Details

analyze1.6s

Algorithm

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

sample198.0ms

Algorithm

intervals

Results

74.0ms	73×	body	2560	valid
71.0ms	122×	body	1280	valid
10.0ms	32×	body	640	valid
10.0ms	21×	body	1280	overflowed
6.0ms	314×	pre	80	true
3.0ms	6×	body	2560	overflowed
2.0ms	11×	body	320	valid
2.0ms	8×	body	640	overflowed
2.0ms	8×	body	320	overflowed
1.0ms	6×	body	160	valid
1.0ms	12×	body	80	valid
1.0ms	10×	body	80	overflowed
1.0ms	1×	body	1280	invalid
1.0ms	4×	body	160	overflowed

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 60.4b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.3b	(- (exp (* a eps)) 1.0)
3.4b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

16.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series89.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
7.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify26.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5458	1421

prune129.0ms

Filtered

67 candidates to 82 candidates (-22.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Merged error: 0.2b

Counts

84 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

12.0ms

(+ (/ 1 b) (/ 1 a))

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

(+ (/ 1 b) (/ 1 a))

simplify67.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune31.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	20	4	24

Merged error: 0.2b

Counts

24 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ -1 a) a)
0.3b	(/ 1 (* b b))
3.9b	(+ (/ 1 (* b b)) (/ (/ -1 a) a))
29.7b	(/ (+ (/ 1 (* b b)) (/ (/ -1 a) a)) (+ (/ 1 b) (/ -1 a)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

127×	`*-un-lft-identity`
120×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
34×	`distribute-lft-out`
22×	`add-exp-log`
21×	`div-inv` `associate-/l*`
16×	`add-cbrt-cube`
12×	`pow1`
10×	`associate-/r*`
8×	`div-exp`
6×	`cbrt-undiv` `pow-flip` `add-log-exp`
4×	`associate-/l/`
3×	`frac-2neg` `flip3-+` `frac-add` `prod-exp` `clear-num` `associate-/r/` `flip-+`
2×	`rec-exp` `1-exp`
1×	`+-commutative` `pow2` `pow-plus` `pow-prod-down` `sum-log` `pow-sqr` `pow-prod-up` `cbrt-unprod` `inv-pow`

Counts

4 → 175

Calls

4 calls:

5.0ms	(/ (/ -1 a) a)
5.0ms	(/ 1 (* b b))
20.0ms	(+ (/ 1 (* b b)) (/ (/ -1 a) a))
35.0ms	(/ (+ (/ 1 (* b b)) (/ (/ -1 a) a)) (+ (/ 1 b) (/ -1 a)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (/ -1 a) a)
5.0ms	(/ 1 (* b b))
5.0ms	(+ (/ 1 (* b b)) (/ (/ -1 a) a))
7.0ms	(/ (+ (/ 1 (* b b)) (/ (/ -1 a) a)) (+ (/ 1 b) (/ -1 a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5047	2624

prune192.0ms

Filtered

107 candidates to 187 candidates (-74.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	186	5	191

Merged error: 0.2b

Counts

191 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (+ (/ -1 a) (/ 1 b))) (cbrt (+ (/ -1 a) (/ 1 b))))
3.9b	(+ (/ 1 (* b b)) (/ -1 (* a a)))
6.1b	(/ (+ (/ 1 (* b b)) (/ -1 (* a a))) (cbrt (+ (/ -1 a) (/ 1 b))))
23.5b	(* (/ 1 (* (cbrt (+ (/ -1 a) (/ 1 b))) (cbrt (+ (/ -1 a) (/ 1 b))))) (/ (+ (/ 1 (* b b)) (/ -1 (* a a))) (cbrt (+ (/ -1 a) (/ 1 b)))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

240×	`*-un-lft-identity`
135×	`times-frac`
109×	`cbrt-prod`
93×	`distribute-lft-out`
85×	`add-sqr-sqrt`
61×	`associate-r`
56×	`add-cube-cbrt`
54×	`cbrt-div`
53×	`add-exp-log`
42×	`div-inv`
31×	`associate-l`
21×	`prod-exp` `associate-/r/`
20×	`flip3-+` `frac-add` `flip-+`
19×	`frac-times` `add-cbrt-cube`
16×	`div-exp`
15×	`swap-sqr`
13×	`pow1` `unswap-sqr`
9×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
7×	`associate-r/` `associate-l/`
6×	`pow1/3` `add-log-exp`
5×	`associate-/l*`
4×	`rec-exp` `1-exp`
3×	`pow-prod-down` `associate-/l/`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `pow2` `frac-2neg` `pow-plus` `clear-num` `sum-log`

Counts

4 → 276

Calls

4 calls:

30.0ms	(* (cbrt (+ (/ -1 a) (/ 1 b))) (cbrt (+ (/ -1 a) (/ 1 b))))
9.0ms	(+ (/ 1 (* b b)) (/ -1 (* a a)))
23.0ms	(/ (+ (/ 1 (* b b)) (/ -1 (* a a))) (cbrt (+ (/ -1 a) (/ 1 b))))
76.0ms	(* (/ 1 (* (cbrt (+ (/ -1 a) (/ 1 b))) (cbrt (+ (/ -1 a) (/ 1 b))))) (/ (+ (/ 1 (* b b)) (/ -1 (* a a))) (cbrt (+ (/ -1 a) (/ 1 b)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (cbrt (+ (/ -1 a) (/ 1 b))) (cbrt (+ (/ -1 a) (/ 1 b))))
5.0ms	(+ (/ 1 (* b b)) (/ -1 (* a a)))
18.0ms	(/ (+ (/ 1 (* b b)) (/ -1 (* a a))) (cbrt (+ (/ -1 a) (/ 1 b))))
8.0ms	(* (/ 1 (* (cbrt (+ (/ -1 a) (/ 1 b))) (cbrt (+ (/ -1 a) (/ 1 b))))) (/ (+ (/ 1 (* b b)) (/ -1 (* a a))) (cbrt (+ (/ -1 a) (/ 1 b)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5000	6138

prune651.0ms

Filtered

151 candidates to 288 candidates (-90.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	288	5	293

Merged error: 0.2b

Counts

293 → 5

regimes152.0ms

Accuracy

0% (3.0b remaining)

Error of 3.2b against oracle of 0.2b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	2547×	body	2560	valid
2.0s	3468×	body	1280	valid
365.0ms	1074×	body	640	valid
306.0ms	701×	body	1280	overflowed
197.0ms	9722×	pre	80	true
106.0ms	156×	body	2560	overflowed
104.0ms	361×	body	640	overflowed
84.0ms	347×	body	320	valid
39.0ms	186×	body	320	overflowed
32.0ms	431×	body	80	valid
20.0ms	133×	body	160	valid
16.0ms	226×	body	80	overflowed
13.0ms	91×	body	160	overflowed
1.0ms	1×	body	1280	invalid

Details

analyze1.6s

sample198.0ms

simplify38.0ms

prune14.0ms

localize16.0ms

rewrite30.0ms

series89.0ms

simplify26.0ms

prune129.0ms

localize5.0ms

rewrite12.0ms

series2.0ms

simplify67.0ms

prune31.0ms

localize10.0ms

rewrite73.0ms

series20.0ms

simplify60.0ms

prune192.0ms

localize19.0ms

rewrite152.0ms

series50.0ms

simplify129.0ms

prune651.0ms

regimes152.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling