Details

sample179.0ms

Algorithm

intervals

Results

70.0ms	1227×	body	80	nan
28.0ms	404×	body	80	valid
5.0ms	14×	body	640	valid
4.0ms	5×	body	1280	valid
2.0ms	16×	body	160	valid
1.0ms	5×	body	320	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

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: 1.5b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.6b	(log (- 1.0 z))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 182

Calls

4 calls:

9.0ms	(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))

series440.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
73.0ms	(* y (- (log z) t))
181.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(log (- 1.0 z))

simplify99.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	904	1913
1	3501	1501
2	5001	1500

prune567.0ms

Filtered

194 candidates to 126 candidates (64.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	4	195

Merged error: 0.0b

Counts

195 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

108×	`prod-diff`
96×	`*-un-lft-identity`
93×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
74×	`associate-+r+`
71×	`distribute-rgt-in` `distribute-lft-in`
52×	`associate--l+`
34×	`associate-+l+`
33×	`pow1`
25×	`log-pow`
18×	`log-prod`
14×	`distribute-lft-out--`
10×	`associate-r/` `associate-r*`
9×	`add-log-exp`
8×	`sub-neg` `add-cbrt-cube`
7×	`add-exp-log` `difference-of-squares`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`exp-prod`
2×	`exp-sum` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `flip-+`

Counts

4 → 221

Calls

4 calls:

25.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
18.0ms	(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)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
168.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
68.0ms	(* y (- (log z) t))
245.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify127.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1066	3859
1	4195	3046
2	5001	3040

prune901.0ms

Filtered

233 candidates to 147 candidates (63.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	232	5	237

Merged error: 0.0b

Counts

237 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

108×	`prod-diff`
98×	`add-sqr-sqrt` `*-un-lft-identity`
77×	`add-cube-cbrt`
74×	`associate-+r+`
71×	`distribute-rgt-in` `distribute-lft-in`
52×	`associate--l+`
34×	`associate-+l+`
32×	`pow1`
25×	`log-pow`
18×	`log-prod`
14×	`associate-r` `distribute-lft-out--`
13×	`add-exp-log`
10×	`associate-*r/`
8×	`sub-neg` `add-cbrt-cube`
7×	`unpow-prod-down` `difference-of-squares`
6×	`associate-l` `add-log-exp`
5×	`flip3--` `prod-exp` `flip--`
4×	`expm1-log1p-u` `frac-add` `pow-exp` `log1p-expm1-u` `unswap-sqr`
3×	`pow-unpow` `sqr-pow`
2×	`unpow-prod-up` `pow-to-exp` `e-exp-1` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `pow-pow` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `flip-+`

Counts

4 → 235

Calls

4 calls:

16.0ms	(* x (pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
16.0ms	(pow E (+ (* 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))
34.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series748.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* x (pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
181.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
75.0ms	(* y (- (log z) t))
245.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify138.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1134	4155
1	4628	3356
2	5001	3354

prune946.0ms

Filtered

247 candidates to 154 candidates (62.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	247	5	252

Merged error: 0.0b

Counts

252 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (- (log z) t))
0.2b	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.6b	(log (- 1.0 z))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 185

Calls

4 calls:

8.0ms	(* y (- (log z) t))
6.0ms	(log (exp (exp (+ (* 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))

series441.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* y (- (log z) t))
142.0ms	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))
189.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms	(log (- 1.0 z))

simplify105.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	919	2004
1	3521	1568
2	5001	1567

prune644.0ms

Filtered

197 candidates to 130 candidates (66.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	198	4	202

Merged error: 0.0b

Counts

202 → 4

regimes208.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	16
1	37	16
2	37	16

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	41085×	body	80	nan
811.0ms	12535×	body	80	valid
124.0ms	354×	body	640	valid
83.0ms	380×	body	320	valid
52.0ms	66×	body	1280	valid
40.0ms	286×	body	160	valid