Details

sample1.1s

Algorithm

intervals

Results

656.0ms	62×	body	640	valid
315.0ms	99×	body	1280	valid
35.0ms	27×	body	320	valid
21.0ms	61×	body	80	valid
6.0ms	7×	body	160	valid

simplify61.0ms

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize88.0ms

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)))

rewrite75.0ms

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:

27.0ms	(* (sin theta) (sin delta))
27.0ms	(* (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)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin theta) (sin delta))
257.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
16.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
318.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify2.7s

Counts

84 → 84

Iterations

Useful iterations: done (2.7s)

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

prune780.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

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)))
0.9b	(log (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

22.0ms	(* (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))))
8.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
14.0ms	(log (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

series853.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
9.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
306.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
292.0ms	(log (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

simplify2.6s

Counts

86 → 86

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	156	2434
1	293	2305
2	650	2020
3	1787	1880
done	5000	1872

prune877.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize68.0ms

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) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
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`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `expm1-udef` `associate--r-` `difference-of-squares`

Counts

4 → 81

Calls

4 calls:

19.0ms	(* (sin theta) (sin delta))
21.0ms	(* (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))))
14.0ms	(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

series687.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin theta) (sin delta))
235.0ms	(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
14.0ms	(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
361.0ms	(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

simplify3.1s

Counts

93 → 93

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	181	2957
1	361	2183
2	864	1840
3	2618	1635
done	5000	1625

prune825.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
0.5b	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
1.3b	(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))
1.3b	(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

22×	`log-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
12×	`prod-diff` `log-pow`
10×	`exp-sum`
8×	`pow1` `sqrt-pow1` `add-log-exp`
6×	`add-exp-log` `exp-prod` `fma-neg`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 96

Calls

4 calls:

10.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
8.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
21.0ms	(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))
21.0ms	(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

272.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
264.0ms	(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
594.0ms	(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))
612.0ms	(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))

simplify2.1s

Counts

108 → 108

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	135	3760
1	253	3626
2	543	3188
3	1538	3000
done	5001	2858

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes787.0ms

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	23	34
1	29	34
done	29	34

end0.0ms

sample22.0s

Algorithm

intervals

Results

13.8s	3179×	body	1280	valid
4.9s	1812×	body	640	valid
1.4s	682×	body	320	valid
1.0s	2010×	body	80	valid
283.0ms	317×	body	160	valid