Details

sample10.0ms

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	7	3
1	7	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))

rewrite7.0ms

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` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

6.0ms

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

series63.0ms

Counts

1 → 3

Calls

1 calls:

62.0ms

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

simplify55.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	171	215
1	589	196
2	1979	191
3	5002	186

prune71.0ms

Filtered

34 candidates to 29 candidates (85.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	2	35

Merged error: 0b

Counts

35 → 2

localize11.0ms

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))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

40×	`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×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `sqrt-pow1` `pow1/2` `div-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `clear-num` `hypot-def` `div-inv`
1×	`rec-exp` `1-exp` `inv-pow`

Counts

4 → 128

Calls

4 calls:

7.0ms	(/ x (sqrt (+ (* x x) 1.0)))
8.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
5.0ms	(sqrt (+ (* x x) 1.0))

series308.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ x (sqrt (+ (* x x) 1.0)))
81.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
52.0ms	(sqrt (+ (* x x) 1.0))
45.0ms	(sqrt (+ (* x x) 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	409	1002
1	1606	916
2	5001	867

prune290.0ms

Filtered

140 candidates to 97 candidates (69.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	140	2	142

Merged error: 0b

Counts

142 → 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)))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

1934×	`times-frac`
1319×	`add-sqr-sqrt`
1235×	`*-un-lft-identity`
1170×	`add-cube-cbrt`
1000×	`prod-diff`
650×	`unpow-prod-down`
251×	`cube-prod`
238×	`sqr-pow`
79×	`cube-mult` `unpow3`
72×	`div-inv`
63×	`difference-of-squares`
25×	`fma-neg`
21×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
7×	`add-cbrt-cube` `distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 1240

Calls

3 calls:

5.0ms	(/ 1 (pow x 5))
6.0ms	(/ 1 (pow x 3))
76.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series175.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 1 (pow x 5))
33.0ms	(/ 1 (pow x 3))
96.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify262.0ms

Algorithm

egg-herbie

Counts

1249 → 1249

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	2381	32316
1	5002	18140

prune456.0ms

Filtered

1249 candidates to 124 candidates (9.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	1249	0	1249
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	1249	2	1251

Merged error: 0b

Counts

1251 → 2

regimes21.0ms

Accuracy

100% (0.0b remaining)

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

bsearch65.0ms

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	31	16
1	31	16

end0.0ms

sample229.0ms

Algorithm

intervals

Results

135.0ms

8000×

body

valid