Details

sample180.0ms

Algorithm

intervals

Results

88.0ms	84×	body	1280	valid
26.0ms	42×	body	640	valid
14.0ms	18×	body	2560	valid
12.0ms	31×	body	320	valid
6.0ms	65×	body	80	valid
4.0ms	16×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ x (hypot 1 x))
3.6b	(log (+ x (hypot 1 x)))

rewrite15.0ms

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:

8.0ms	(+ x (hypot 1 x))
6.0ms	(log (+ x (hypot 1 x)))

series267.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(+ x (hypot 1 x))
177.0ms	(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

prune224.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.1b	(* x (* x x))
17.7b	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

rewrite15.0ms

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)
14.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

series331.0ms

Counts

3 → 9

Calls

3 calls:

191.0ms	(fma 3/40 (pow x 5) x)
46.0ms	(* x (* x x))
94.0ms	(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

prune194.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (hypot 1 x) x)
3.6b	(log (+ (hypot 1 x) 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:

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

series242.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(+ (hypot 1 x) x)
174.0ms	(log (+ (hypot 1 x) x))

simplify1.0s

Counts

42 → 42

Iterations

Iter	Nodes
done	2008
4	2008
3	1631
2	586
1	216
0	93

prune230.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (hypot 1 x) x)
3.6b	(log (+ (hypot 1 x) x))
3.6b	(log (+ (hypot 1 x) x))
3.6b	(log (+ (hypot 1 x) x))

rewrite17.0ms

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:

4.0ms	(+ (hypot 1 x) x)
3.0ms	(log (+ (hypot 1 x) x))
3.0ms	(log (+ (hypot 1 x) x))
6.0ms	(log (+ (hypot 1 x) x))

series541.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (hypot 1 x) x)
165.0ms	(log (+ (hypot 1 x) x))
154.0ms	(log (+ (hypot 1 x) x))
150.0ms	(log (+ (hypot 1 x) x))

simplify1.0s

Counts

84 → 84

Iterations

Iter	Nodes
done	2008
4	2008
3	1631
2	586
1	216
0	93

prune398.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.0b

bsearch129.0ms

Steps

Iters	Range		Point
10	3.4946005567744297e-15	48819.349325626084	0.00612647097016585
9	-6838974.188497498	-0.005838610583870787	-1.0580774043529224

simplify4.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	2395×	body	1280	valid
752.0ms	1561×	body	640	valid
522.0ms	797×	body	2560	valid
256.0ms	767×	body	320	valid
178.0ms	2085×	body	80	valid
65.0ms	395×	body	160	valid