Details

sample78.0ms

Algorithm

intervals

Results

35.0ms	79×	body	1280	valid
15.0ms	55×	body	640	valid
12.0ms	36×	body	2560	valid
4.0ms	26×	body	320	valid
2.0ms	47×	body	80	valid
1.0ms	13×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 55.8b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
2.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.4b	(sqrt (+ (* x x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
5.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series17.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify142.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	309	393
1	1027	364
2	4764	348
3	5002	347

prune121.0ms

Filtered

51 candidates to 42 candidates (17.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.0b

Counts

52 → 7

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
181×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
117×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`unswap-sqr`
24×	`add-exp-log`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 270

Calls

1 calls:

51.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify92.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	725	1757
1	3832	1368
2	5001	1368

prune324.0ms

Filtered

273 candidates to 95 candidates (65.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	273	7	280

Merged error: 0.0b

Counts

280 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (neg 0.0625) (pow x 5))
0.2b	(/ 0.125 (pow x 3))
15.6b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
17.0b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
110×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
47×	`unpow-prod-down`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
19×	`associate-/r*`
17×	`sqr-pow`
15×	`add-exp-log`
14×	`cube-prod` `distribute-lft-out--`
13×	`associate-/l*`
12×	`log-prod`
10×	`difference-of-squares`
9×	`add-log-exp`
8×	`neg-mul-1` `frac-sub` `add-cbrt-cube`
6×	`div-exp`
5×	`pow1` `log-div`
4×	`cube-mult` `flip3--` `unpow3` `flip--`
3×	`diff-log` `associate--r+`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `pow-exp` `clear-num` `div-inv` `associate--r-`
1×	`distribute-frac-neg` `rem-log-exp` `log-pow`

Counts

4 → 223

Calls

4 calls:

6.0ms	(/ (neg 0.0625) (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
69.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
70.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (neg 0.0625) (pow x 5))
4.0ms	(/ 0.125 (pow x 3))
10.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
9.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify100.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	837	1963
1	3794	1884
2	5002	1876

prune446.0ms

Filtered

235 candidates to 152 candidates (35.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	236	6	242

Merged error: 0.0b

Counts

242 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

4.3b	(sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
15.6b	(log (* (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))) (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))))
17.0b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))
17.0b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

65×	`sqrt-div`
60×	`frac-sub`
56×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
35×	`log-div`
30×	`flip3--` `times-frac` `flip--`
25×	`frac-times`
21×	`pow1` `distribute-lft-out--`
15×	`difference-of-squares`
14×	`log-pow` `add-log-exp`
12×	`sqrt-prod`
9×	`sqrt-pow1` `pow1/2`
7×	`add-exp-log`
6×	`diff-log` `associate--r+`
5×	`add-cube-cbrt` `associate-r/` `associate-l/` `pow-prod-up`
4×	`sub-neg` `add-cbrt-cube` `associate--r-`
3×	`unpow-prod-down` `distribute-rgt-neg-in` `cube-prod` `pow-prod-down` `pow-sqr` `sqr-pow`
2×	`neg-sub0` `div-sub` `rem-log-exp`
1×	`pow2` `rem-sqrt-square` `log-prod` `pow-plus` `prod-exp`

Counts

4 → 144

Calls

4 calls:

70.0ms	(sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
162.0ms	(log (* (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))) (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))))
74.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))
72.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
10.0ms	(log (* (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))) (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))))
5.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))
5.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify80.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	692	3941
1	2109	3621
2	5001	3597

prune569.0ms

Filtered

156 candidates to 109 candidates (30.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	156	6	162

Merged error: 0.0b

Counts

162 → 6

regimes106.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.4b

bsearch34.0ms

Steps

Iters	Range		Point
11	0.2782392895240894	2.360957873277065e+21	0.8839294129265153
8	-30.828342702616126	-0.08379789005612633	-1.0132957994632394

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	2529×	body	1280	valid
488.0ms	1742×	body	640	valid
340.0ms	999×	body	2560	valid
142.0ms	848×	body	320	valid
63.0ms	1463×	body	80	valid
45.0ms	419×	body	160	valid

Details

sample78.0ms

simplify5.0ms

prune3.0ms

localize12.0ms

rewrite16.0ms

series17.0ms

simplify142.0ms

prune121.0ms

localize11.0ms

rewrite255.0ms

series16.0ms

simplify92.0ms

prune324.0ms

localize15.0ms

rewrite159.0ms

series26.0ms

simplify100.0ms

prune446.0ms

localize19.0ms

rewrite385.0ms

series30.0ms

simplify80.0ms

prune569.0ms

regimes106.0ms

bsearch34.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling