Details

sample75.0ms

Algorithm

intervals

Results

34.0ms	63×	body	1280	valid
16.0ms	57×	body	640	valid
8.0ms	22×	body	2560	valid
5.0ms	28×	body	320	valid
3.0ms	77×	body	80	valid
1.0ms	9×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
0.8b	(+ x (hypot 1 x))
2.4b	(log (+ x (hypot 1 x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

0.0ms	(hypot 1 x)
6.0ms	(+ x (hypot 1 x))
8.0ms	(log (+ x (hypot 1 x)))

series254.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(hypot 1 x)
71.0ms	(+ x (hypot 1 x))
129.0ms	(log (+ x (hypot 1 x)))

simplify1.7s

Counts

56 → 56

Iterations

Iter	Nodes
done	5010
3	2035
2	666
1	244
0	108

prune232.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (* (* x x) x) -1/6 x)
0.1b	(* (* x x) x)
17.3b	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma (* (* x x) x) -1/6 x)
23.0ms	(* (* x x) x)
0.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

series242.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(fma (* (* x x) x) -1/6 x)
56.0ms	(* (* x x) x)
74.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

simplify1.6s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
3	1430
2	359
1	134
0	71

prune243.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ x (hypot 1 x))
0.8b	(+ x (hypot 1 x))
2.2b	(log (sqrt (+ x (hypot 1 x))))
2.2b	(log (sqrt (+ x (hypot 1 x))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

10.0ms	(+ x (hypot 1 x))
11.0ms	(+ x (hypot 1 x))
11.0ms	(log (sqrt (+ x (hypot 1 x))))
7.0ms	(log (sqrt (+ x (hypot 1 x))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ x (hypot 1 x))
75.0ms	(+ x (hypot 1 x))
153.0ms	(log (sqrt (+ x (hypot 1 x))))
167.0ms	(log (sqrt (+ x (hypot 1 x))))

simplify1.8s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	1478
2	554
1	217
0	101

prune412.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ x (hypot 1 x))
2.2b	(log (sqrt (+ x (hypot 1 x))))
2.2b	(log (sqrt (sqrt (+ x (hypot 1 x)))))
2.2b	(log (sqrt (sqrt (+ x (hypot 1 x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
26×	`sqrt-prod`
21×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `log-pow` `add-cube-cbrt`
12×	`pow1`
10×	`sqrt-div`
9×	`sqrt-pow1`
7×	`add-exp-log`
6×	`log-div` `add-log-exp`
5×	`pow1/2`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-def` `rem-log-exp`
1×	`+-commutative` `sum-log`

Counts

4 → 97

Calls

4 calls:

8.0ms	(+ x (hypot 1 x))
9.0ms	(log (sqrt (+ x (hypot 1 x))))
6.0ms	(log (sqrt (sqrt (+ x (hypot 1 x)))))
7.0ms	(log (sqrt (sqrt (+ x (hypot 1 x)))))

series868.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ x (hypot 1 x))
190.0ms	(log (sqrt (+ x (hypot 1 x))))
314.0ms	(log (sqrt (sqrt (+ x (hypot 1 x)))))
281.0ms	(log (sqrt (sqrt (+ x (hypot 1 x)))))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5002
3	2264
2	811
1	324
0	162

prune540.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch67.0ms

Steps

Iters	Range		Point
9	1.7877411926250683e-07	0.113095154289168	0.007740212044415701
7	-1.1375194732999505	-0.018988436667384805	-1.0681179944727555

simplify6.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.8s	2359×	body	1280	valid
584.0ms	1599×	body	640	valid
319.0ms	768×	body	2560	valid
207.0ms	812×	body	320	valid
134.0ms	2063×	body	80	valid
48.0ms	399×	body	160	valid