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: 12.4b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

12.4b

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`associate-/r*`
4×	`associate-l`
3×	`add-exp-log` `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 → 37

Calls

1 calls:

9.0ms

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

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

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

simplify54.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	165	240
1	555	225
2	1839	222
3	5001	222

prune59.0ms

Filtered

40 candidates to 26 candidates (65.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	2	41

Merged error: 0b

Counts

41 → 2

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
12.3b	(sqrt (+ (* x x) 1.0))
12.3b	(sqrt (+ (* x x) 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
50×	`sqrt-prod`
48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`associate-/r*`
10×	`add-exp-log` `associate-l`
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 → 138

Calls

4 calls:

11.0ms	(/ x (sqrt (+ (* x x) 1.0)))
11.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
8.0ms	(sqrt (+ (* x x) 1.0))
8.0ms	(sqrt (+ (* x x) 1.0))

series279.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ x (sqrt (+ (* x x) 1.0)))
68.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
46.0ms	(sqrt (+ (* x x) 1.0))
41.0ms	(sqrt (+ (* x x) 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	388	1084
1	1519	973
2	5002	927

prune243.0ms

Filtered

150 candidates to 85 candidates (56.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	150	2	152

Merged error: 0b

Counts

152 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.6b	(/ 1 (pow x 3))
18.3b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

303×	`add-sqr-sqrt`
301×	`associate-/r*`
234×	`frac-sub`
219×	`*-un-lft-identity`
173×	`times-frac`
154×	`add-cube-cbrt`
149×	`unpow-prod-down`
99×	`associate-/l*`
71×	`sqr-pow`
65×	`cube-prod`
63×	`difference-of-squares`
33×	`frac-2neg` `clear-num`
21×	`add-exp-log`
17×	`cube-mult` `unpow3`
12×	`pow-flip` `div-exp`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `pow-exp` `div-inv`
5×	`add-log-exp`
2×	`cbrt-undiv` `pow-pow` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 452

Calls

3 calls:

6.0ms	(/ 1 (pow x 5))
6.0ms	(/ 1 (pow x 3))
58.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series168.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 1 (pow x 5))
30.0ms	(/ 1 (pow x 3))
92.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify88.0ms

Algorithm

egg-herbie

Counts

461 → 461

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2146	4486
1	5001	3793

prune417.0ms

Filtered

461 candidates to 130 candidates (28.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	461	0	461
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	461	2	463

Merged error: 0b

Counts

463 → 2

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch66.0ms

Steps

Iters	Range		Point
9	0.3235305135594418	1774840.6331059302	464.71461514553374
10	-85019.06990604498	-4.503960361653909e-11	-3914.142121382234

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	17
1	34	17

end0.0ms

sample221.0ms

Algorithm

intervals

Results

140.0ms

8000×

body

valid