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: 15.2b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

15.2b

(/ 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))

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(/ 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

prune62.0ms

Filtered

32 candidates to 26 candidates (81.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0b

Counts

33 → 3

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)))
15.1b	(sqrt (+ (* x x) 1.0))
15.1b	(sqrt (+ (* x x) 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`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` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 262

Calls

4 calls:

20.0ms	(/ (/ 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))

series268.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
120.0ms	(/ x (sqrt (+ (* x x) 1.0)))
47.0ms	(sqrt (+ (* x x) 1.0))
42.0ms	(sqrt (+ (* x x) 1.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	774	3878
1	2962	3482
2	5001	3411

prune406.0ms

Filtered

274 candidates to 148 candidates (54.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	274	3	277

Merged error: 0b

Counts

277 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

4.9b	(/ x (+ (- (* 1.0 1.0)) (pow x 4)))
20.0b	(* (/ x (+ (- (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
18×	`associate-l`
9×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
4×	`pow1` `associate-r` `associate-/r*` `associate-/r/`
3×	`associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `difference-of-squares`

Counts

2 → 79

Calls

2 calls:

7.0ms	(/ x (+ (- (* 1.0 1.0)) (pow x 4)))
15.0ms	(* (/ x (+ (- (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

series233.0ms

Counts

2 → 6

Calls

2 calls:

126.0ms	(/ x (+ (- (* 1.0 1.0)) (pow x 4)))
107.0ms	(* (/ x (+ (- (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	427	860
1	1887	778
2	5003	745

prune178.0ms

Filtered

85 candidates to 63 candidates (74.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	85	3	88

Merged error: 0b

Counts

88 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x))
0.2b	(/ 1 (pow x 5))
0.6b	(/ 1 (pow x 3))
17.2b	(- (+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x)) (* 1.0 (/ 1 (pow x 3))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

57×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`cube-prod` `div-exp`
11×	`add-log-exp`
8×	`frac-sub` `add-cbrt-cube` `sqr-pow`
7×	`associate-*r/` `un-div-inv`
6×	`pow-to-exp` `rec-exp` `1-exp` `frac-add` `pow-exp` `associate-/l*`
4×	`pow1` `cube-mult` `unpow3`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `diff-log` `clear-num` `sum-log` `div-inv` `inv-pow`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 161

Calls

4 calls:

8.0ms	(+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))
11.0ms	(- (+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x)) (* 1.0 (/ 1 (pow x 3))))

series213.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x))
49.0ms	(/ 1 (pow x 5))
31.0ms	(/ 1 (pow x 3))
46.0ms	(- (+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x)) (* 1.0 (/ 1 (pow x 3))))

simplify83.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	505	1102
1	2799	909
2	5002	900

prune231.0ms

Filtered

173 candidates to 74 candidates (42.8%)

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

regimes28.0ms

Accuracy

100% (0.0b remaining)

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

bsearch68.0ms

Steps

Iters	Range		Point
9	372.40568780262197	10938932741.588787	1451.9414734741647
9	-205992.06318510068	-1.7822032022535685	-8974.472873556428

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	17
1	42	17

end0.0ms

sample213.0ms

Algorithm

intervals

Results

131.0ms

8000×

body

valid