Details

sample37.0ms

Algorithm

intervals

Results

11.0ms	69×	body	1280	valid
7.0ms	72×	body	10240	exit
7.0ms	68×	body	640	valid
2.0ms	27×	body	320	valid
1.0ms	82×	body	80	valid
0.0ms	10×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.1b	(- (exp x) 1.0)

rewrite34.0ms

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×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

20.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series43.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify191.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (184.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune148.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

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 1/12 x (/ 1 x))

series49.0ms

Counts

1 → 3

Calls

1 calls:

48.0ms

(fma 1/12 x (/ 1 x))

simplify60.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	43
1	49	38
2	150	38
3	482	38
4	2338	38
5	5002	38

prune24.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))
0.5b	(cbrt (fma 1/12 x (/ 1 x)))
0.5b	(cbrt (fma 1/12 x (/ 1 x)))
0.5b	(cbrt (fma 1/12 x (/ 1 x)))

rewrite18.0ms

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:

14.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))
104.0ms	(cbrt (fma 1/12 x (/ 1 x)))
103.0ms	(cbrt (fma 1/12 x (/ 1 x)))
103.0ms	(cbrt (fma 1/12 x (/ 1 x)))

simplify135.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	277	823
1	911	765
2	4122	688
3	5001	652

prune237.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma 1/12 x (/ 1 x)))
0.5b	(cbrt (fma 1/12 x (/ 1 x)))
0.5b	(cbrt (fma 1/12 x (/ 1 x)))
1.5b	(exp (log (cbrt (fma 1/12 x (/ 1 x)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod` `exp-sum`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-pow`
1×	`rem-exp-log`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
4.0ms	(exp (log (cbrt (fma 1/12 x (/ 1 x)))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (fma 1/12 x (/ 1 x)))
107.0ms	(cbrt (fma 1/12 x (/ 1 x)))
105.0ms	(cbrt (fma 1/12 x (/ 1 x)))
109.0ms	(exp (log (cbrt (fma 1/12 x (/ 1 x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	174	575
1	418	539
2	1397	493
3	5001	447

prune247.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

97.7% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 21.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

379.0ms	2245×	body	1280	valid
255.0ms	2527×	body	10240	exit
170.0ms	1642×	body	640	valid
58.0ms	877×	body	320	valid
54.0ms	2824×	body	80	valid
17.0ms	412×	body	160	valid