Details

sample48.0ms

Algorithm

intervals

Results

14.0ms	94×	body	10240	exit
13.0ms	68×	body	1280	valid
7.0ms	54×	body	640	valid
3.0ms	31×	body	320	valid
3.0ms	92×	body	80	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.9b	(- (exp x) 1.0)

rewrite36.0ms

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:

25.0ms	(/ (exp x) (- (exp x) 1.0))
9.0ms	(- (exp x) 1.0)

series72.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (exp x) (- (exp x) 1.0))
23.0ms	(- (exp x) 1.0)

simplify755.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	897
1	253
0	117

prune259.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/12 x 1/2)

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(fma 1/12 x 1/2)

simplify1.7s

Counts

13 → 13

Iterations

Iter	Nodes
done	5001
4	950
3	208
2	59
1	21
0	15

prune68.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma 1/12 x 1/2))
0.1b	(fma 1/12 x 1/2)
0.1b	(fma 1/12 x 1/2)
0.7b	(* (sqrt (fma 1/12 x 1/2)) (sqrt (fma 1/12 x 1/2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (fma 1/12 x 1/2))
0.0ms	(fma 1/12 x 1/2)
0.0ms	(fma 1/12 x 1/2)
11.0ms	(* (sqrt (fma 1/12 x 1/2)) (sqrt (fma 1/12 x 1/2)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (fma 1/12 x 1/2))
48.0ms	(fma 1/12 x 1/2)
60.0ms	(fma 1/12 x 1/2)
46.0ms	(* (sqrt (fma 1/12 x 1/2)) (sqrt (fma 1/12 x 1/2)))

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	975
1	189
0	85

prune465.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (log (fma x 1/12 1/2)))
0.1b	(fma x 1/12 1/2)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `exp-prod` `*-un-lft-identity` `add-cube-cbrt`
3×	`pow1` `log-prod` `exp-sum`
2×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
1×	`log-pow` `fma-udef` `rem-exp-log`

Counts

2 → 27

Calls

2 calls:

5.0ms	(exp (log (fma x 1/12 1/2)))
1.0ms	(fma x 1/12 1/2)

series125.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(exp (log (fma x 1/12 1/2)))
66.0ms	(fma x 1/12 1/2)

simplify2.5s

Counts

33 → 33

Iterations

Iter	Nodes
done	5000
4	1501
3	378
2	128
1	59
0	41

prune159.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

regimes121.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 21.7b

bsearch2.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	20

end0.0ms

sample2.8s

Algorithm

intervals

Results

793.0ms	2334×	body	1280	valid
708.0ms	2597×	body	10240	exit
613.0ms	2820×	body	80	valid
335.0ms	1560×	body	640	valid
105.0ms	868×	body	320	valid
34.0ms	419×	body	160	valid