Details

sample24.0ms

Algorithm

intervals

Results

8.0ms

266×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma a c (* b d))
28.4b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite6.0ms

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))
5.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series140.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(fma a c (* b d))
98.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify1.8s

Counts

45 → 45

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	64	725
1	101	714
2	249	622
3	725	622
4	2204	622
done	5001	622

prune136.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.0b	(/ 1 (hypot c d))
0.3b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
16.6b	(/ (fma a c (* b d)) (hypot c d))

rewrite40.0ms

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:

0.0ms	(fma a c (* b d))
5.0ms	(/ 1 (hypot c d))
25.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
5.0ms	(/ (fma a c (* b d)) (hypot c d))

series410.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma a c (* b d))
58.0ms	(/ 1 (hypot c d))
189.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
124.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify2.8s

Counts

142 → 142

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	153	2192
1	351	2009
2	1090	1759
3	3940	1759
done	5000	1726

prune311.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
16.6b	(/ (fma a c (* b d)) (hypot c d))

rewrite23.0ms

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:

0.0ms	(fma a c (* b d))
14.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
5.0ms	(/ (fma a c (* b d)) (hypot c d))

series294.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(fma a c (* b d))
127.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
122.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	160	2484
1	322	2423
2	705	2246
3	2036	2192
done	5001	2130

prune362.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
16.6b	(/ (hypot c d) (fma a c (* b d)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

0.0ms	(fma a c (* b d))
25.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
9.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
5.0ms	(/ (hypot c d) (fma a c (* b d)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma a c (* b d))
193.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
122.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
101.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify1.3s

Counts

331 → 331

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	458	8797
1	1013	7708
2	1900	7150
done	5000	6968

prune640.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.4b

regimes147.0ms

Accuracy

34.6% (7.3b remaining)

Error of 13.3b against oracle of 6.0b and baseline of 17.2b

bsearch71.0ms

Steps

Iters	Range		Point
8	2.5290916539296384e+176	1.2288273184511015e+181	1.743552084367146e+178
9	-1.0864288282932928e+169	-4.354416350763856e+162	-4.57826742033894e+162

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	41
1	27	35
done	27	35

end0.0ms

sample559.0ms

Algorithm

intervals

Results

269.0ms

8444×

body

valid