Details

sample193.0ms

Algorithm

intervals

Results

84.0ms	1390×	body	80	nan
26.0ms	400×	body	80	valid
5.0ms	12×	body	640	valid
3.0ms	14×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	1×	body	1280	valid

simplify46.0ms

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: 2.1b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.0b	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.1b	(* y (- (log z) t))
6.3b	(log (- 1.0 z))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

96×	`prod-diff`
95×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
89×	`associate-r`
75×	`add-cube-cbrt`
74×	`exp-sum`
72×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
37×	`pow1` `log-prod`
34×	`associate-+l+`
32×	`associate--l+`
27×	`log-pow`
12×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`associate-l` `distribute-lft-out--`
8×	`sub-neg`
7×	`difference-of-squares`
4×	`expm1-log1p-u` `associate-*r/` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
2×	`log-div`
1×	`+-commutative` `rem-log-exp`

Counts

4 → 235

Calls

4 calls:

11.0ms	(* a (- (log (- 1.0 z)) b))
55.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
9.0ms	(* y (- (log z) t))
4.0ms	(log (- 1.0 z))

series363.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* a (- (log (- 1.0 z)) b))
163.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
77.0ms	(* y (- (log z) t))
51.0ms	(log (- 1.0 z))

simplify112.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1085	2465
1	3767	1823
2	5001	1823

prune676.0ms

Filtered

247 candidates to 131 candidates (53.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	245	3	248

Merged error: 0.0b

Counts

248 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

612×	`*-un-lft-identity`
340×	`prod-diff`
214×	`associate-r`
203×	`add-sqr-sqrt`
190×	`exp-sum`
188×	`distribute-rgt-in` `distribute-lft-in`
177×	`associate-l`
168×	`distribute-lft-out`
167×	`add-cube-cbrt`
159×	`associate--l+`
154×	`associate-+r+`
145×	`distribute-lft-out--`
121×	`pow1`
111×	`log-pow`
34×	`associate-+l+`
27×	`log-prod`
15×	`difference-of-squares`
13×	`sub-neg`
11×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`add-log-exp`
4×	`expm1-log1p-u` `fma-neg` `associate-*r/` `prod-exp` `log1p-expm1-u`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
2×	`diff-log`
1×	`+-commutative`

Counts

4 → 495

Calls

4 calls:

10.0ms	(- (log z) t)
165.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
94.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
8.0ms	(* y (- (log z) t))

series473.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (log z) t)
226.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
107.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
80.0ms	(* y (- (log z) t))

simplify175.0ms

Algorithm

egg-herbie

Counts

507 → 507

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1306	9314
1	4375	6799
2	5001	6575

prune1.1s

Filtered

507 candidates to 157 candidates (31.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	505	2	507
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	508	2	510

Merged error: 0.0b

Counts

510 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (log z))
0.4b	(cbrt (log z))
0.4b	(cbrt (log z))
0.5b	(* (cbrt (log z)) (cbrt (log z)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`pow1`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`pow1/3` `swap-sqr` `log-pow`
8×	`add-cbrt-cube`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 92

Calls

4 calls:

1.0ms	(cbrt (log z))
1.0ms	(cbrt (log z))
1.0ms	(cbrt (log z))
7.0ms	(* (cbrt (log z)) (cbrt (log z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt (log z))
266.0ms	(cbrt (log z))
276.0ms	(cbrt (log z))
284.0ms	(* (cbrt (log z)) (cbrt (log z)))

simplify97.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	134	554
1	479	462
2	3486	394
3	5001	387

prune520.0ms

Filtered

104 candidates to 64 candidates (61.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	104	2	106

Merged error: 0.0b

Counts

106 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite445.0ms

Algorithm

rewrite-expression-head

Rules

604×	`*-un-lft-identity`
404×	`sqrt-prod`
398×	`associate-r`
380×	`exp-sum`
376×	`prod-diff`
308×	`associate-+r+`
236×	`add-sqr-sqrt`
222×	`distribute-rgt-in` `distribute-lft-in`
194×	`add-cube-cbrt`
172×	`associate-l`
168×	`associate--l+`
160×	`distribute-lft-out`
128×	`pow1`
124×	`distribute-lft-out--`
114×	`log-pow`
68×	`associate-+l+`
36×	`log-prod`
16×	`sub-neg`
14×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `associate-r/` `pow-prod-down` `-commutative` `log1p-expm1-u` `add-log-exp`
2×	`+-commutative` `flip3--` `pow1/2` `prod-exp` `flip--` `cbrt-unprod`

Counts

4 → 550

Calls

4 calls:

9.0ms	(* y (- (log z) t))
8.0ms	(* y (- (log z) t))
178.0ms	(sqrt (* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
177.0ms	(sqrt (* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

71.0ms	(* y (- (log z) t))
71.0ms	(* y (- (log z) t))
464.0ms	(sqrt (* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
668.0ms	(sqrt (* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))

simplify223.0ms

Algorithm

egg-herbie

Counts

562 → 562

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1496	15480
1	4154	12606
2	5001	12598

prune1.1s

Filtered

562 candidates to 134 candidates (23.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	562	0	562
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	562	2	564

Merged error: 0.0b

Counts

564 → 2

regimes157.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	28
1	56	28
2	56	28

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	41475×	body	80	nan
824.0ms	12590×	body	80	valid
135.0ms	371×	body	640	valid
90.0ms	405×	body	320	valid
53.0ms	67×	body	1280	valid
38.0ms	283×	body	160	valid