Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

271×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(fma a c (* b d))
27.7b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma a c (* b d))
2.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series131.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(fma a c (* b d))
91.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify1.6s

Counts

45 → 45

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	64	725
1	99	714
2	248	622
3	711	622
4	2079	622
done	5001	622

prune146.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.3b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.5b	(fma a c (* b d))
14.9b	(/ (fma a c (* b d)) (hypot c d))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

2.0ms	(/ 1 (hypot c d))
15.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.0ms	(fma a c (* b d))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series397.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (hypot c d))
186.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
42.0ms	(fma a c (* b d))
117.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.0s

Counts

142 → 142

Iterations

Useful iterations: 2 (168.0ms)

Iter	Nodes	Cost
0	153	2192
1	372	2009
2	1097	1759
3	4396	1759
done	5000	1759

prune327.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.5b	(fma a c (* b d))
14.9b	(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

6.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.0ms	(fma a c (* b d))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series277.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
37.0ms	(fma a c (* b d))
122.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify1.8s

Counts

120 → 120

Iterations

Useful iterations: 3 (619.0ms)

Iter	Nodes	Cost
0	160	2484
1	327	2423
2	788	2246
3	2269	2192
done	5000	2192

prune387.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.1b	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.5b	(fma a c (* b d))
15.1b	(* (fma a c (* b d)) (/ 1 (hypot c d)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`associate-r`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 110

Calls

4 calls:

2.0ms	(/ 1 (hypot c d))
6.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.0ms	(fma a c (* b d))
8.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1 (hypot c d))
116.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
38.0ms	(fma a c (* b d))
119.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

simplify3.3s

Counts

122 → 122

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	132	1652
1	295	1440
2	848	1212
3	3246	1198
done	5000	1198

prune275.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.7b

regimes197.0ms

Accuracy

17.1% (9.3b remaining)

Error of 15.2b against oracle of 5.9b and baseline of 17.1b

bsearch39.0ms

Steps

Iters	Range		Point
8	2.628607714327905e+165	1.5081126682302347e+169	1.188025612414445e+166

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	18	33
1	23	29
done	23	29

end0.0ms

sample490.0ms

Algorithm

intervals

Results

282.0ms

8497×

body

valid