Details

sample69.0ms

Algorithm

intervals

Results

35.0ms	76×	body	1280	valid
13.0ms	56×	body	640	valid
7.0ms	26×	body	2560	valid
3.0ms	21×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 53.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
1.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b	(sqrt (+ (* x x) 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

3×	`flip3-+` `flip-+`
2×	`log-div` `sqrt-div`
1×	`+-commutative` `pow1/2`

Counts

3 → 8

Calls

3 calls:

3.0ms	(+ x (sqrt (+ (* x x) 1.0)))
3.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms	(sqrt (+ (* x x) 1.0))

series272.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+ x (sqrt (+ (* x x) 1.0)))
169.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms	(sqrt (+ (* x x) 1.0))

simplify114.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	255	176
1	860	174
2	4067	158
3	5002	158

prune62.0ms

Filtered

17 candidates to 17 candidates (100.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	13	4	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	4	18

Merged error: 0.0b

Counts

18 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`associate-*r/`
16×	`frac-sub`
10×	`unpow3` `sqr-pow`
8×	`flip3-+` `flip-+`
6×	`clear-num` `associate-/r` `associate-/l`
5×	`associate-r`
4×	`times-frac`
3×	`frac-2neg` `un-div-inv`
2×	`associate--l+`
1×	`+-commutative` `sub-neg` `flip3--` `*-commutative` `flip--` `div-inv`

Counts

2 → 36

Calls

2 calls:

8.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
5.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series293.0ms

Counts

2 → 6

Calls

2 calls:

157.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
135.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify52.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	344	855
1	1657	810
2	5003	808

prune129.0ms

Filtered

42 candidates to 33 candidates (78.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Merged error: 0.0b

Counts

46 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.1b	(/ 0.125 (pow x 3))
10.7b	(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`frac-sub`
8×	`log-div` `flip3--` `flip--`
5×	`frac-2neg` `clear-num`
2×	`sub-neg` `associate-/r*` `associate--r+`
1×	`unpow3` `div-inv` `associate--r-` `sqr-pow`

Counts

3 → 26

Calls

3 calls:

8.0ms	(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
2.0ms	(/ 0.125 (pow x 3))
11.0ms	(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series243.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
36.0ms	(/ 0.125 (pow x 3))
159.0ms	(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	383	575
1	1620	557
2	5001	542

prune101.0ms

Filtered

35 candidates to 27 candidates (77.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	35	4	39

Merged error: 0.0b

Counts

39 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.125 (pow x 3))
0.4b	(/ (- 0.0625) (pow x 5))
13.9b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.9b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

320×	`frac-sub`
116×	`frac-2neg` `clear-num`
101×	`associate-/r*`
87×	`log-div`
67×	`sqr-pow`
35×	`unpow3`
32×	`neg-mul-1`
31×	`associate-/l*`
12×	`flip3--` `flip--`
3×	`associate--r+`
2×	`neg-sub0` `sub-neg` `div-sub` `div-inv` `associate--r-`
1×	`times-frac` `distribute-frac-neg`

Counts

4 → 193

Calls

4 calls:

2.0ms	(/ 0.125 (pow x 3))
3.0ms	(/ (- 0.0625) (pow x 5))
17.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 0.125 (pow x 3))
53.0ms	(/ (- 0.0625) (pow x 5))
180.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
59.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify86.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1913	4619
1	5002	4414

prune637.0ms

Filtered

205 candidates to 163 candidates (79.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	205	4	209

Merged error: 0.0b

Counts

209 → 4

regimes31.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.2b

bsearch77.0ms

Steps

Iters	Range		Point
9	0.09117784756913819	2697524.489058797	0.8902423635659321
10	-1421.6155834850151	-1.485944467815708e-07	-1.0153027309600835

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample1.9s

Algorithm

intervals

Results

976.0ms	2342×	body	1280	valid
375.0ms	1525×	body	640	valid
236.0ms	839×	body	2560	valid
102.0ms	731×	body	320	valid
70.0ms	2144×	body	80	valid
34.0ms	419×	body	160	valid