	2541
3	1405	2500
4	4729	2298
done	5000	2298

prune838.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes500.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	30	35
done	30	35

end0.0ms

sample19.6s

Algorithm

intervals

Results

11.4s	3075×	body	1280	valid
5.3s	1899×	body	640	valid
1.1s	2028×	body	80	valid
1.1s	700×	body	320	valid
200.0ms	298×	body	160	valid