Details

sample53.0ms

Algorithm

intervals

Results

20.0ms

276×

body

valid

simplify9.0ms

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: 29.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma a c (* b d))
28.7b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite8.0ms

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))
6.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series519.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(fma a c (* b d))
475.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify2.4s

Counts

45 → 45

Iterations

Useful iterations: 2 (38.0ms)

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

prune229.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.7b

localize18.0ms

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)))
18.4b	(/ (fma a c (* b d)) (hypot c d))

rewrite56.0ms

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:

1.0ms	(fma a c (* b d))
10.0ms	(/ 1 (hypot c d))
32.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
5.0ms	(/ (fma a c (* b d)) (hypot c d))

series472.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma a c (* b d))
56.0ms	(/ 1 (hypot c d))
219.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
143.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.5s

Counts

142 → 142

Iterations

Useful iterations: done (3.5s)

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

prune421.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

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))
18.4b	(/ (fma a c (* b d)) (hypot c d))

rewrite27.0ms

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))
11.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
11.0ms	(/ (fma a c (* b d)) (hypot c d))

series390.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(fma a c (* b d))
160.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
166.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify2.0s

Counts

120 → 120

Iterations

Useful iterations: done (2.0s)

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

prune535.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.0b

localize19.0ms

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))))
18.4b	(/ (hypot c d) (fma a c (* b d)))

rewrite109.0ms

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))
49.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
17.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
9.0ms	(/ (hypot c d) (fma a c (* b d)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma a c (* b d))
260.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
138.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
150.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify1.7s

Counts

331 → 331

Iterations

Useful iterations: done (1.7s)

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

prune913.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.0b

regimes320.0ms

Accuracy

14.1% (9.6b remaining)

Error of 15.6b against oracle of 6.0b and baseline of 17.2b

bsearch97.0ms

Steps

Iters	Range		Point
4	3.7814851271247773e+143	6.3746339385449325e+143	5.272132631092594e+143
5	1.557953025117785e+75	3.5154020895545546e+75	1.5752088644431916e+75
7	8.020431405482978e+54	5.532752403792931e+56	5.439241435777368e+56

simplify6.0ms

Iterations

Useful iterations: done (6.0ms)

Iter	Nodes	Cost
0	26	70
1	32	58
done	32	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

635.0ms

8489×

body

valid