Details

analyze659.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample58.0ms

Algorithm

intervals

Results

26.0ms	70×	body	1280	valid
13.0ms	55×	body	640	valid
5.0ms	90×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	19×	body	160	valid

simplify450.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5131	12

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 40.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
4.9b	(- (pow (exp x) 2.0) 1.0)
4.9b	(- (exp x) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
35×	`times-frac`
30×	`difference-of-squares`
21×	`add-cube-cbrt`
16×	`distribute-lft-out--`
10×	`unpow-prod-down`
8×	`add-log-exp` `sqr-pow`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`flip3--` `pow-pow` `flip--`
3×	`pow-unpow` `exp-prod`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `div-sub` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 112

Calls

4 calls:

3.0ms	(pow (exp x) 2.0)
11.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
6.0ms	(- (pow (exp x) 2.0) 1.0)
6.0ms	(- (exp x) 1.0)

series39.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (exp x) 2.0)
10.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify95.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4908	1696
1	4908	1696

prune218.0ms

Filtered

90 candidates to 124 candidates (-37.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	2	125

Merged error: 0.0b

Counts

125 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (+ 2 (* x (* x 1/2))))
9.9b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

5.0ms	(+ x (+ 2 (* x (* x 1/2))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ x (+ 2 (* x (* x 1/2))))
7.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5225	486

prune56.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Merged error: 0b

Counts

38 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))) (cbrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))))
9.9b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
9.9b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
9.9b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-prod`
44×	`add-sqr-sqrt`
40×	`sqrt-prod`
39×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`sqrt-div`
14×	`pow1` `swap-sqr`
12×	`cbrt-div`
10×	`associate-r` `associate-l`
9×	`flip3-+` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

16.0ms	(* (cbrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))) (cbrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (cbrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))) (cbrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))))
4.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
4.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4895	2591
1	4895	2591

prune301.0ms

Filtered

83 candidates to 129 candidates (-55.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	129	3	132

Merged error: 0b

Counts

132 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)))
0.0b	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
4.9b	(- (pow (exp x) 2.0) 1.0)
4.9b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

490×	`times-frac`
404×	`add-sqr-sqrt`
348×	`*-un-lft-identity`
260×	`difference-of-squares`
148×	`add-cube-cbrt`
74×	`unpow-prod-down` `sqr-pow`
64×	`distribute-lft-out`
38×	`associate-/r*` `unpow2`
36×	`distribute-lft-out--`
19×	`associate-/r/`
14×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
9×	`flip3-+` `flip-+`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 383

Calls

4 calls:

22.0ms	(/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)))
10.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
6.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series19.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)))
9.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
4.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify110.0ms

Algorithm

egg-herbie

Counts

395 → 395

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5502	11708

prune881.0ms

Filtered

233 candidates to 395 candidates (-69.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	395	0	395
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	395	3	398

Merged error: 0b

Counts

398 → 3

regimes40.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.0b

bsearch19.0ms

Steps

Iters	Range		Point
10	-0.011620329425797153	-6.733038577272367e-13	-1.737755627072116e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms

sample1.6s

Algorithm

intervals

Results

822.0ms	2307×	body	1280	valid
374.0ms	1655×	body	640	valid
126.0ms	2824×	body	80	valid
122.0ms	812×	body	320	valid
40.0ms	402×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze659.0ms

sample58.0ms

simplify450.0ms

prune10.0ms

localize10.0ms

rewrite31.0ms

series39.0ms

simplify95.0ms

prune218.0ms

localize7.0ms

rewrite10.0ms

series10.0ms

simplify37.0ms

prune56.0ms

localize11.0ms

rewrite35.0ms

series21.0ms

simplify78.0ms

prune301.0ms

localize13.0ms

rewrite71.0ms

series19.0ms

simplify110.0ms

prune881.0ms

regimes40.0ms

bsearch19.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling