Details

sample196.0ms

Algorithm

intervals

Results

78.0ms	59×	body	10240	exit
36.0ms	61×	body	1280	valid
28.0ms	41×	body	640	valid
27.0ms	336×	body	80	valid
5.0ms	21×	body	320	valid
2.0ms	11×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 4 (262.0ms)

Iter	Nodes	Cost
0	19	29
1	47	29
2	124	29
3	353	27
4	1008	26
5	4514	26
done	5000	26

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(exp (- (* (- 1.0 eps) x)))
0.0b	(exp (- (* (+ 1.0 eps) x)))
2.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite136.0ms

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/`
29×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
18×	`un-div-inv`
12×	`add-sqr-sqrt` `exp-prod`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `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--` `difference-of-squares` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

32.0ms	(* (- 1.0 eps) x)
9.0ms	(exp (- (* (- 1.0 eps) x)))
12.0ms	(exp (- (* (+ 1.0 eps) x)))
69.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (- 1.0 eps) x)
53.0ms	(exp (- (* (- 1.0 eps) x)))
62.0ms	(exp (- (* (+ 1.0 eps) x)))
310.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.6s

Counts

171 → 171

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	386	7581
1	1072	6808
2	3839	6373
done	5000	6305

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.6666666666666667 (pow x 3) 2.0)
4.8b	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

2 → 31

Calls

2 calls:

0.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
7.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series172.0ms

Counts

2 → 6

Calls

2 calls:

119.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
53.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify3.3s

Counts

37 → 37

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	53	544
1	119	518
2	387	468
3	2205	433
done	5000	386

prune165.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

simplify1.8s

Counts

13 → 13

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	25	180
1	51	177
2	122	151
3	383	151
4	2187	151
done	5000	151

prune70.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
8.7b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
8.7b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
8.7b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--`

Counts

4 → 55

Calls

4 calls:

50.0ms	(- (* (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
2.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
2.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
2.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
731.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
629.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
660.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

simplify2.6s

Counts

67 → 67

Iterations

Useful iterations: 3 (980.0ms)

Iter	Nodes	Cost
0	119	1694
1	298	1644
2	946	1200
3	4538	1017
done	5000	1017

prune405.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes141.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 16.4b

bsearch255.0ms

Steps

Iters	Range		Point
8	0.16004325332292868	3739.899882177282	45.88594712019422

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	46
1	42	44
2	44	44
done	44	44

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.9s	1764×	body	1280	valid
2.0s	1923×	body	10240	exit
1.5s	10075×	body	80	valid
1.3s	1291×	body	640	valid
226.0ms	650×	body	320	valid
74.0ms	324×	body	160	valid