Details

sample508.0ms

Algorithm

intervals

Results

297.0ms	91×	body	1280	valid
111.0ms	67×	body	640	valid
44.0ms	67×	body	80	valid
25.0ms	20×	body	320	valid
9.0ms	11×	body	160	valid

simplify75.0ms

Counts

1 → 1

Iterations

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

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize92.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

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` `insert-posit16` `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 → 75

Calls

4 calls:

48.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
13.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
10.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
6.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
190.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
255.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify3.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	5004
3	3385
2	1011
1	377
0	170

prune933.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.3b	(* (sin phi1) (sin (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)))))))
0.5b	(expm1 (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`asin-acos` `expm1-log1p` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `sin-mult` `expm1-udef` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
27.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
13.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
0.0ms	(expm1 (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

series891.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
188.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
257.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
440.0ms	(expm1 (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

simplify2.6s

Counts

78 → 78

Iterations

Iter	Nodes
done	5002
3	2523
2	844
1	338
0	151

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin delta) (* (cos phi1) (sin theta)))
0.3b	(* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1)))))
0.4b	(- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1))))))
0.5b	(expm1 (- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1)))))))

rewrite73.0ms

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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef` `insert-posit16`
3×	`fma-neg` `prod-diff`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `associate--r+`
1×	`expm1-log1p` `sub-neg` `flip3--` `diff-log` `flip--` `expm1-udef` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

48.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
10.0ms	(* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1)))))
8.0ms	(- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1))))))
1.0ms	(expm1 (- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1)))))))

series971.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
215.0ms	(* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1)))))
264.0ms	(- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1))))))
380.0ms	(expm1 (- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (cos theta) (* (sin delta) (cos phi1)))))))

simplify1.8s

Counts

91 → 91

Iterations

Iter	Nodes
done	5014
2	1324
1	410
0	168

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (* (sin phi1) (cos delta)))
0.3b	(* (sin delta) (* (cos phi1) (sin theta)))
0.5b	(expm1 (- (- (cos delta) (* (sin phi1) (* (sin phi1) (cos delta)))) (* (sin phi1) (* (cos theta) (* (sin delta) (cos phi1))))))
0.6b	(- (cos delta) (* (sin phi1) (* (sin phi1) (cos delta))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16`
3×	`fma-neg` `prod-diff`
2×	`associate-r` `*-commutative`
1×	`expm1-log1p` `sub-neg` `flip3--` `diff-log` `associate-*r/` `sin-cos-mult` `flip--` `expm1-udef`

Counts

4 → 76

Calls

4 calls:

42.0ms	(* (sin phi1) (* (sin phi1) (cos delta)))
57.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms	(expm1 (- (- (cos delta) (* (sin phi1) (* (sin phi1) (cos delta)))) (* (sin phi1) (* (cos theta) (* (sin delta) (cos phi1))))))
20.0ms	(- (cos delta) (* (sin phi1) (* (sin phi1) (cos delta))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin phi1) (* (sin phi1) (cos delta)))
92.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
337.0ms	(expm1 (- (- (cos delta) (* (sin phi1) (* (sin phi1) (cos delta)))) (* (sin phi1) (* (cos theta) (* (sin delta) (cos phi1))))))
110.0ms	(- (cos delta) (* (sin phi1) (* (sin phi1) (cos delta))))

simplify2.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1452
1	421
0	172

prune847.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes684.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample18.9s

Algorithm

intervals

Results

12.2s	3092×	body	1280	valid
3.9s	1841×	body	640	valid
1.1s	2026×	body	80	valid
974.0ms	719×	body	320	valid
292.0ms	322×	body	160	valid