Details

sample206.0ms

Algorithm

intervals

Results

87.0ms	1482×	body	80	nan
25.0ms	386×	body	80	valid
6.0ms	7×	body	1280	valid
5.0ms	15×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.8b	(log (- 1.0 z))

rewrite72.0ms

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:

21.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
15.0ms	(* y (- (log z) t))
22.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series440.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
70.0ms	(* y (- (log z) t))
187.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify95.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (77.0ms)

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

prune637.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* 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)))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

120×	`prod-diff`
106×	`*-un-lft-identity`
100×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
74×	`associate-+r+`
71×	`distribute-rgt-in` `distribute-lft-in`
55×	`associate--l+`
36×	`pow1`
34×	`associate-+l+`
30×	`log-pow`
21×	`log-prod`
16×	`distribute-lft-out--`
10×	`associate-*r/` `add-log-exp`
9×	`sub-neg`
8×	`difference-of-squares`
6×	`add-exp-log` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
4×	`expm1-log1p-u` `fma-neg` `frac-add` `log1p-expm1-u`
3×	`exp-prod` `associate-l`
2×	`sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

6.0ms	(- (log z) t)
111.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
16.0ms	(* y (- (log z) t))
181.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (log z) t)
167.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
73.0ms	(* y (- (log z) t))
236.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify113.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	996	3661
1	3785	2813
2	5001	2807

prune969.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
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))))
0.1b	(* 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)))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

120×	`prod-diff`
107×	`*-un-lft-identity`
101×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
74×	`associate-+r+`
71×	`distribute-rgt-in` `distribute-lft-in`
55×	`associate--l+`
37×	`pow1`
34×	`associate-+l+`
30×	`log-pow`
21×	`log-prod`
16×	`distribute-lft-out--`
10×	`associate-*r/`
9×	`sub-neg`
8×	`difference-of-squares`
7×	`add-exp-log` `add-log-exp`
6×	`flip3--` `associate-r` `add-cbrt-cube` `flip--`
4×	`expm1-log1p-u` `fma-neg` `frac-add` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `associate-l`
2×	`pow-exp`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `e-exp-1` `pow-pow` `fma-def` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr` `sqr-pow`

Counts

4 → 242

Calls

4 calls:

5.0ms	(- (log z) t)
96.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
18.0ms	(* y (- (log z) t))
180.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (log z) t)
174.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
71.0ms	(* y (- (log z) t))
242.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify145.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1051	3813
1	4177	2970
2	5001	2958

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 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)))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite579.0ms

Algorithm

rewrite-expression-head

Rules

276×	`prod-diff`
229×	`*-un-lft-identity`
222×	`associate-+r+`
212×	`add-sqr-sqrt`
179×	`distribute-rgt-in` `distribute-lft-in`
172×	`add-cube-cbrt`
144×	`associate--l+`
102×	`associate-+l+`
67×	`pow1`
61×	`log-pow`
42×	`log-prod`
38×	`distribute-lft-out--`
26×	`associate-*r/`
20×	`sub-neg`
19×	`difference-of-squares`
13×	`flip3--` `flip--`
12×	`frac-add`
10×	`add-log-exp`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`+-commutative` `fma-def` `flip3-+` `associate-l` `sum-log` `flip-+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 437

Calls

4 calls:

15.0ms	(* y (- (log z) t))
175.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
173.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
176.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* y (- (log z) t))
240.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
237.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
229.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify154.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	899	8279
1	3403	6503
2	5001	6485

prune2.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes196.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

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

sample5.4s

Algorithm

intervals

Results

2.3s	40966×	body	80	nan
824.0ms	12566×	body	80	valid
149.0ms	406×	body	640	valid
94.0ms	415×	body	320	valid
49.0ms	65×	body	1280	valid
41.0ms	295×	body	160	valid