Details

analyze398.0ms

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

sample48.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
9.0ms	143×	body	80	nan
0.0ms	1×	body	80	invalid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5198	16

prune14.0ms

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: 0.2b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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)
15.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
9.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))
7.0ms	(* (- a 0.5) (log t))

series90.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* (- a 0.5) (log t)) t)
52.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
19.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))
10.0ms	(* (- a 0.5) (log t))

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5038	1469

prune171.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	0	1	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:

0.0b	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
0.1b	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
0.1b	(* (- a 0.5) (log t))
0.4b	(+ (log z) (log (sqrt (+ x y))))

rewrite55.0ms

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:

19.0ms	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
16.0ms	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
7.0ms	(* (- a 0.5) (log t))
8.0ms	(+ (log z) (log (sqrt (+ x y))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
36.0ms	(+ (- (* (- 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))))

simplify38.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5022	2551

prune183.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	142	9	151

Merged error: 0.0b

Counts

151 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

7.0ms	(- (+ (log (+ x y)) (log z)) t)
12.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
6.0ms	(* (- a 0.5) (log t))
7.0ms	(+ (log (+ x y)) (log z))

series107.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (+ (log (+ x y)) (log z)) t)
49.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
9.0ms	(* (- a 0.5) (log t))
16.0ms	(+ (log (+ x y)) (log z))

simplify29.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5089	1608

prune152.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	112	9	121

Merged error: 0.0b

Counts

121 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a 0.5) (log (cbrt t)))
0.3b	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-+l+`
12×	`associate-+r+`
10×	`associate-*l/`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`frac-add`
3×	`pow1/3`
2×	`log-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

7.0ms	(* (- a 0.5) (log (cbrt t)))
14.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series106.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (- a 0.5) (log (cbrt t)))
36.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
25.0ms	(cbrt t)
21.0ms	(cbrt t)

simplify81.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4936	1252
1	4936	1252

prune149.0ms

Filtered

94 candidates to 122 candidates (-29.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	4	2	6
Picked	1	0	1
Done	0	2	2
Total	124	7	131

Merged error: 0b

Counts

131 → 7

regimes1.0s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

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

603.0ms	8000×	body	80	valid
296.0ms	4383×	body	80	nan
2.0ms	30×	body	80	invalid

Details

analyze398.0ms

sample48.0ms

simplify92.0ms

prune14.0ms

localize15.0ms

rewrite41.0ms

series90.0ms

simplify56.0ms

prune171.0ms

localize17.0ms

rewrite55.0ms

series122.0ms

simplify38.0ms

prune183.0ms

localize15.0ms

rewrite36.0ms

series107.0ms

simplify29.0ms

prune152.0ms

localize22.0ms

rewrite28.0ms

series106.0ms

simplify81.0ms

prune149.0ms

regimes1.0s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling