Details

analyze371.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	68.6%	31.4%	5
0%	65.5%	34.5%	6
0%	59.2%	40.8%	7
0%	51.4%	48.6%	8
0%	41.3%	58.7%	9
0%	28.4%	71.6%	10
2.3%	22.3%	75.4%	11
2.3%	21%	76.7%	12
2.7%	18%	79.3%	13
2.7%	16.4%	80.8%	14

sample44.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	119×	body	80	nan
0.0ms	2×	body	80	invalid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5198	16

prune15.0ms

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: 0.3b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (- a 0.5) (log t)) t)
0.1b	(+ (log z) (- (* (- a 0.5) (log t)) t))
0.2b	(* (- a 0.5) (log t))
0.2b	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

7.0ms	(- (* (- a 0.5) (log t)) t)
9.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))
7.0ms	(* (- a 0.5) (log t))
13.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* (- a 0.5) (log t)) t)
20.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))
9.0ms	(* (- a 0.5) (log t))
52.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5038	1469

prune177.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	9	112

Merged error: 0.0b

Counts

112 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
0.2b	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
0.2b	(* (- a 0.5) (log t))
0.5b	(+ (log z) (log (sqrt (+ x y))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
45×	`distribute-lft-out`
29×	`pow1` `log-prod`
23×	`log-pow`
21×	`add-log-exp`
19×	`add-sqr-sqrt`
18×	`sum-log`
17×	`associate-+l+`
15×	`add-cube-cbrt`
13×	`associate-+r-`
9×	`associate-+r+` `flip3-+` `flip-+`
8×	`log-div` `sqrt-div` `sqrt-prod`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-cbrt-cube`
5×	`associate-l`
4×	`associate-+l-` `diff-log` `associate-r` `frac-add`
3×	`+-commutative` `flip3--` `flip--`
2×	`associate-*l/`
1×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

14.0ms	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
19.0ms	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
7.0ms	(* (- a 0.5) (log t))
7.0ms	(+ (log z) (log (sqrt (+ x y))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
50.0ms	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
9.0ms	(* (- a 0.5) (log t))
25.0ms	(+ (log z) (log (sqrt (+ x y))))

simplify37.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5022	2551

prune187.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	142	9	151

Merged error: 0.0b

Counts

151 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- a 0.5) (log t)) (+ (log z) (log (+ x y)))) t)
0.2b	(* (- a 0.5) (log t))
0.2b	(+ (* (- a 0.5) (log t)) (+ (log z) (log (+ x y))))
0.6b	(+ (log z) (log (+ x y)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

13.0ms	(- (+ (* (- a 0.5) (log t)) (+ (log z) (log (+ x y)))) t)
7.0ms	(* (- a 0.5) (log t))
11.0ms	(+ (* (- a 0.5) (log t)) (+ (log z) (log (+ x y))))
6.0ms	(+ (log z) (log (+ x y)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (+ (* (- a 0.5) (log t)) (+ (log z) (log (+ x y)))) t)
9.0ms	(* (- a 0.5) (log t))
35.0ms	(+ (* (- a 0.5) (log t)) (+ (log z) (log (+ x y))))
15.0ms	(+ (log z) (log (+ x y)))

simplify43.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4985	1663
1	4985	1663

prune169.0ms

Filtered

86 candidates to 108 candidates (-25.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	108	9	117

Merged error: 0.0b

Counts

117 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
0.2b	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (cbrt t))) t))
0.5b	(cbrt t)
0.5b	(cbrt t)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

39×	`log-prod`
37×	`associate-+r+`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`cbrt-prod`
21×	`*-un-lft-identity`
19×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-log-exp`
12×	`associate--l+`
7×	`sum-log`
4×	`pow1` `add-exp-log` `associate-+l+` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `flip3--` `pow1/3` `diff-log` `flip--`
1×	`associate-+r-` `sub-neg` `distribute-lft-out`

Counts

4 → 94

Calls

4 calls:

7.0ms	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
16.0ms	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (cbrt t))) t))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series151.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
49.0ms	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (cbrt t))) t))
22.0ms	(cbrt t)
21.0ms	(cbrt t)

simplify50.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4990	1695
1	4990	1695

prune153.0ms

Filtered

86 candidates to 106 candidates (-23.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	4	2	6
Picked	0	1	1
Done	0	2	2
Total	107	8	115

Merged error: 0.0b

Counts

115 → 8

regimes919.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

590.0ms	8000×	body	80	valid
280.0ms	4207×	body	80	nan
2.0ms	30×	body	80	invalid

Details

analyze371.0ms

sample44.0ms

simplify101.0ms

prune15.0ms

localize19.0ms

rewrite38.0ms

series90.0ms

simplify59.0ms

prune177.0ms

localize17.0ms

rewrite51.0ms

series121.0ms

simplify37.0ms

prune187.0ms

localize17.0ms

rewrite40.0ms

series88.0ms

simplify43.0ms

prune169.0ms

localize21.0ms

rewrite29.0ms

series151.0ms

simplify50.0ms

prune153.0ms

regimes919.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.3s

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