Details

sample180.0ms

Algorithm

intervals

Results

76.0ms	1280×	body	80	nan
24.0ms	371×	body	80	valid
6.0ms	19×	body	640	valid
4.0ms	20×	body	320	valid
3.0ms	3×	body	1280	valid
1.0ms	5×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10

prune4.0ms

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: 1.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.2b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.5b	(log (- 1.0 z))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
69×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
57×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
28×	`pow1`
27×	`log-prod`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-r/` `associate-r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sub-neg` `flip3--` `associate-l` `flip--` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `exp-sum` `sum-log` `flip-+`

Counts

4 → 188

Calls

4 calls:

12.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
8.0ms	(* y (- (log z) t))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series445.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
68.0ms	(* y (- (log z) t))
186.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
41.0ms	(log (- 1.0 z))

simplify100.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	947	2029
1	3790	1591
2	5001	1590

prune602.0ms

Filtered

200 candidates to 130 candidates (65.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	194	6	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	195	6	201

Merged error: 0.0b

Counts

201 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.2b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

168×	`prod-diff`
156×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
110×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
92×	`associate--l+`
74×	`associate-+r+`
48×	`pow1`
38×	`log-pow`
34×	`associate-+l+`
31×	`distribute-lft-out--`
24×	`log-prod`
17×	`associate-r`
14×	`difference-of-squares`
12×	`sub-neg` `associate-*r/`
10×	`add-cbrt-cube`
9×	`add-exp-log` `associate-l`
6×	`flip3--` `flip--` `add-log-exp`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `exp-sum` `sum-log` `flip-+`

Counts

4 → 306

Calls

4 calls:

22.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
24.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
8.0ms	(* y (- (log z) t))
30.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
218.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
67.0ms	(* y (- (log z) t))
230.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify158.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1119	6148
1	4676	4554
2	5001	4552

prune992.0ms

Filtered

318 candidates to 161 candidates (50.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	317	1	318
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	319	5	324

Merged error: 0.0b

Counts

324 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.3b	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity`
72×	`prod-diff`
71×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
43×	`associate--l+`
37×	`distribute-rgt-in` `distribute-lft-in`
26×	`pow1`
19×	`distribute-lft-out--`
18×	`log-pow`
11×	`associate-r`
9×	`log-prod`
8×	`add-cbrt-cube` `difference-of-squares`
7×	`add-exp-log`
6×	`associate-l`
5×	`sub-neg` `add-log-exp`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`flip3--` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`diff-log` `exp-sum`

Counts

4 → 167

Calls

4 calls:

5.0ms	(- (log z) t)
23.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
5.0ms	(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
1.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (log z) t)
103.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
227.0ms	(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
241.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify92.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	654	3469
1	2373	2422
2	5002	2230

prune478.0ms

Filtered

179 candidates to 82 candidates (45.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	179	5	184

Merged error: 0.0b

Counts

184 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.5b	(log (- 1.0 z))
5.5b	(log (- 1.0 z))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

96×	`prod-diff`
82×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`associate-+r+`
72×	`distribute-rgt-in` `distribute-lft-in`
70×	`add-cube-cbrt`
68×	`associate-+l+`
42×	`log-prod`
32×	`associate--l+`
30×	`pow1`
26×	`log-pow`
16×	`associate-*r/`
10×	`flip3--` `flip--`
8×	`sub-neg` `frac-add` `add-log-exp`
6×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 216

Calls

4 calls:

22.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
18.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))
4.0ms	(log (- 1.0 z))

series466.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
188.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
49.0ms	(log (- 1.0 z))
42.0ms	(log (- 1.0 z))

simplify79.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	701	2428
1	2388	1992
2	5003	1942

prune1.1s

Filtered

228 candidates to 170 candidates (74.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	228	5	233

Merged error: 0.0b

Counts

233 → 5

regimes425.0ms

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	29	15
1	29	15

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	40429×	body	80	nan
829.0ms	12456×	body	80	valid
147.0ms	400×	body	640	valid
90.0ms	397×	body	320	valid
55.0ms	76×	body	1280	valid
34.0ms	243×	body	160	valid