Details

analyze267.0ms

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

sample39.0ms

Algorithm

intervals

Results

13.0ms	139×	body	160	valid
8.0ms	293×	pre	80	true
6.0ms	117×	body	80	valid
2.0ms	37×	body	80	nan

simplify179.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (177.0ms)

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: 27.3b

Counts

2 → 1

localize10.0ms

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))
27.1b	(- (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:

4.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))
10.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
9.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

series51.0ms

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)

simplify49.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5461	1199

prune133.0ms

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: 0.5b

Counts

86 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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))
11.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a (neg c)))
13.0ms	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

series101.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
53.0ms	(/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
3.0ms	(* 3.0 (* a (neg c)))
41.0ms	(/ (/ (* 3.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

simplify52.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4983	1982
1	4983	1982

prune185.0ms

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

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

6.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
15.0ms	(* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c))
7.0ms	(/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a c))

series116.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
52.0ms	(* (/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (neg c))
47.0ms	(/ a (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
3.0ms	(* 3.0 (* a c))

simplify49.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4982	1870
1	4982	1870

prune190.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 0.0b

Counts

129 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (* 3.0 (* a c))) (cbrt (* 3.0 (* a c))))
0.6b	(cbrt (* 3.0 (* a c)))
0.6b	(cbrt (* 3.0 (* a c)))
0.6b	(cbrt (* 3.0 (* a c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

6.0ms	(* (cbrt (* 3.0 (* a c))) (cbrt (* 3.0 (* a c))))
4.0ms	(cbrt (* 3.0 (* a c)))
4.0ms	(cbrt (* 3.0 (* a c)))
4.0ms	(cbrt (* 3.0 (* a c)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (cbrt (* 3.0 (* a c))) (cbrt (* 3.0 (* a c))))
16.0ms	(cbrt (* 3.0 (* a c)))
16.0ms	(cbrt (* 3.0 (* a c)))
16.0ms	(cbrt (* 3.0 (* a c)))

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5126	506

prune112.0ms

Filtered

47 candidates to 70 candidates (-48.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 0.0b

Counts

78 → 8

regimes202.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	34
1	85	34

end0.0ms

sample1.1s

Algorithm

intervals

Results

434.0ms	4501×	body	160	valid
259.0ms	9013×	pre	80	true
173.0ms	3499×	body	80	valid
49.0ms	1013×	body	80	nan

Details

analyze267.0ms

sample39.0ms

simplify179.0ms

prune8.0ms

localize10.0ms

rewrite30.0ms

series51.0ms

simplify49.0ms

prune133.0ms

localize14.0ms

rewrite39.0ms

series101.0ms

simplify52.0ms

prune185.0ms

localize14.0ms

rewrite36.0ms

series116.0ms

simplify49.0ms

prune190.0ms

localize20.0ms

rewrite19.0ms

series77.0ms

simplify34.0ms

prune112.0ms

regimes202.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

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