Details

sample367.0ms

Algorithm

intervals

Results

143.0ms	55×	body	10240	exit
68.0ms	322×	body	80	valid
64.0ms	45×	body	1280	valid
44.0ms	46×	body	640	valid
11.0ms	18×	body	320	valid
4.0ms	9×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
5	3307
4	836
3	312
2	122
1	47
0	19

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 eps) x)
0.1b	(exp (- (* (- 1 eps) x)))
0.1b	(exp (- (* (+ 1 eps) x)))
2.7b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
28×	`flip3-+` `flip3--` `flip-+` `flip--`
18×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 158

Calls

4 calls:

26.0ms	(* (+ 1 eps) x)
14.0ms	(exp (- (* (- 1 eps) x)))
10.0ms	(exp (- (* (+ 1 eps) x)))
61.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (+ 1 eps) x)
29.0ms	(exp (- (* (- 1 eps) x)))
22.0ms	(exp (- (* (+ 1 eps) x)))
165.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.3s

Counts

170 → 170

Iterations

Iter	Nodes
2	3134
1	1230
0	373

prune2.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* x x) x)
7.2b	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

27.0ms	(* (* x x) x)
0.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(* (* x x) x)
52.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

simplify3.5s

Counts

46 → 46

Iterations

Iter	Nodes
4	5332
3	1119
2	320
1	110
0	53

prune384.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

7.2b	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
11.6b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
11.6b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
11.6b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
96.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
121.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
93.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

simplify3.5s

Counts

61 → 61

Iterations

Iter	Nodes
4	8243
3	1523
2	422
1	154
0	75

prune621.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize65.0ms

Local error

Found 4 expressions with local error:

7.2b	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
7.2b	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
11.6b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
11.6b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 46

Calls

4 calls:

0.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
0.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
35.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
98.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
117.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

simplify3.7s

Counts

58 → 58

Iterations

Iter	Nodes
4	8243
3	1523
2	422
1	154
0	75

prune372.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes203.0ms

Accuracy

96% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.4b

bsearch282.0ms

Steps

Iters	Range		Point
9	0.4148577645705283	50016.8179159125	226.33586080847886

simplify15.0ms

Iterations

Iter	Nodes
4	55
3	55
2	53
1	44
0	30

end0.0ms

sample12.2s

Algorithm

intervals

Results

4.2s	1975×	body	10240	exit
3.3s	1743×	body	1280	valid
2.2s	10116×	body	80	valid
1.4s	1265×	body	640	valid
425.0ms	624×	body	320	valid
119.0ms	309×	body	160	valid