Details

analyze270.0ms

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

sample40.0ms

Algorithm

intervals

Results

12.0ms	129×	body	160	valid
8.0ms	127×	body	80	valid
8.0ms	279×	pre	80	true
1.0ms	23×	body	80	nan

simplify186.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (185.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune11.0ms

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: 27.1b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.3b	(* 3.0 (* a c))
0.4b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
27.0b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

rewrite29.0ms

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:

4.0ms	(- (* 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))
8.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

series57.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(* 3.0 (* a c))
26.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
18.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

simplify48.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5461	1199

prune136.0ms

Filtered

59 candidates to 85 candidates (-44.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Merged error: 0.4b

Counts

87 → 6

localize18.0ms

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))))))
0.4b	(/ (/ (* 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))
5.0ms	(* 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))

series110.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
4.0ms	(* 3.0 (* a (neg c)))
55.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
48.0ms	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

simplify55.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4983	1982
1	4983	1982

prune194.0ms

Filtered

76 candidates to 126 candidates (-65.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	11	126
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 0b

Counts

132 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
5×	`distribute-lft-out`
4×	`associate-/r*`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `associate-r` `clear-num` `sum-log` `*-commutative` `flip--` `div-inv`

Counts

4 → 74

Calls

4 calls:

10.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
6.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))

series74.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
15.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
9.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(* 3.0 (* a c))

simplify67.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4925	1187
1	4925	1187

prune149.0ms

Filtered

61 candidates to 86 candidates (-41.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	90	7	97

Merged error: 0b

Counts

97 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.3b	(* 3.0 (* a (* a (* c c))))
0.4b	(/ (- (pow b 4) (* 3.0 (* 3.0 (* a (* a (* c c)))))) (+ (* 3.0 (* a c)) (* b b)))
0.4b	(* 3.0 (* 3.0 (* a (* a (* c c)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
43×	`pow1`
28×	`pow-prod-down` `prod-exp` `cbrt-unprod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac` `associate-l`
4×	`add-log-exp`
3×	`associate-r` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
10.0ms	(* 3.0 (* a (* a (* c c))))
12.0ms	(/ (- (pow b 4) (* 3.0 (* 3.0 (* a (* a (* c c)))))) (+ (* 3.0 (* a c)) (* b b)))
13.0ms	(* 3.0 (* 3.0 (* a (* a (* c c)))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
8.0ms	(* 3.0 (* a (* a (* c c))))
22.0ms	(/ (- (pow b 4) (* 3.0 (* 3.0 (* a (* a (* c c)))))) (+ (* 3.0 (* a c)) (* b b)))
8.0ms	(* 3.0 (* 3.0 (* a (* a (* c c)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5107	1786

prune153.0ms

Filtered

63 candidates to 113 candidates (-79.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Merged error: 0b

Counts

120 → 7

regimes186.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	31
1	148	31

end0.0ms

sample1.1s

Algorithm

intervals

Results

441.0ms	4509×	body	160	valid
254.0ms	8952×	pre	80	true
180.0ms	3491×	body	80	valid
46.0ms	952×	body	80	nan

Details

analyze270.0ms

sample40.0ms

simplify186.0ms

prune11.0ms

localize11.0ms

rewrite29.0ms

series57.0ms

simplify48.0ms

prune136.0ms

localize18.0ms

rewrite40.0ms

series110.0ms

simplify55.0ms

prune194.0ms

localize12.0ms

rewrite27.0ms

series74.0ms

simplify67.0ms

prune149.0ms

localize27.0ms

rewrite44.0ms

series42.0ms

simplify63.0ms

prune153.0ms

regimes186.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.1s

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