Details

sample11.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

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: 14.3b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

14.3b

(/ 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))

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

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

simplify59.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (55.0ms)

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

prune67.0ms

Filtered

34 candidates to 29 candidates (85.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Merged error: 0b

Counts

35 → 4

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
14.3b	(sqrt (+ (* x x) 1.0))
14.3b	(sqrt (+ (* x x) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
166×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`
1×	`associate-/l/`

Counts

4 → 272

Calls

4 calls:

16.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
6.0ms	(/ x (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series273.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
120.0ms	(/ x (sqrt (+ (* x x) 1.0)))
48.0ms	(sqrt (+ (* x x) 1.0))
43.0ms	(sqrt (+ (* x x) 1.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	793	3897
1	3057	3471
2	5001	3383

prune376.0ms

Filtered

284 candidates to 159 candidates (56.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	284	4	288

Merged error: 0b

Counts

288 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 3))
22.4b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite213.0ms

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))
69.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ 1 (pow x 5))
31.0ms	(/ 1 (pow x 3))
105.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify291.0ms

Algorithm

egg-herbie

Counts

1249 → 1249

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2381	31548
1	5001	18062

prune385.0ms

Filtered

1249 candidates to 124 candidates (9.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1249	0	1249
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	1249	4	1253

Merged error: 0b

Counts

1253 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

2.7b	(/ (sqrt x) (fma x x 1.0))
4.2b	(* (sqrt x) (/ (sqrt x) (fma x x 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
29×	`sqrt-prod`
22×	`associate-r`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`pow1`
3×	`associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 91

Calls

2 calls:

4.0ms	(/ (sqrt x) (fma x x 1.0))
10.0ms	(* (sqrt x) (/ (sqrt x) (fma x x 1.0)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (sqrt x) (fma x x 1.0))
65.0ms	(* (sqrt x) (/ (sqrt x) (fma x x 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	336	710
1	1461	612
2	5002	589

prune148.0ms

Filtered

97 candidates to 66 candidates (68.0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	97	4	101

Merged error: 0b

Counts

101 → 4

regimes52.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.6b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	21
1	30	21

end0.0ms

sample261.0ms

Algorithm

intervals

Results

174.0ms

8000×

body

valid