Details

analyze1.0ms

Algorithm: search

sample11.0ms

Algorithm

intervals

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: 15.7b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

15.7b

(/ 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))

series5.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify57.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (15.0ms)

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

prune53.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
15.6b	(sqrt (+ (* x x) 1.0))
15.6b	(sqrt (+ (* x x) 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 158

Calls

4 calls:

26.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
9.0ms	(/ x (sqrt (+ (* x x) 1.0)))
6.0ms	(sqrt (+ (* x x) 1.0))
6.0ms	(sqrt (+ (* x x) 1.0))

series20.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify85.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	615	1742
1	2885	1548
2	5001	1440

prune240.0ms

Filtered

113 candidates to 170 candidates (-50.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	170	2	172

Merged error: 0b

Counts

172 → 2

localize12.0ms

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 3))
0.5b	(/ 1 (pow x 5))
17.9b	(- (/ 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:

50.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
5.0ms	(/ 1 (pow x 3))
5.0ms	(/ 1 (pow x 5))
45.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
3.0ms	(/ 1 (pow x 3))
4.0ms	(/ 1 (pow x 5))
8.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify90.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	687	2009
1	2879	1720
2	5001	1719

prune224.0ms

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

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch43.0ms

Steps

Iters	Range		Point
10	9.921986998393984e-14	1396.4409915148824	425.46223074227794
10	-2.4889062785384105e+157	-1.607008260279264e+146	-1.3461293532668978e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	17
1	34	17

end0.0ms

analyze1.0ms

Algorithm: search

sample291.0ms

Algorithm

intervals

Results

195.0ms

8000×

body

valid

Details

analyze1.0ms

sample11.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite6.0ms

series5.0ms

simplify57.0ms

prune53.0ms

localize10.0ms

rewrite52.0ms

series20.0ms

simplify85.0ms

prune240.0ms

localize12.0ms

rewrite116.0ms

series20.0ms

simplify90.0ms

prune224.0ms

regimes36.0ms

bsearch43.0ms

simplify2.0ms

end0.0ms

analyze1.0ms

sample291.0ms

Profiling