Details

sample74.0ms

Algorithm

intervals

Results

34.0ms	74×	body	1280	valid
13.0ms	52×	body	640	valid
6.0ms	20×	body	2560	valid
5.0ms	33×	body	320	valid
2.0ms	59×	body	80	valid
2.0ms	18×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 54.2b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
5.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
11.7b	(sqrt (+ (* x x) 1.0))

rewrite22.0ms

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)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms	(sqrt (+ (* x x) 1.0))

series341.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(+ x (sqrt (+ (* x x) 1.0)))
211.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
54.0ms	(sqrt (+ (* x x) 1.0))

simplify145.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (139.0ms)

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

prune238.0ms

Filtered

51 candidates to 42 candidates (17.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.0b

Counts

52 → 5

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.2b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

12.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
54.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series377.0ms

Counts

2 → 6

Calls

2 calls:

206.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
172.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify114.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	854	2137
1	4687	1743
2	5001	1743

prune897.0ms

Filtered

292 candidates to 111 candidates (62.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	292	5	297

Merged error: 0.0b

Counts

297 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (neg 0.0625) (pow x 5))
0.8b	(/ 0.125 (pow x 3))
12.4b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
18.8b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite162.0ms

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)))))
73.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (neg 0.0625) (pow x 5))
52.0ms	(/ 0.125 (pow x 3))
231.0ms	(log (- (/ 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))))

simplify108.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (79.0ms)

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

prune2.7s

Filtered

235 candidates to 152 candidates (35.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	235	5	240

Merged error: 0.0b

Counts

240 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.0b	(+ x (/ 0.5 x))
0.8b	(/ 0.125 (pow x 3))
10.7b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
36×	`times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-log-exp`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1` `sum-log`
4×	`cube-mult` `unpow3` `distribute-lft-out--` `sqr-pow`
3×	`associate-+r+` `flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`+-commutative` `log-div` `diff-log`
1×	`cbrt-undiv` `pow-to-exp` `associate-+r-` `sub-neg` `frac-2neg` `rem-log-exp` `pow-exp` `associate--l+` `clear-num` `log-pow` `div-inv`

Counts

4 → 114

Calls

4 calls:

20.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
8.0ms	(+ x (/ 0.5 x))
5.0ms	(/ 0.125 (pow x 3))
20.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
51.0ms	(+ x (/ 0.5 x))
45.0ms	(/ 0.125 (pow x 3))
178.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	436	780
1	2073	718
2	5001	718

prune575.0ms

Filtered

126 candidates to 73 candidates (42.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	126	5	131

Merged error: 0.0b

Counts

131 → 5

regimes126.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.0b

bsearch92.0ms

Steps

Iters	Range		Point
8	3.9971791970784e-05	0.9384348231062936	0.8957578485938503
9	-57514.079310754976	-0.04031575958609914	-1.0266525549484173

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	2301×	body	1280	valid
416.0ms	1566×	body	640	valid
256.0ms	803×	body	2560	valid
124.0ms	765×	body	320	valid
83.0ms	2151×	body	80	valid
39.0ms	414×	body	160	valid

Details

sample74.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite22.0ms

series341.0ms

simplify145.0ms

prune238.0ms

localize13.0ms

rewrite85.0ms

series377.0ms

simplify114.0ms

prune897.0ms

localize14.0ms

rewrite162.0ms

series414.0ms

simplify108.0ms

prune2.7s

localize11.0ms

rewrite56.0ms

series326.0ms

simplify61.0ms

prune575.0ms

regimes126.0ms

bsearch92.0ms

simplify1.0ms

end0.0ms

sample2.1s

Profiling