Details

sample405.0ms

Algorithm

intervals

Results

297.0ms	24×	body	320	valid
47.0ms	71×	body	1280	valid
20.0ms	48×	body	640	valid
10.0ms	100×	body	80	valid
6.0ms	84×	body	80	overflowed
2.0ms	13×	body	160	valid

simplify747.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5131	12

prune18.0ms

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: 38.2b

Counts

2 → 1

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.0b	(pow (exp x) 2.0)
3.8b	(- (pow (exp x) 2.0) 1.0)
3.9b	(- (exp x) 1.0)

rewrite59.0ms

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 → 114

Calls

4 calls:

21.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
6.0ms	(pow (exp x) 2.0)
10.0ms	(- (pow (exp x) 2.0) 1.0)
11.0ms	(- (exp x) 1.0)

series69.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
28.0ms	(pow (exp x) 2.0)
7.0ms	(- (pow (exp x) 2.0) 1.0)
16.0ms	(- (exp x) 1.0)

simplify159.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4908	1700
1	4908	1700

prune411.0ms

Filtered

90 candidates to 126 candidates (-40.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	4	127

Merged error: 0b

Counts

127 → 4

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (+ 2 (* x (* x 1/2))))
12.4b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

rewrite19.0ms

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:

9.0ms	(+ x (+ 2 (* x (* x 1/2))))
9.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

series14.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ x (+ 2 (* x (* x 1/2))))
9.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5225	486

prune106.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	37	3	40

Merged error: 0b

Counts

40 → 3

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ x 2) (* x (* x 1/2)))
12.4b	(sqrt (+ (+ x 2) (* x (* x 1/2))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

11.0ms	(+ (+ x 2) (* x (* x 1/2)))
10.0ms	(sqrt (+ (+ x 2) (* x (* x 1/2))))

series13.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ (+ x 2) (* x (* x 1/2)))
8.0ms	(sqrt (+ (+ x 2) (* x (* x 1/2))))

simplify87.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4912	454
1	4912	454

prune97.0ms

Filtered

27 candidates to 34 candidates (-25.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0b

Counts

37 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(pow (exp x) 2)
3.8b	(- (pow (exp x) 2.0) 1.0)
3.8b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `pow-pow` `add-log-exp`
7×	`difference-of-squares`
6×	`pow1` `pow-unpow` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `unpow2`
1×	`distribute-lft-out--`

Counts

4 → 73

Calls

4 calls:

7.0ms	(pow (exp x) 2.0)
7.0ms	(pow (exp x) 2)
10.0ms	(- (pow (exp x) 2.0) 1.0)
9.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series52.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (exp x) 2.0)
5.0ms	(pow (exp x) 2)
7.0ms	(- (pow (exp x) 2.0) 1.0)
7.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4908	618
1	4908	618

prune262.0ms

Filtered

60 candidates to 85 candidates (-41.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	85	3	88

Merged error: 0b

Counts

88 → 3

regimes74.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 20.8b

bsearch24.0ms

Steps

Iters	Range		Point
6	-1.1294785154268786e-05	-9.709340229875236e-07	-1.0675671953547258e-05

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	2319×	body	1280	valid
696.0ms	1672×	body	640	valid
220.0ms	2864×	body	80	valid
213.0ms	784×	body	320	valid
176.0ms	2494×	body	80	overflowed
73.0ms	421×	body	160	valid

Details

sample405.0ms

simplify747.0ms

prune18.0ms

localize47.0ms

rewrite59.0ms

series69.0ms

simplify159.0ms

prune411.0ms

localize12.0ms

rewrite19.0ms

series14.0ms

simplify68.0ms

prune106.0ms

localize12.0ms

rewrite23.0ms

series13.0ms

simplify87.0ms

prune97.0ms

localize24.0ms

rewrite37.0ms

series52.0ms

simplify52.0ms

prune262.0ms

regimes74.0ms

bsearch24.0ms

simplify3.0ms

end0.0ms

sample3.2s

Profiling