Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

prune1.0ms

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: 14.6b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

14.6b

(/ 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))

series62.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

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

simplify54.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	165	210
1	555	195
2	1839	192
3	5001	192

prune65.0ms

Filtered

32 candidates to 26 candidates (81.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	4	33

Merged error: 0b

Counts

33 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
14.5b	(sqrt (+ (* x x) 1.0))
14.5b	(sqrt (+ (* x x) 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
30×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `associate-/l*`
2×	`rem-sqrt-square`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 164

Calls

4 calls:

24.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
7.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series231.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
76.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
43.0ms	(sqrt (+ (* x x) 1.0))
49.0ms	(sqrt (+ (* x x) 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	625	1749
1	3124	1546
2	5001	1414

prune239.0ms

Filtered

176 candidates to 106 candidates (60.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	176	4	180

Merged error: 0b

Counts

180 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (/ (+ (* x x) 1.0) x))
14.5b	(/ (+ (* x x) 1.0) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`pow1`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `add-log-exp`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

2 → 105

Calls

2 calls:

7.0ms	(/ 1 (/ (+ (* x x) 1.0) x))
6.0ms	(/ (+ (* x x) 1.0) x)

series136.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ 1 (/ (+ (* x x) 1.0) x))
73.0ms	(/ (+ (* x x) 1.0) x)

simplify47.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	397	899
1	1720	800
2	5001	722

prune105.0ms

Filtered

111 candidates to 61 candidates (55.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	112	3	115

Merged error: 0b

Counts

115 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (/ 1.0 x))
0.1b	(/ 1 (+ x (/ 1.0 x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-exp-log`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `clear-num` `sum-log` `div-inv` `inv-pow`

Counts

2 → 49

Calls

2 calls:

5.0ms	(+ x (/ 1.0 x))
11.0ms	(/ 1 (+ x (/ 1.0 x)))

series90.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ x (/ 1.0 x))
45.0ms	(/ 1 (+ x (/ 1.0 x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	185	292
1	596	260
2	1982	240
3	5002	240

prune46.0ms

Filtered

55 candidates to 30 candidates (54.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	55	3	58

Merged error: 0b

Counts

58 → 3

regimes16.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample213.0ms

Algorithm

intervals

Results

134.0ms

8000×

body

valid