Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	92×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	5

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
17.7b	(sqrt (+ (* x x) y))

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`add-log-exp`
3×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
2×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `fma-def` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

2 → 32

Calls

2 calls:

311.0ms	(+ (* x x) y)
10.0ms	(sqrt (+ (* x x) y))

series109.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (* x x) y)
72.0ms	(sqrt (+ (* x x) y))

simplify876.0ms

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
2	738
1	163
0	63

prune206.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (fma x x y) (sqrt (fma x x y)))
17.7b	(sqrt (fma x x y))
31.3b	(cbrt (* (fma x x y) (sqrt (fma x x y))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1`
7×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
6×	`associate-r`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow3` `pow-prod-up` `unswap-sqr`
1×	`cbrt-prod` `rem-sqrt-square` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

3 → 54

Calls

3 calls:

15.0ms	(* (fma x x y) (sqrt (fma x x y)))
2.0ms	(sqrt (fma x x y))
8.0ms	(cbrt (* (fma x x y) (sqrt (fma x x y))))

series256.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* (fma x x y) (sqrt (fma x x y)))
65.0ms	(sqrt (fma x x y))
92.0ms	(cbrt (* (fma x x y) (sqrt (fma x x y))))

simplify2.9s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	4730
2	689
1	198
0	89

prune265.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (/ (* -1/2 y) x) x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`prod-diff`
18×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`times-frac`
7×	`fma-neg`
4×	`div-inv`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 44

Calls

1 calls:

24.0ms

(- (/ (* -1/2 y) x) x)

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

(- (/ (* -1/2 y) x) x)

simplify2.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	3127
2	533
1	185
0	82

prune175.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/2 (/ y x) x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/2 (/ y x) x)

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(fma 1/2 (/ y x) x)

simplify2.8s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
5	3875
4	692
3	157
2	48
1	21
0	16

prune66.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes268.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.5b

bsearch72.0ms

Steps

Iters	Range		Point
11	1.8832230334659124e+24	1.4313346338374724e+48	1.4171690306065683e+48
9	-1.951179920997044e+156	-6.518035068066237e+150	-1.3378267015828925e+154

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample826.0ms

Algorithm

intervals

Results

325.0ms	8000×	body	80	valid
78.0ms	2523×	body	80	nan