Details

sample166.0ms

Algorithm

intervals

Results

84.0ms	1745×	body	80	nan
14.0ms	257×	body	80	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 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 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 114

Calls

3 calls:

27.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
6.0ms	(* (- a 0.5) (log t))
6.0ms	(+ (log (+ x y)) (log z))

series353.0ms

Counts

3 → 9

Calls

3 calls:

215.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
60.0ms	(* (- a 0.5) (log t))
78.0ms	(+ (log (+ x y)) (log z))

simplify63.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	639	1104
1	2272	1047
2	5003	1031

prune265.0ms

Filtered

123 candidates to 73 candidates (59.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Merged error: 0.0b

Counts

124 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

111×	`*-un-lft-identity`
50×	`distribute-lft-out`
34×	`add-log-exp`
33×	`log-prod`
30×	`distribute-lft-out--`
27×	`pow1`
26×	`associate-+r+`
23×	`associate-l`
22×	`add-sqr-sqrt`
21×	`log-pow`
17×	`sum-log`
16×	`add-cube-cbrt`
15×	`associate-+l+`
12×	`associate--l+`
9×	`distribute-rgt-in` `distribute-lft-in`
8×	`diff-log`
6×	`add-exp-log` `associate--l-` `associate-+l-` `log-div` `flip3--` `associate-*l/` `add-cbrt-cube` `flip--`
5×	`flip3-+` `flip-+`
4×	`associate-r` `frac-add`
3×	`+-commutative` `associate-+r-` `sub-neg`
2×	`difference-of-squares`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 150

Calls

4 calls:

6.0ms	(- (log (+ x y)) t)
22.0ms	(+ (- (log (+ x y)) t) (* (- a 0.5) (log t)))
22.0ms	(+ (log z) (+ (- (log (+ x y)) t) (* (- a 0.5) (log t))))
7.0ms	(* (- a 0.5) (log t))

series517.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (log (+ x y)) t)
142.0ms	(+ (- (log (+ x y)) t) (* (- a 0.5) (log t)))
212.0ms	(+ (log z) (+ (- (log (+ x y)) t) (* (- a 0.5) (log t))))
63.0ms	(* (- a 0.5) (log t))

simplify67.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	708	1377
1	2364	1309
2	5003	1290

prune337.0ms

Filtered

162 candidates to 98 candidates (60.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	162	7	169

Merged error: 0.0b

Counts

169 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

333×	`*-un-lft-identity`
194×	`distribute-lft-out`
108×	`associate-+r+`
92×	`associate-l`
82×	`distribute-lft-out--`
79×	`log-prod`
63×	`pow1`
61×	`log-pow`
60×	`distribute-rgt-in` `distribute-lft-in`
57×	`associate-+l+`
49×	`add-log-exp`
42×	`cbrt-prod`
40×	`add-sqr-sqrt`
38×	`associate-r`
36×	`add-cube-cbrt`
33×	`sum-log`
13×	`distribute-rgt-out`
8×	`diff-log` `associate-*l/`
4×	`add-exp-log` `+-commutative` `flip3--` `pow1/3` `frac-add` `associate--l+` `add-cbrt-cube` `flip--`
3×	`associate-+l-` `associate-+r-` `flip3-+` `flip-+`
2×	`associate--l-` `log-div` `*-commutative` `difference-of-squares`
1×	`sub-neg`

Counts

4 → 241

Calls

4 calls:

68.0ms	(+ (log z) (+ (- (log (+ x y)) t) (+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))))
37.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series1.0s

Counts

4 → 12

Calls

4 calls:

458.0ms	(+ (log z) (+ (- (log (+ x y)) t) (+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))))
203.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
200.0ms	(cbrt t)
183.0ms	(cbrt t)

simplify136.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	1146	2914
1	4463	2409
2	5001	2348

prune929.0ms

Filtered

253 candidates to 147 candidates (58.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	253	7	260

Merged error: 0b

Counts

260 → 7

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (log z) (+ (- (log (+ x y)) t) (+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow (/ 1 t) -1/3))))))
0.3b	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow (/ 1 t) -1/3))))
0.6b	(cbrt t)
5.0b	(pow (/ 1 t) -1/3)

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

358×	`*-un-lft-identity`
196×	`associate-+r+`
194×	`distribute-lft-out`
123×	`log-prod`
92×	`associate-l`
82×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out--`
69×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `unpow-prod-down`
60×	`pow1`
57×	`associate-+l+` `log-pow`
49×	`add-log-exp`
45×	`times-frac`
33×	`sum-log`
27×	`cbrt-prod`
14×	`associate-r`
9×	`add-exp-log`
8×	`diff-log` `associate-*l/`
5×	`pow-pow` `div-inv` `sqr-pow`
4×	`+-commutative` `flip3--` `frac-add` `pow-exp` `associate--l+` `add-cbrt-cube` `flip--`
3×	`associate-+l-` `associate-+r-` `pow-unpow` `distribute-rgt-out` `flip3-+` `pow1/3` `flip-+`
2×	`associate--l-` `log-div` `pow-flip` `div-exp` `*-commutative` `inv-pow` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `rec-exp` `1-exp`

Counts

4 → 296

Calls

4 calls:

86.0ms	(+ (log z) (+ (- (log (+ x y)) t) (+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow (/ 1 t) -1/3))))))
49.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow (/ 1 t) -1/3))))
1.0ms	(cbrt t)
5.0ms	(pow (/ 1 t) -1/3)

series1.4s

Counts

4 → 12

Calls

4 calls:

659.0ms	(+ (log z) (+ (- (log (+ x y)) t) (+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow (/ 1 t) -1/3))))))
372.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (pow (/ 1 t) -1/3))))
209.0ms	(cbrt t)
195.0ms	(pow (/ 1 t) -1/3)

simplify82.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1595	3832
1	5002	3517

prune1.0s

Filtered

308 candidates to 187 candidates (60.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	309	6	315

Merged error: 0b

Counts

315 → 6

regimes418.0ms

Accuracy

0% (0.3b 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 (0.0ms)

Iter	Nodes	Cost
0	34	17
1	34	17

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.6s	56471×	body	80	nan
444.0ms	8026×	body	80	valid