Details

sample907.0ms

Algorithm

intervals

Results

466.0ms	32×	body	320	valid
285.0ms	101×	body	1280	valid
101.0ms	51×	body	640	valid
20.0ms	63×	body	80	valid
6.0ms	9×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

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

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize133.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (sin theta)))
0.3b	(* (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))))
0.4b	(- (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` `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 → 71

Calls

4 calls:

23.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
19.0ms	(* (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:

92.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
237.0ms	(* (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))))
261.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify2.8s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	3391
2	995
1	370
0	166

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize205.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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))))
0.3b	(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))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`asin-acos` `associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

9.0ms	(* (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))))
1.0ms	(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))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
14.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
8.0ms	(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))))

simplify2.6s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
4	1860
3	834
2	342
1	154
0	78

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize292.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `asin-acos` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
7.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
12.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
14.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))

simplify4.1s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
9	1435
8	439
7	192
6	121
5	87
4	68
3	58
2	44
1	34
0	28

prune940.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize146.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
0.3b	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
0.4b	(- (cos delta) (cbrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))
17.5b	(cbrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`prod-diff` `add-cube-cbrt` `sin-mult`
7×	`cbrt-div`
6×	`add-log-exp`
5×	`frac-times` `associate-*r/`
4×	`cbrt-prod` `expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-neg` `associate-*l/`
2×	`asin-acos`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `cube-unmult` `rem-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

1.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
1.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
13.0ms	(- (cos delta) (cbrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))
100.0ms	(cbrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
9.0ms	(asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))
276.0ms	(- (cos delta) (cbrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))
233.0ms	(cbrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))

simplify3.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5002
3	2460
2	750
1	325
0	150

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample20.0s

Algorithm

intervals

Results

12.3s	3199×	body	1280	valid
5.3s	1808×	body	640	valid
903.0ms	745×	body	320	valid
818.0ms	1934×	body	80	valid
222.0ms	314×	body	160	valid