Details

analyze263.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample73.0ms

Algorithm

intervals

Results

37.0ms	82×	body	1280	valid
13.0ms	48×	body	640	valid
7.0ms	21×	body	2560	valid
5.0ms	25×	body	320	valid
3.0ms	70×	body	80	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune3.0ms

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: 54.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (sqrt (+ (* x x) 1.0)))
2.3b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.8b	(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:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series16.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms	(sqrt (+ (* x x) 1.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5075	600

prune110.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

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: 0b

Counts

52 → 5

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-l`
48×	`add-sqr-sqrt`
40×	`times-frac`
29×	`add-cube-cbrt` `*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
9×	`add-exp-log`
8×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-r` `add-cbrt-cube`
2×	`pow-exp` `div-inv` `sqr-pow`
1×	`pow1` `cube-div` `cube-mult` `pow-to-exp` `unpow3` `div-exp` `associate-l/` `-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 75

Calls

1 calls:

13.0ms

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

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

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

simplify40.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4973	758
1	4973	758

prune126.0ms

Filtered

40 candidates to 78 candidates (-95.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0b

Counts

83 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
0.1b	(/ 0.125 (pow x 3))
10.9b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

28.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
32.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
5.0ms	(/ 0.125 (pow x 3))
34.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series23.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
4.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
3.0ms	(/ 0.125 (pow x 3))
9.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify32.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5226	1749

prune175.0ms

Filtered

82 candidates to 136 candidates (-65.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	136	5	141

Merged error: 0b

Counts

141 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.125 (pow x 3))
0.2b	(/ 0.0625 (pow x 5))
13.9b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.3b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
71×	`times-frac`
68×	`*-un-lft-identity`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
14×	`cube-prod`
11×	`log-prod`
10×	`difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`cube-mult` `unpow3` `distribute-lft-out`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
35.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
36.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
9.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
5.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify55.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5361	2493

prune293.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	171	5	176

Merged error: 0b

Counts

176 → 5

regimes141.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.4b

bsearch32.0ms

Steps

Iters	Range		Point
9	2.2613564567857214e-08	29.904758181447523	0.9002939444000406
10	-43.11385858101192	-1.5839292604365353e-15	-0.9960767900717074

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	55
1	94	55

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	2359×	body	1280	valid
623.0ms	1537×	body	640	valid
266.0ms	790×	body	2560	valid
135.0ms	796×	body	320	valid
89.0ms	2159×	body	80	valid
37.0ms	359×	body	160	valid

Details

analyze263.0ms

sample73.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite16.0ms

series16.0ms

simplify38.0ms

prune110.0ms

localize9.0ms

rewrite17.0ms

series17.0ms

simplify40.0ms

prune126.0ms

localize10.0ms

rewrite103.0ms

series23.0ms

simplify32.0ms

prune175.0ms

localize12.0ms

rewrite85.0ms

series21.0ms

simplify55.0ms

prune293.0ms

regimes141.0ms

bsearch32.0ms

simplify2.0ms

end0.0ms

sample2.4s

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