Details

analyze382.0ms

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

sample86.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

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: 0.1b

Counts

2 → 2

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.6b	(+ (log (+ x y)) (log z))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 79

Calls

3 calls:

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

series77.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
9.0ms	(* (- a 0.5) (log t))
15.0ms	(+ (log (+ x y)) (log z))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4976	1313
1	4976	1313

prune159.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	7	90

Merged error: 0.0b

Counts

90 → 7

localize17.0ms

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))

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)
13.0ms	(+ (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))

series87.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* (- a 0.5) (log t)) t)
48.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
21.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))
9.0ms	(* (- a 0.5) (log t))

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5038	1469

prune154.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	112	5	117

Merged error: 0.0b

Counts

117 → 5

localize22.0ms

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))))

rewrite52.0ms

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))))))
14.0ms	(+ (- (* (- 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))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
34.0ms	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
12.0ms	(* (- a 0.5) (log t))
23.0ms	(+ (log z) (log (sqrt (+ x y))))

simplify41.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5022	2551

prune173.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	142	5	147

Merged error: 0.0b

Counts

147 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a 0.5) (log (cbrt t)))
0.1b	(+ (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (* 2 (log (cbrt t)))))) (* (- a 0.5) (log (cbrt t))))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

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

series166.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (- a 0.5) (log (cbrt t)))
97.0ms	(+ (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (* 2 (log (cbrt t)))))) (* (- a 0.5) (log (cbrt t))))
21.0ms	(cbrt t)
23.0ms	(cbrt t)

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4940	1747
1	4940	1747

prune134.0ms

Filtered

76 candidates to 104 candidates (-36.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

regimes1.1s

Accuracy

0% (0.2b 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

sample2.8s

Algorithm

intervals

Results

543.0ms

8000×

body

valid

Details

analyze382.0ms

sample86.0ms

simplify97.0ms

prune15.0ms

localize17.0ms

rewrite31.0ms

series77.0ms

simplify45.0ms

prune159.0ms

localize17.0ms

rewrite38.0ms

series87.0ms

simplify60.0ms

prune154.0ms

localize22.0ms

rewrite52.0ms

series123.0ms

simplify41.0ms

prune173.0ms

localize22.0ms

rewrite27.0ms

series166.0ms

simplify61.0ms

prune134.0ms

regimes1.1s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling