Details

sample588.0ms

Algorithm

intervals

Results

374.0ms	108×	body	1280	valid
128.0ms	57×	body	640	valid
21.0ms	65×	body	80	valid
17.0ms	17×	body	320	valid
9.0ms	9×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	75
4	75
3	73
2	61
1	36
0	22

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`fma-udef`
1×	`asin-acos` `associate-r` `*-commutative`

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))
21.0ms	(* (sin theta) (* (cos phi1) (sin delta)))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.0ms	(fma (- (sin phi1)) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (cos delta))

series614.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))
110.0ms	(* (sin theta) (* (cos phi1) (sin delta)))
8.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
292.0ms	(fma (- (sin phi1)) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (cos delta))

simplify1.7s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	3254
2	757
1	226
0	115

prune802.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos delta) (sin phi1))
0.2b	(* (sin theta) (* (cos phi1) (sin delta)))
0.3b	(* (sin phi1) (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))
0.4b	(- (cos delta) (* (sin phi1) (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u`
3×	`fma-neg` `prod-diff` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `associate--r+` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 84

Calls

4 calls:

10.0ms	(* (cos delta) (sin phi1))
21.0ms	(* (sin theta) (* (cos phi1) (sin delta)))
15.0ms	(* (sin phi1) (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))
9.0ms	(- (cos delta) (* (sin phi1) (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1)))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos delta) (sin phi1))
85.0ms	(* (sin theta) (* (cos phi1) (sin delta)))
226.0ms	(* (sin phi1) (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))
246.0ms	(- (cos delta) (* (sin phi1) (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1)))))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	2167
1	436
0	174

prune954.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin delta) (cos theta)) (cos phi1))
0.2b	(* (sin theta) (* (cos phi1) (sin delta)))
0.2b	(* (sin phi1) (* (cos delta) (sin phi1)))
0.4b	(- (fma (- (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)) (cos delta)) (* (sin phi1) (* (cos delta) (sin phi1))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
7×	`associate-l`
6×	`add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `associate-*l/` `associate--l+` `fma-udef` `sin-cos-mult` `flip--`

Counts

4 → 82

Calls

4 calls:

42.0ms	(* (* (sin delta) (cos theta)) (cos phi1))
50.0ms	(* (sin theta) (* (cos phi1) (sin delta)))
40.0ms	(* (sin phi1) (* (cos delta) (sin phi1)))
13.0ms	(- (fma (- (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)) (cos delta)) (* (sin phi1) (* (cos delta) (sin phi1))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (sin delta) (cos theta)) (cos phi1))
107.0ms	(* (sin theta) (* (cos phi1) (sin delta)))
90.0ms	(* (sin phi1) (* (cos delta) (sin phi1)))
266.0ms	(- (fma (- (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)) (cos delta)) (* (sin phi1) (* (cos delta) (sin phi1))))

simplify1.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	2267
1	444
0	178

prune956.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin delta) (cos theta)) (cos phi1))
0.2b	(* (* (cos phi1) (sin theta)) (sin delta))
0.2b	(* (sin phi1) (* (cos delta) (sin phi1)))
0.4b	(- (fma (- (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)) (cos delta)) (* (sin phi1) (* (cos delta) (sin phi1))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
7×	`associate-r`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `associate-*l/` `associate--l+` `fma-udef` `sin-cos-mult` `flip--`

Counts

4 → 82

Calls

4 calls:

29.0ms	(* (* (sin delta) (cos theta)) (cos phi1))
26.0ms	(* (* (cos phi1) (sin theta)) (sin delta))
20.0ms	(* (sin phi1) (* (cos delta) (sin phi1)))
20.0ms	(- (fma (- (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)) (cos delta)) (* (sin phi1) (* (cos delta) (sin phi1))))

series541.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (* (sin delta) (cos theta)) (cos phi1))
94.0ms	(* (* (cos phi1) (sin theta)) (sin delta))
63.0ms	(* (sin phi1) (* (cos delta) (sin phi1)))
272.0ms	(- (fma (- (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)) (cos delta)) (* (sin phi1) (* (cos delta) (sin phi1))))

simplify1.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2521
1	458
0	181

prune898.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes736.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample22.2s

Algorithm

intervals

Results

14.5s	3053×	body	1280	valid
4.1s	1912×	body	640	valid
1.5s	2014×	body	80	valid
1.0s	700×	body	320	valid
348.0ms	321×	body	160	valid