Details

sample47.0ms

Algorithm

intervals

Results

14.0ms	64×	body	1280	valid
10.0ms	76×	body	10240	exit
6.0ms	49×	body	640	valid
3.0ms	98×	body	80	valid
3.0ms	29×	body	320	valid
1.0ms	16×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize12.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ (exp x) (- (exp x) 1.0))
3.7b	(- (exp x) 1.0)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

41.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

series65.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (exp x) (- (exp x) 1.0))
23.0ms	(- (exp x) 1.0)

simplify624.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	897
1	253
0	117

prune274.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x 1/2) (/ 1 x))
0.1b	(fma 1/12 x 1/2)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `flip-+` `div-inv`

Counts

2 → 29

Calls

2 calls:

10.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
0.0ms	(fma 1/12 x 1/2)

series79.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
43.0ms	(fma 1/12 x 1/2)

simplify2.8s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
3	3869
2	503
1	115
0	42

prune207.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma 1/12 x 1/2))
0.2b	(cbrt (fma 1/12 x 1/2))
0.2b	(cbrt (fma 1/12 x 1/2))
0.8b	(* (cbrt (fma 1/12 x 1/2)) (cbrt (fma 1/12 x 1/2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
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:

1.0ms	(cbrt (fma 1/12 x 1/2))
1.0ms	(cbrt (fma 1/12 x 1/2))
1.0ms	(cbrt (fma 1/12 x 1/2))
10.0ms	(* (cbrt (fma 1/12 x 1/2)) (cbrt (fma 1/12 x 1/2)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt (fma 1/12 x 1/2))
75.0ms	(cbrt (fma 1/12 x 1/2))
74.0ms	(cbrt (fma 1/12 x 1/2))
91.0ms	(* (cbrt (fma 1/12 x 1/2)) (cbrt (fma 1/12 x 1/2)))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1006
1	274
0	119

prune601.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (fma 1/12 x 1/2) 2/3)
0.1b	(fma 1/12 x 1/2)
0.1b	(fma 1/12 x 1/2)
0.2b	(cbrt (fma 1/12 x 1/2))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `unpow-prod-down`
2×	`fma-udef`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 52

Calls

4 calls:

2.0ms	(pow (fma 1/12 x 1/2) 2/3)
0.0ms	(fma 1/12 x 1/2)
0.0ms	(fma 1/12 x 1/2)
1.0ms	(cbrt (fma 1/12 x 1/2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(pow (fma 1/12 x 1/2) 2/3)
40.0ms	(fma 1/12 x 1/2)
66.0ms	(fma 1/12 x 1/2)
82.0ms	(cbrt (fma 1/12 x 1/2))

simplify2.8s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4194
2	948
1	283
0	117

prune383.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

regimes120.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 22.1b

bsearch2.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	28

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.0s	2289×	body	1280	valid
728.0ms	2544×	body	10240	exit
405.0ms	1611×	body	640	valid
97.0ms	2894×	body	80	valid
92.0ms	792×	body	320	valid
31.0ms	417×	body	160	valid