Details

sample16.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.993896%

Results

6.0ms

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

prune2.0ms

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: 11.5b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

11.5b

(/ 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))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	165	210
1	555	195
2	1825	192
3	5001	192

prune54.0ms

Filtered

26 candidates to 32 candidates (-23.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	2	33

Merged error: 0b

Counts

33 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
11.4b	(sqrt (+ (* x x) 1.0))
11.4b	(sqrt (+ (* x x) 1.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
58×	`times-frac`
37×	`*-un-lft-identity`
35×	`sqrt-prod`
31×	`add-cube-cbrt`
25×	`add-exp-log`
24×	`associate-r` `associate-l`
15×	`add-cbrt-cube` `unswap-sqr`
8×	`sqrt-div` `div-exp` `prod-exp`
7×	`pow1`
4×	`cbrt-undiv` `flip3-+` `associate-/r/` `cbrt-unprod` `flip-+`
3×	`add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 117

Calls

3 calls:

22.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series12.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
3.0ms	(sqrt (+ (* x x) 1.0))
5.0ms	(sqrt (+ (* x x) 1.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	546	1365
1	2588	1202
2	5001	1095

prune180.0ms

Filtered

82 candidates to 126 candidates (-53.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	126	2	128

Merged error: 0b

Counts

128 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
0.1b	(/ 1 (pow x 5))
0.2b	(/ 1 (pow x 3))
22.5b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-sqr-sqrt`
173×	`times-frac`
112×	`*-un-lft-identity`
63×	`difference-of-squares`
56×	`unpow-prod-down`
47×	`add-cube-cbrt`
40×	`sqr-pow`
26×	`cube-prod`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `div-inv` `associate-/l*`
4×	`pow1` `cube-mult` `associate-+l+` `unpow3`
3×	`sub-neg` `associate-*r/` `frac-add`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `pow-flip` `frac-2neg` `distribute-lft-in` `clear-num` `frac-sub` `flip--` `inv-pow`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 227

Calls

4 calls:

51.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))
41.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series19.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
4.0ms	(/ 1 (pow x 5))
3.0ms	(/ 1 (pow x 3))
8.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify90.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	687	1905
1	2879	1620
2	5001	1619

prune220.0ms

Filtered

92 candidates to 239 candidates (-159.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	239	2	241

Merged error: 0b

Counts

241 → 2

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch29.0ms

Steps

Iters	Range		Point
9	0.0011257954942388445	13207.579563402003	408.3325882294671
7	-4.147905375942034e+155	-7.432040220826916e+153	-1.3381015503053828e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	17
1	34	17

end0.0ms

sample341.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.993896%

Results

194.0ms

8000×

body

valid

Details

sample16.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite6.0ms

series4.0ms

simplify53.0ms

prune54.0ms

localize9.0ms

rewrite35.0ms

series12.0ms

simplify68.0ms

prune180.0ms

localize14.0ms

rewrite116.0ms

series19.0ms

simplify90.0ms

prune220.0ms

regimes35.0ms

bsearch29.0ms

simplify2.0ms

end0.0ms

sample341.0ms

Profiling