Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	73×	body	1280	valid
5.0ms	43×	body	640	valid
4.0ms	168×	body	80	valid
3.0ms	32×	body	320	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 39.0b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series6.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(/ (- (exp x) 1.0) x)
2.0ms	(- (exp x) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2717	309
3	5001	309

prune80.0ms

Filtered

43 candidates to 58 candidates (-34.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Merged error: 0.0b

Counts

59 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

7.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
5.0ms	(* 1/6 (pow x 2))

series6.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
3.0ms	(* 1/6 (pow x 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	201	222
1	825	201
2	5001	198

prune65.0ms

Filtered

29 candidates to 46 candidates (-58.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Merged error: 0.0b

Counts

50 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.1b	(pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)
0.2b	(* 1/6 (pow x 2))
6.2b	(cbrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
10×	`add-exp-log` `unpow-prod-down`
9×	`add-log-exp`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`cube-prod`
5×	`pow1`
4×	`cube-div` `unswap-sqr` `sqr-pow`
3×	`pow-unpow` `flip3-+` `associate-l` `prod-exp` `sum-log` `flip-+`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `unpow3` `pow-exp` `unpow2`
1×	`+-commutative` `associate-+r+` `pow-pow` `pow1/3` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 88

Calls

4 calls:

9.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
8.0ms	(pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)
5.0ms	(* 1/6 (pow x 2))
7.0ms	(cbrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))

series14.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
4.0ms	(pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)
3.0ms	(* 1/6 (pow x 2))
3.0ms	(cbrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	346	731
1	1596	682
2	5001	676

prune149.0ms

Filtered

57 candidates to 100 candidates (-75.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	100	5	105

Merged error: 0.0b

Counts

105 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))
2.5b	(sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))
13.2b	(cbrt (sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)))
13.2b	(cbrt (sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-prod`
30×	`cbrt-prod`
24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
14×	`unpow-prod-down` `cube-prod`
8×	`cube-div` `rem-sqrt-square` `sqrt-div`
6×	`sqr-pow`
4×	`pow1` `add-exp-log` `cube-mult` `cbrt-div` `flip3-+` `unpow3` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 104

Calls

4 calls:

8.0ms	(sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))
8.0ms	(sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))
9.0ms	(cbrt (sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)))
11.0ms	(cbrt (sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)))

series21.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))
6.0ms	(sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3))
4.0ms	(cbrt (sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)))
6.0ms	(cbrt (sqrt (pow (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)) 3)))

simplify52.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	318	1478
1	1251	1396
2	5001	1382

prune360.0ms

Filtered

78 candidates to 116 candidates (-48.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	116	5	121

Merged error: 0.0b

Counts

121 → 5

regimes42.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.9b

bsearch12.0ms

Steps

Iters	Range		Point
8	-0.017383324682467557	-3.831560156749637e-05	-0.00015196441307829825

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	17
1	35	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

456.0ms	2361×	body	1280	valid
205.0ms	1656×	body	640	valid
120.0ms	5354×	body	80	valid
66.0ms	807×	body	320	valid
21.0ms	398×	body	160	valid

Details

sample35.0ms

simplify5.0ms

prune2.0ms

localize4.0ms

rewrite11.0ms

series6.0ms

simplify75.0ms

prune80.0ms

localize7.0ms

rewrite13.0ms

series6.0ms

simplify34.0ms

prune65.0ms

localize10.0ms

rewrite31.0ms

series14.0ms

simplify56.0ms

prune149.0ms

localize14.0ms

rewrite38.0ms

series21.0ms

simplify52.0ms

prune360.0ms

regimes42.0ms

bsearch12.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling