Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

sample32.0ms

Algorithm

intervals

Results

14.0ms	75×	body	1280	valid
7.0ms	55×	body	640	valid
2.0ms	86×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	16×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	228	6
1	228	6

prune2.0ms

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: 40.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.5b	(- (exp x) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series9.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- (exp x) 1.0) x)
2.0ms	(- (exp x) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4909	534
1	4909	534

prune86.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 0.1b

Counts

58 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* x (+ 1/2 (* x 1/6))))
0.1b	(* x (+ 1/2 (* x 1/6)))
0.4b	(* x 1/6)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ 1 (* x (+ 1/2 (* x 1/6))))
5.0ms	(* x (+ 1/2 (* x 1/6)))
3.0ms	(* x 1/6)

series11.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(+ 1 (* x (+ 1/2 (* x 1/6))))
6.0ms	(* x (+ 1/2 (* x 1/6)))
2.0ms	(* x 1/6)

simplify51.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4963	483
1	4963	483

prune71.0ms

Filtered

44 candidates to 62 candidates (-40.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	62	4	66

Merged error: 0.1b

Counts

66 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
0.0b	(pow (exp x) 2)
0.0b	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
4.4b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac`
175×	`*-un-lft-identity`
147×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
88×	`difference-of-squares`
41×	`associate-/l*`
36×	`distribute-lft-out`
25×	`unpow-prod-down`
23×	`unpow2` `sqr-pow`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `pow-pow` `div-exp`
3×	`pow-unpow` `exp-prod` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp`

Counts

4 → 247

Calls

4 calls:

15.0ms	(/ (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
3.0ms	(pow (exp x) 2)
10.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series32.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
3.0ms	(pow (exp x) 2)
10.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4944	4877
1	4944	4877

prune345.0ms

Filtered

168 candidates to 259 candidates (-54.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	259	4	263

Merged error: 0.0b

Counts

263 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (- (pow (exp x) 2) (* 1.0 1.0))) (/ (cbrt (- (pow (exp x) 2) (* 1.0 1.0))) (sqrt (+ (exp x) 1.0))))
4.4b	(- (pow (exp x) 2) (* 1.0 1.0))
4.4b	(- (pow (exp x) 2) (* 1.0 1.0))
4.4b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
78×	`times-frac`
76×	`associate-r`
65×	`cbrt-prod`
61×	`*-un-lft-identity`
44×	`sqrt-prod` `difference-of-squares`
41×	`add-cube-cbrt`
11×	`unpow-prod-down` `unpow2` `sqr-pow`
10×	`associate-l` `distribute-lft-out` `add-log-exp` `unswap-sqr`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
5×	`flip3--` `flip--`
4×	`cbrt-div`
3×	`sub-neg` `diff-log`
2×	`frac-times` `sqrt-div` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip-+` `div-inv`

Counts

4 → 159

Calls

4 calls:

34.0ms	(* (cbrt (- (pow (exp x) 2) (* 1.0 1.0))) (/ (cbrt (- (pow (exp x) 2) (* 1.0 1.0))) (sqrt (+ (exp x) 1.0))))
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series54.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cbrt (- (pow (exp x) 2) (* 1.0 1.0))) (/ (cbrt (- (pow (exp x) 2) (* 1.0 1.0))) (sqrt (+ (exp x) 1.0))))
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4941	3561
1	4941	3561

prune560.0ms

Filtered

114 candidates to 171 candidates (-50.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0.0b

Counts

175 → 4

regimes38.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.5b

bsearch15.0ms

Steps

Iters	Range		Point
8	-0.0013620247224148134	-9.61763392707139e-07	-0.00015264209877748183

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	33
1	54	33

end0.0ms

sample895.0ms

Algorithm

intervals

Results

427.0ms	2279×	body	1280	valid
196.0ms	1618×	body	640	valid
69.0ms	2847×	body	80	valid
67.0ms	811×	body	320	valid
23.0ms	445×	body	160	valid

Details

analyze3.0ms

sample32.0ms

simplify10.0ms

prune2.0ms

localize4.0ms

rewrite11.0ms

series9.0ms

simplify43.0ms

prune86.0ms

localize6.0ms

rewrite15.0ms

series11.0ms

simplify51.0ms

prune71.0ms

localize9.0ms

rewrite49.0ms

series32.0ms

simplify83.0ms

prune345.0ms

localize17.0ms

rewrite57.0ms

series54.0ms

simplify72.0ms

prune560.0ms

regimes38.0ms

bsearch15.0ms

simplify1.0ms

end0.0ms

sample895.0ms

Profiling