Details

sample164.0ms

Algorithm

intervals

Results

90.0ms	79×	body	1280	valid
24.0ms	41×	body	640	valid
21.0ms	26×	body	2560	valid
10.0ms	22×	body	320	valid
7.0ms	75×	body	80	valid
3.0ms	13×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ x (hypot 1 x))
2.7b	(log (+ x (hypot 1 x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt` `add-log-exp`
3×	`pow1` `fma-def` `add-exp-log`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `rem-log-exp` `log-pow`

Counts

2 → 36

Calls

2 calls:

5.0ms	(+ x (hypot 1 x))
4.0ms	(log (+ x (hypot 1 x)))

series242.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(+ x (hypot 1 x))
168.0ms	(log (+ x (hypot 1 x)))

simplify1.1s

Counts

42 → 42

Iterations

Iter	Nodes
done	2001
4	2001
3	1585
2	577
1	215
0	93

prune231.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.1b	(* x (* x x))
21.1b	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `pow-prod-up`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
22.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

series348.0ms

Counts

3 → 9

Calls

3 calls:

203.0ms	(fma 3/40 (pow x 5) x)
46.0ms	(* x (* x x))
99.0ms	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

simplify1.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	2003
4	2003
3	1342
2	341
1	119
0	70

prune192.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ x (hypot 1 x))
2.7b	(log (+ x (hypot 1 x)))
2.7b	(log (+ x (hypot 1 x)))
2.7b	(log (+ x (hypot 1 x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`log-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-def` `rem-log-exp` `log-pow`
1×	`+-commutative` `sum-log`

Counts

4 → 72

Calls

4 calls:

13.0ms	(+ x (hypot 1 x))
7.0ms	(log (+ x (hypot 1 x)))
7.0ms	(log (+ x (hypot 1 x)))
7.0ms	(log (+ x (hypot 1 x)))

series654.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ x (hypot 1 x))
206.0ms	(log (+ x (hypot 1 x)))
170.0ms	(log (+ x (hypot 1 x)))
178.0ms	(log (+ x (hypot 1 x)))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	2001
4	2001
3	1585
2	577
1	215
0	93

prune412.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

2.7b	(log (+ x (hypot 1 x)))
2.7b	(log (+ x (hypot 1 x)))
2.7b	(log (+ x (hypot 1 x)))
2.7b	(log (+ x (hypot 1 x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `pow1` `log-div` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `rem-log-exp` `log-pow` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

5.0ms	(log (+ x (hypot 1 x)))
5.0ms	(log (+ x (hypot 1 x)))
4.0ms	(log (+ x (hypot 1 x)))
6.0ms	(log (+ x (hypot 1 x)))

series893.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(log (+ x (hypot 1 x)))
425.0ms	(log (+ x (hypot 1 x)))
130.0ms	(log (+ x (hypot 1 x)))
164.0ms	(log (+ x (hypot 1 x)))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	2000
4	2000
3	949
2	355
1	145
0	69

prune561.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch114.0ms

Steps

Iters	Range		Point
11	5.037382729650074e-10	1937402784720.5117	0.006188922223074722
7	-3.5555834389191174	-0.13673991589698092	-1.076228701950242

simplify7.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.2s	2345×	body	1280	valid
824.0ms	1530×	body	640	valid
528.0ms	818×	body	2560	valid
262.0ms	802×	body	320	valid
156.0ms	2105×	body	80	valid
70.0ms	400×	body	160	valid