Details

sample238.0ms

Algorithm

intervals

Results

108.0ms	1764×	body	80	nan
18.0ms	257×	body	80	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	59	9
2	153	9
3	360	9
4	813	9
5	1639	9
6	3143	9
7	5001	9

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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 → 1

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))

rewrite40.0ms

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`
7×	`associate-+l+`
6×	`add-exp-log` `distribute-rgt-in` `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 → 102

Calls

4 calls:

10.0ms	(- (+ (log (+ x y)) (log z)) t)
12.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
7.0ms	(* (- a 0.5) (log t))
6.0ms	(+ (log (+ x y)) (log z))

series129.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (+ (log (+ x y)) (log z)) t)
51.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
17.0ms	(* (- a 0.5) (log t))
26.0ms	(+ (log (+ x y)) (log z))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	681	1040
1	2483	977
2	5001	932

prune705.0ms

Filtered

114 candidates to 80 candidates (29.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	104	10	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	10	115

Merged error: 0b

Counts

115 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a 0.5) (log t))
0.5b	(cbrt (pow (+ (log (+ x y)) (log z)) 3))
0.5b	(+ (log (+ x y)) (log z))
0.7b	(pow (+ (log (+ x y)) (log z)) 3)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
28×	`pow1`
21×	`log-pow` `distribute-lft-out`
20×	`cbrt-prod` `add-sqr-sqrt`
16×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
13×	`log-prod`
7×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`cube-div` `associate-+l+` `flip3-+` `associate-r` `flip-+` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `associate-+r+` `distribute-lft-in`
2×	`cube-mult` `associate-+l-` `log-div` `cbrt-div` `unpow3` `associate-*l/` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

6.0ms	(* (- a 0.5) (log t))
5.0ms	(cbrt (pow (+ (log (+ x y)) (log z)) 3))
6.0ms	(+ (log (+ x y)) (log z))
6.0ms	(pow (+ (log (+ x y)) (log z)) 3)

series122.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (- a 0.5) (log t))
19.0ms	(cbrt (pow (+ (log (+ x y)) (log z)) 3))
14.0ms	(+ (log (+ x y)) (log z))
72.0ms	(pow (+ (log (+ x y)) (log z)) 3)

simplify71.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	453	880
1	1649	825
2	5003	779

prune685.0ms

Filtered

129 candidates to 72 candidates (44.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	129	10	139

Merged error: 0b

Counts

139 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

18.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
7.0ms	(* (- a 0.5) (log t))
10.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
9.0ms	(* (- a 0.5) (log t))
23.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
20.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify72.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	841	1445
1	3188	1317
2	5002	1269

prune1.2s

Filtered

127 candidates to 87 candidates (31.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	128	9	137

Merged error: 0b

Counts

137 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
0.5b	(+ (log (+ x y)) (log z))
0.5b	(cbrt t)
0.5b	(cbrt t)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

43×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
28×	`associate-+l+`
26×	`*-un-lft-identity`
24×	`cbrt-prod`
20×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`associate-+r+`
8×	`pow1` `associate-*l/`
6×	`distribute-lft-out` `add-log-exp`
4×	`add-exp-log` `flip3--` `frac-add` `log-pow` `add-cbrt-cube` `flip--`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `associate-+l-` `log-div` `pow1/3` `sum-log`

Counts

4 → 98

Calls

4 calls:

13.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
6.0ms	(+ (log (+ x y)) (log z))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series100.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
15.0ms	(+ (log (+ x y)) (log z))
26.0ms	(cbrt t)
22.0ms	(cbrt t)

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	637	941
1	2068	825
2	5001	778

prune998.0ms

Filtered

110 candidates to 95 candidates (13.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	110	9	119

Merged error: 0b

Counts

119 → 9

regimes1.2s

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 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.5s	56205×	body	80	nan
584.0ms	8035×	body	80	valid

Details

sample238.0ms

simplify56.0ms

prune6.0ms

localize15.0ms

rewrite40.0ms

series129.0ms

simplify60.0ms

prune705.0ms

localize19.0ms

rewrite27.0ms

series122.0ms

simplify71.0ms

prune685.0ms

localize17.0ms

rewrite49.0ms

series111.0ms

simplify72.0ms

prune1.2s

localize24.0ms

rewrite26.0ms

series100.0ms

simplify60.0ms

prune998.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.4s

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