Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	62×	body	640	valid
15.0ms	63×	body	1280	valid
5.0ms	169×	body	80	valid
3.0ms	28×	body	320	valid
1.0ms	10×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.6b	(- (exp x) 1.0)

rewrite57.0ms

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:

40.0ms	(/ (- (exp x) 1.0) x)
13.0ms	(- (exp x) 1.0)

series104.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (- (exp x) 1.0) x)
36.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	127	854
1	297	748
2	1007	667
done	5000	648

prune198.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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))

simplify724.0ms

Counts

13 → 13

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	23	158
1	43	152
2	137	134
3	785	107
done	5000	107

prune59.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (fma x (fma x 1/6 1/2) 1)) (cbrt (fma x (fma x 1/6 1/2) 1)))
10.1b	(cbrt (fma x (fma x 1/6 1/2) 1))
10.1b	(cbrt (fma x (fma x 1/6 1/2) 1))
10.1b	(cbrt (fma x (fma x 1/6 1/2) 1))

rewrite32.0ms

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:

23.0ms	(* (cbrt (fma x (fma x 1/6 1/2) 1)) (cbrt (fma x (fma x 1/6 1/2) 1)))
2.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
2.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
2.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))

series355.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (cbrt (fma x (fma x 1/6 1/2) 1)) (cbrt (fma x (fma x 1/6 1/2) 1)))
73.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
101.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))
81.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))

simplify4.1s

Counts

93 → 93

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	108	1792
1	234	1668
2	729	1553
3	3812	1332
done	5000	1286

prune403.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma x (fma x 1/12 1/3) 1) (cbrt (fma x (fma x 1/6 1/2) 1)))
0.1b	(fma x 1/6 1/2)
0.2b	(fma x 1/12 1/3)
10.1b	(cbrt (fma x (fma x 1/6 1/2) 1))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

17.0ms	(* (fma x (fma x 1/12 1/3) 1) (cbrt (fma x (fma x 1/6 1/2) 1)))
1.0ms	(fma x 1/6 1/2)
1.0ms	(fma x 1/12 1/3)
3.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))

series317.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (fma x (fma x 1/12 1/3) 1) (cbrt (fma x (fma x 1/6 1/2) 1)))
43.0ms	(fma x 1/6 1/2)
64.0ms	(fma x 1/12 1/3)
83.0ms	(cbrt (fma x (fma x 1/6 1/2) 1))

simplify3.1s

Counts

69 → 69

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	123	1026
1	240	999
2	712	909
3	4503	857
done	5000	854

prune396.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

regimes21.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch38.0ms

Steps

Iters	Range		Point
10	-1106898266.2167518	-2.9526231381329305e-09	-0.00016682842998557644

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	30	35
done	30	35

end0.0ms

sample1.9s

Algorithm

intervals

Results

770.0ms	2203×	body	1280	valid
377.0ms	1750×	body	640	valid
339.0ms	5512×	body	80	valid
105.0ms	816×	body	320	valid
35.0ms	412×	body	160	valid