Details

sample725.0ms

Algorithm

intervals

Results

378.0ms	89×	body	1280	valid
157.0ms	67×	body	640	valid
65.0ms	21×	body	320	valid
29.0ms	63×	body	80	valid
18.0ms	16×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

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	(* (sin delta) (* (cos phi1) (sin theta)))
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)))))))

rewrite52.0ms

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:

15.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
28.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
125.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
6.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
274.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	2006
3	2006
2	1012
1	374
0	170

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (sin delta)) (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)))))))

rewrite93.0ms

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-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `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:

54.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
23.0ms	(* (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))))
14.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series644.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
242.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
11.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
291.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.6s

Counts

87 → 87

Iterations

Iter	Nodes
done	2006
3	2006
2	1135
1	388
0	171

prune814.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

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))))
0.4b	(log1p (- (cos delta) (* (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)))))))

rewrite33.0ms

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×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`asin-acos` `log1p-udef` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

14.0ms	(* (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))))
10.0ms	(log1p (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series861.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
11.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
339.0ms	(log1p (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
237.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	2003
3	2003
2	874
1	343
0	155

prune980.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize120.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1)))))
0.3b	(* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1))
0.4b	(log1p (- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1))))
0.4b	(- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1)))

rewrite34.0ms

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×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`log1p-udef` `expm1-log1p` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `expm1-udef` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

0.0ms	(expm1 (log1p (- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1)))))
18.0ms	(* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1))
1.0ms	(log1p (- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1))))
14.0ms	(- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

332.0ms	(expm1 (log1p (- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1)))))
207.0ms	(* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1))
369.0ms	(log1p (- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1))))
231.0ms	(- (cos delta) (* (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))) (sin phi1)))

simplify1.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	2016
3	2016
2	1008
1	312
0	141

prune862.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes648.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample26.3s

Algorithm

intervals

Results

15.1s	3096×	body	1280	valid
6.9s	1840×	body	640	valid
1.6s	2047×	body	80	valid
1.3s	690×	body	320	valid
904.0ms	327×	body	160	valid