Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

sample10.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	6	7

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: 15.6b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

15.6b

(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/ x (+ (* x x) 1.0))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(/ x (+ (* x x) 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5303	373

prune50.0ms

Filtered

26 candidates to 32 candidates (-23.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	3	33

Merged error: 0b

Counts

33 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
15.6b	(sqrt (+ (* x x) 1.0))
15.6b	(sqrt (+ (* x x) 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
30×	`sqrt-prod`
12×	`associate-/r*`
10×	`add-exp-log`
8×	`pow1` `sqrt-div` `add-cbrt-cube`
6×	`associate-/l*`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`pow-flip` `sqrt-pow1` `pow1/2` `div-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `clear-num` `div-inv`
1×	`rec-exp` `1-exp` `inv-pow`

Counts

4 → 118

Calls

4 calls:

7.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
8.0ms	(/ x (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series19.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
7.0ms	(/ x (sqrt (+ (* x x) 1.0)))
3.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5094	1539

prune187.0ms

Filtered

88 candidates to 130 candidates (-47.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	130	3	133

Merged error: 0b

Counts

133 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (pow x 3))
0.2b	(/ 1.0 (pow x 5))
0.2b	(- (/ 1 x) (/ 1.0 (pow x 3)))
21.3b	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
84×	`times-frac`
70×	`*-un-lft-identity`
45×	`add-cube-cbrt`
27×	`unpow-prod-down`
19×	`associate-/r*`
15×	`cube-prod` `difference-of-squares`
14×	`add-exp-log`
11×	`add-log-exp` `sqr-pow`
8×	`add-cbrt-cube`
6×	`div-exp` `associate-/l*` `distribute-lft-out--`
4×	`pow1` `cube-mult` `unpow3` `div-inv` `distribute-lft-out`
3×	`frac-add`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `associate-+r+` `flip3-+` `flip-+`

Counts

4 → 161

Calls

4 calls:

5.0ms	(/ 1.0 (pow x 3))
4.0ms	(/ 1.0 (pow x 5))
30.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
52.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

series18.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 1.0 (pow x 3))
4.0ms	(/ 1.0 (pow x 5))
6.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
5.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

simplify37.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5093	2078

prune245.0ms

Filtered

106 candidates to 173 candidates (-63.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	173	3	176

Merged error: 0b

Counts

176 → 3

regimes71.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.4b

bsearch23.0ms

Steps

Iters	Range		Point
10	6.063140110131574e-08	1748087.6563862176	412.3562449850672
9	-7.025160610237671e+45	-1.6883142252933943e+39	-4.34418770362715e+45

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	31
1	43	31

end0.0ms

sample259.0ms

Algorithm

intervals

Results

174.0ms

8000×

body

valid

Details

analyze1.0ms

sample10.0ms

simplify2.0ms

prune2.0ms

localize4.0ms

rewrite6.0ms

series5.0ms

simplify57.0ms

prune50.0ms

localize8.0ms

rewrite26.0ms

series19.0ms

simplify51.0ms

prune187.0ms

localize10.0ms

rewrite97.0ms

series18.0ms

simplify37.0ms

prune245.0ms

regimes71.0ms

bsearch23.0ms

simplify1.0ms

end0.0ms

sample259.0ms

Profiling