Details

sample77.0ms

Algorithm

intervals

Results

32.0ms	58×	body	1280	valid
18.0ms	43×	body	640	valid
11.0ms	131×	body	80	valid
4.0ms	14×	body	320	valid
2.0ms	10×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2017
8	2017
7	682
6	240
5	101
4	51
3	30
2	22
1	18
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* -2 x))))
0.0b	(+ 1 (exp (* -2 x)))
2.6b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
63×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-cbrt-cube` `div-inv`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`expm1-def` `difference-of-sqr-1` `div-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 150

Calls

3 calls:

20.0ms	(/ 2 (+ 1 (exp (* -2 x))))
12.0ms	(+ 1 (exp (* -2 x)))
83.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series119.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ 2 (+ 1 (exp (* -2 x))))
17.0ms	(+ 1 (exp (* -2 x)))
80.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.3s

Counts

159 → 159

Iterations

Iter	Nodes
done	2000
3	2000
2	944
1	426
0	183

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* x -2))))
0.0b	(+ 1 (exp (* x -2)))
2.6b	(- (/ 2 (+ 1 (exp (* x -2)))) 1)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
63×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-cbrt-cube` `div-inv`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`expm1-def` `difference-of-sqr-1` `div-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 150

Calls

3 calls:

19.0ms	(/ 2 (+ 1 (exp (* x -2))))
7.0ms	(+ 1 (exp (* x -2)))
76.0ms	(- (/ 2 (+ 1 (exp (* x -2)))) 1)

series133.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 2 (+ 1 (exp (* x -2))))
23.0ms	(+ 1 (exp (* x -2)))
74.0ms	(- (/ 2 (+ 1 (exp (* x -2)))) 1)

simplify1.2s

Counts

159 → 159

Iterations

Iter	Nodes
done	2003
3	2003
2	1079
1	432
0	185

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 x)
0.1b	(* (* x x) x)
19.1b	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

rewrite23.0ms

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 (pow x 5) 2/15 x)
22.0ms	(* (* x x) x)
1.0ms	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

series331.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(fma (pow x 5) 2/15 x)
66.0ms	(* (* x x) x)
91.0ms	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

simplify1.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	2033
4	2033
3	1648
2	385
1	134
0	70

prune612.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

13.3b	(cbrt (fma (pow x 5) 2/15 x))
13.3b	(cbrt (fma (pow x 5) 2/15 x))
13.3b	(cbrt (fma (pow x 5) 2/15 x))
19.1b	(fma (* (* x x) x) -1/3 (* (* (cbrt (fma (pow x 5) 2/15 x)) (cbrt (fma (pow x 5) 2/15 x))) (cbrt (fma (pow x 5) 2/15 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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (fma (pow x 5) 2/15 x))
1.0ms	(cbrt (fma (pow x 5) 2/15 x))
1.0ms	(cbrt (fma (pow x 5) 2/15 x))
0.0ms	(fma (* (* x x) x) -1/3 (* (* (cbrt (fma (pow x 5) 2/15 x)) (cbrt (fma (pow x 5) 2/15 x))) (cbrt (fma (pow x 5) 2/15 x))))

series2.5s

Counts

4 → 12

Calls

4 calls:

870.0ms	(cbrt (fma (pow x 5) 2/15 x))
780.0ms	(cbrt (fma (pow x 5) 2/15 x))
796.0ms	(cbrt (fma (pow x 5) 2/15 x))
91.0ms	(fma (* (* x x) x) -1/3 (* (* (cbrt (fma (pow x 5) 2/15 x)) (cbrt (fma (pow x 5) 2/15 x))) (cbrt (fma (pow x 5) 2/15 x))))

simplify964.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
4	2000
3	1476
2	466
1	187
0	90

prune620.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes127.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.1b

bsearch106.0ms

Steps

Iters	Range		Point
7	0.00021366299023797085	0.0042870261776910435	0.004220693910151683
9	-0.41146448125146995	-7.139329650713034e-08	-0.0076877843038582255

simplify4.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	1702×	body	1280	valid
409.0ms	1218×	body	640	valid
391.0ms	4125×	body	80	valid
177.0ms	630×	body	320	valid
47.0ms	325×	body	160	valid