Details

sample218.0ms

Algorithm

intervals

Results

102.0ms	1371×	body	80	nan
34.0ms	411×	body	80	valid
3.0ms	7×	body	640	valid
3.0ms	3×	body	1280	valid
2.0ms	8×	body	320	valid
2.0ms	14×	body	160	valid

simplify42.0ms

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: 1.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
7.2b	(log (- 1.0 z))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 203

Calls

4 calls:

5.0ms	(- (log z) t)
8.0ms	(* y (- (log z) t))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

series357.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (log z) t)
71.0ms	(* y (- (log z) t))
182.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(log (- 1.0 z))

simplify117.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	856	1981
1	3296	1486
2	5002	1485

prune745.0ms

Filtered

215 candidates to 131 candidates (60.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	214	2	216

Merged error: 0.0b

Counts

216 → 2

localize22.0ms

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	(* 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)))

rewrite108.0ms

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	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
22.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
8.0ms	(* y (- (log z) t))
33.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series640.0ms

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)))))
104.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
73.0ms	(* y (- (log z) t))
237.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify153.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 2 (101.0ms)

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

prune950.0ms

Filtered

318 candidates to 161 candidates (50.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	315	3	318
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	315	5	320

Merged error: 0.0b

Counts

320 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

216×	`prod-diff`
182×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
148×	`associate-+r+`
142×	`distribute-rgt-in` `distribute-lft-in`
140×	`add-cube-cbrt`
104×	`associate--l+`
68×	`associate-+l+`
58×	`pow1`
50×	`log-pow`
36×	`log-prod`
28×	`distribute-lft-out--`
20×	`associate-*r/`
16×	`sub-neg`
14×	`difference-of-squares`
12×	`associate-r`
10×	`flip3--` `flip--`
8×	`add-exp-log` `frac-add` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 370

Calls

4 calls:

9.0ms	(* y (- (log z) t))
8.0ms	(* y (- (log z) t))
36.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
30.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series648.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* y (- (log z) t))
76.0ms	(* 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)))
254.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify141.0ms

Algorithm

egg-herbie

Counts

382 → 382

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	899	6250
1	3403	4818
2	5001	4806

prune1.9s

Filtered

382 candidates to 222 candidates (58.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	382	0	382
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	382	5	387

Merged error: 0.0b

Counts

387 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))))
0.0b	(- (log z) t)
0.1b	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
7.2b	(log (- 1.0 z))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`pow1` `prod-diff`
8×	`log-prod`
6×	`add-exp-log` `log-pow` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `fma-neg` `associate-r` `log1p-expm1-u`
3×	`associate-l` `associate--l+` `distribute-lft-out--`
2×	`log-div` `flip3--` `flip--` `fma-udef` `difference-of-squares`
1×	`sub-neg` `diff-log` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* x (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))))
5.0ms	(- (log z) t)
1.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series465.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* x (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))))
64.0ms	(- (log z) t)
195.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
46.0ms	(log (- 1.0 z))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	457	761
1	1408	594
2	5002	587

prune292.0ms

Filtered

97 candidates to 71 candidates (73.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	97	5	102

Merged error: 0.0b

Counts

102 → 5

regimes244.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.0s	41072×	body	80	nan
1.0s	12544×	body	80	valid
159.0ms	360×	body	640	valid
113.0ms	407×	body	320	valid
61.0ms	76×	body	1280	valid
44.0ms	257×	body	160	valid