Details

analyze263.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample58.0ms

Algorithm

intervals

Results

14.0ms	154×	body	160	valid
5.0ms	102×	body	80	valid

simplify174.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (173.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune8.0ms

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: 29.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.3b	(* 3.0 (* a c))
0.3b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
29.3b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

6.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))
11.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
7.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))
24.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
15.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

simplify47.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5461	1199

prune130.0ms

Filtered

59 candidates to 85 candidates (-44.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	7	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 0.4b

Counts

86 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.3b	(* 3.0 (* a (neg c)))
0.3b	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.3b	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log` `add-cbrt-cube`
22×	`times-frac`
20×	`*-un-lft-identity`
19×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
14×	`pow1`
12×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`associate-/l*`
6×	`associate-l` `pow-prod-down` `associate-/r/` `distribute-rgt-neg-out`
5×	`associate-/r*`
4×	`div-inv` `distribute-lft-out` `add-log-exp`
3×	`flip3-+` `distribute-frac-neg` `flip-+`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 114

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
6.0ms	(* 3.0 (* a (neg c)))
11.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

series102.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
5.0ms	(* 3.0 (* a (neg c)))
51.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
43.0ms	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

simplify51.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4983	1982
1	4983	1982

prune180.0ms

Filtered

76 candidates to 126 candidates (-65.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Merged error: 0.0b

Counts

133 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.3b	(/ (* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c)) a)
0.3b	(* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c))
0.3b	(* 3.0 (* a c))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
23×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
21×	`associate-l`
18×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1` `associate-r`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/r*` `distribute-lft-out`
2×	`associate-l/` `associate-/r/` `-commutative` `distribute-rgt-neg-out` `div-inv` `unswap-sqr`
1×	`neg-mul-1` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `distribute-frac-neg` `clear-num` `flip--` `flip-+` `associate-/l/` `associate-/l*`

Counts

4 → 99

Calls

4 calls:

4.0ms	(- (* b b) (* 3.0 (* a c)))
11.0ms	(/ (* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c)) a)
14.0ms	(* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c))
5.0ms	(* 3.0 (* a c))

series108.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
42.0ms	(/ (* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c)) a)
54.0ms	(* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c))
3.0ms	(* 3.0 (* a c))

simplify30.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5124	1611

prune168.0ms

Filtered

81 candidates to 111 candidates (-37.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Merged error: 0b

Counts

120 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ b (sqrt (- (* b b) (* 3.0 (* a c))))) (neg c))
0.2b	(- (* b b) (* 3.0 (* a c)))
0.3b	(* 3.0 (* a c))
0.3b	(/ 1 (/ (+ b (sqrt (- (* b b) (* 3.0 (* a c))))) (neg c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

332×	`times-frac`
270×	`*-un-lft-identity`
168×	`add-sqr-sqrt` `add-cube-cbrt`
63×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
54×	`associate-/r*`
51×	`distribute-lft-out`
22×	`add-exp-log`
21×	`neg-mul-1`
16×	`add-cbrt-cube`
10×	`pow1`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
4×	`cbrt-undiv`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `flip3--` `pow-flip` `flip3-+` `diff-log` `associate-r` `associate-/r/` `*-commutative` `flip--` `flip-+` `inv-pow`

Counts

4 → 297

Calls

4 calls:

9.0ms	(/ (+ b (sqrt (- (* b b) (* 3.0 (* a c))))) (neg c))
4.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))
16.0ms	(/ 1 (/ (+ b (sqrt (- (* b b) (* 3.0 (* a c))))) (neg c)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (+ b (sqrt (- (* b b) (* 3.0 (* a c))))) (neg c))
8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))
31.0ms	(/ 1 (/ (+ b (sqrt (- (* b b) (* 3.0 (* a c))))) (neg c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5077	7214

prune329.0ms

Filtered

161 candidates to 309 candidates (-91.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	306	3	309
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	309	9	318

Merged error: 0b

Counts

318 → 9

regimes204.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	17
1	58	17

end0.0ms

sample1.5s

Algorithm

intervals

Results

402.0ms	4491×	body	160	valid
164.0ms	3509×	body	80	valid

Details

analyze263.0ms

sample58.0ms

simplify174.0ms

prune8.0ms

localize11.0ms

rewrite30.0ms

series50.0ms

simplify47.0ms

prune130.0ms

localize15.0ms

rewrite40.0ms

series102.0ms

simplify51.0ms

prune180.0ms

localize16.0ms

rewrite37.0ms

series108.0ms

simplify30.0ms

prune168.0ms

localize12.0ms

rewrite51.0ms

series59.0ms

simplify88.0ms

prune329.0ms

regimes204.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

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