Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample24.0ms

Algorithm

intervals

Results

7.0ms	53×	body	640	valid
5.0ms	143×	body	80	valid
3.0ms	27×	body	320	valid
3.0ms	15×	body	1280	valid
1.0ms	18×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	880	15
1	880	15

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 9.8b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+l+`

Counts

4 → 112

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
18.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
36.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (- x 1.0))
2.0ms	(/ 1.0 (+ x 1.0))
3.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
10.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4954	1594
1	4954	1594

prune198.0ms

Filtered

95 candidates to 124 candidates (-30.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	4	125

Merged error: 0.1b

Counts

125 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ 1.0 x))
0.2b	(cbrt (+ 1.0 x))
0.2b	(* (/ (cbrt 1.0) (cbrt (+ 1.0 x))) (/ (cbrt 1.0) (cbrt (+ 1.0 x))))
16.9b	(+ (- (* (* (/ (cbrt 1.0) (cbrt (+ 1.0 x))) (/ (cbrt 1.0) (cbrt (+ 1.0 x)))) (/ (cbrt 1.0) (cbrt (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

264×	`cbrt-prod`
232×	`times-frac`
212×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`add-cube-cbrt`
60×	`swap-sqr`
48×	`associate-r` `associate-l`
39×	`distribute-lft-out`
25×	`unswap-sqr`
16×	`add-exp-log`
12×	`cbrt-div`
11×	`pow1`
9×	`frac-add` `add-log-exp`
8×	`associate-/r/` `add-cbrt-cube`
7×	`flip3-+` `frac-sub` `flip-+`
6×	`frac-times` `associate-*l/`
4×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
2×	`pow1/3` `sum-log`
1×	`+-commutative` `pow2` `associate-+l-` `sub-neg` `associate-+l+` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 257

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 x))
3.0ms	(cbrt (+ 1.0 x))
54.0ms	(* (/ (cbrt 1.0) (cbrt (+ 1.0 x))) (/ (cbrt 1.0) (cbrt (+ 1.0 x))))
41.0ms	(+ (- (* (* (/ (cbrt 1.0) (cbrt (+ 1.0 x))) (/ (cbrt 1.0) (cbrt (+ 1.0 x)))) (/ (cbrt 1.0) (cbrt (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 x))
6.0ms	(cbrt (+ 1.0 x))
13.0ms	(* (/ (cbrt 1.0) (cbrt (+ 1.0 x))) (/ (cbrt 1.0) (cbrt (+ 1.0 x))))
19.0ms	(+ (- (* (* (/ (cbrt 1.0) (cbrt (+ 1.0 x))) (/ (cbrt 1.0) (cbrt (+ 1.0 x)))) (/ (cbrt 1.0) (cbrt (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5206	5255

prune795.0ms

Filtered

165 candidates to 269 candidates (-63.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	269	4	273

Merged error: 0.1b

Counts

273 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 1.0 x))
0.1b	(* x (- (* x x) (* 1.0 1.0)))
0.2b	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
16.0b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

40×	`associate-*r/`
16×	`frac-add`
14×	`flip3--` `flip--`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `flip3-+` `flip-+`
8×	`pow1` `add-exp-log` `frac-times` `add-cube-cbrt` `associate-r` `add-cbrt-cube` `add-log-exp`
7×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-l`
5×	`sub-neg`
4×	`associate-+r+` `associate-*l/`
2×	`associate-+l+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `diff-log` `sum-log` `distribute-lft-out` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

6.0ms	(* x (+ 1.0 x))
6.0ms	(* x (- (* x x) (* 1.0 1.0)))
4.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
12.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

series18.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* x (+ 1.0 x))
6.0ms	(* x (- (* x x) (* 1.0 1.0)))
4.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
1.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

simplify40.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5336	2335

prune208.0ms

Filtered

81 candidates to 102 candidates (-25.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	2	2
Picked	1	0	1
Done	1	0	1
Total	103	3	106

Merged error: 0.1b

Counts

106 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (- (* x x) (* 1.0 1.0)))
0.1b	(/ 2.0 (* x (- (* x x) (* 1.0 1.0))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `associate-r/` `associate-r*`
3×	`times-frac` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

2 → 46

Calls

2 calls:

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(* x (- (* x x) (* 1.0 1.0)))
4.0ms	(/ 2.0 (* x (- (* x x) (* 1.0 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5673	585

prune65.0ms

Filtered

39 candidates to 52 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0b

Counts

55 → 4

regimes30.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	11
1	26	11

end0.0ms

sample738.0ms

Algorithm

intervals

Results

262.0ms	1868×	body	640	valid
153.0ms	4185×	body	80	valid
100.0ms	572×	body	1280	valid
93.0ms	885×	body	320	valid
34.0ms	490×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze6.0ms

sample24.0ms

simplify54.0ms

prune4.0ms

localize8.0ms

rewrite70.0ms

series17.0ms

simplify50.0ms

prune198.0ms

localize16.0ms

rewrite121.0ms

series44.0ms

simplify105.0ms

prune795.0ms

localize16.0ms

rewrite32.0ms

series18.0ms

simplify40.0ms

prune208.0ms

localize6.0ms

rewrite15.0ms

series11.0ms

simplify46.0ms

prune65.0ms

regimes30.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample738.0ms

Profiling