Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	76×	body	1280	valid
6.0ms	55×	body	640	valid
3.0ms	167×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	19×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.9b	(- (exp x) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

12.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series56.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

simplify3.0s

Counts

74 → 74

Iterations

Useful iterations: 3 (449.0ms)

Iter	Nodes	Cost
0	127	854
1	288	745
2	888	656
3	4814	637
done	5000	637

prune135.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/6 (* x x) (fma 1/2 x 1))

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:

0.0ms

(fma 1/6 (* x x) (fma 1/2 x 1))

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(fma 1/6 (* x x) (fma 1/2 x 1))

simplify3.0s

Counts

13 → 13

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	23	158
1	39	152
2	106	134
3	479	107
4	3504	107
done	5000	107

prune34.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (fma x 1/6 1/2))
0.1b	(fma x 1/6 1/2)
0.9b	(exp (log1p (* x (fma x 1/6 1/2))))
8.8b	(log1p (* x (fma x 1/6 1/2)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`expm1-log1p-u` `add-log-exp`
4×	`log1p-expm1-u`
3×	`exp-prod` `associate-r` `associate-l` `fma-udef`
2×	`log1p-udef` `rem-exp-log`
1×	`distribute-rgt-in` `distribute-lft-in` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

3.0ms	(* x (fma x 1/6 1/2))
0.0ms	(fma x 1/6 1/2)
1.0ms	(exp (log1p (* x (fma x 1/6 1/2))))
0.0ms	(log1p (* x (fma x 1/6 1/2)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* x (fma x 1/6 1/2))
29.0ms	(fma x 1/6 1/2)
53.0ms	(exp (log1p (* x (fma x 1/6 1/2))))
38.0ms	(log1p (* x (fma x 1/6 1/2)))

simplify2.9s

Counts

69 → 69

Iterations

Useful iterations: 3 (404.0ms)

Iter	Nodes	Cost
0	112	695
1	239	659
2	827	571
3	3892	549
done	5000	549

prune159.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (fma x (fma x 1/6 1/2) 1)) (cbrt (fma x (fma x 1/6 1/2) 1)))
8.7b	(cbrt (fma x (fma x 1/6 1/2) 1))
8.7b	(cbrt (fma x (fma x 1/6 1/2) 1))
8.7b	(cbrt (fma x (fma x 1/6 1/2) 1))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma x (fma x 1/6 1/2) 1)) (cbrt (fma x (fma x 1/6 1/2) 1)))
0.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
0.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
1.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))

series236.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cbrt (fma x (fma x 1/6 1/2) 1)) (cbrt (fma x (fma x 1/6 1/2) 1)))
58.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
55.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
59.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: 3 (334.0ms)

Iter	Nodes	Cost
0	108	1792
1	217	1672
2	674	1553
3	2556	1312
done	5001	1312

prune268.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes24.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.6b

bsearch28.0ms

Steps

Iters	Range		Point
7	-0.0009113054925467739	-1.3606912768451591e-05	-0.00013260409059977256

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27
1	21	27
done	21	27

end0.0ms

sample871.0ms

Algorithm

intervals

Results

389.0ms	2306×	body	1280	valid
170.0ms	1617×	body	640	valid
101.0ms	5519×	body	80	valid
53.0ms	798×	body	320	valid
17.0ms	391×	body	160	valid