Details

sample96.0ms

Algorithm

intervals

Results

37.0ms	753×	body	80	nan
10.0ms	191×	body	80	valid
7.0ms	25×	body	640	valid
5.0ms	9×	body	1280	valid
2.0ms	14×	body	320	valid
2.0ms	17×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 8.0b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.0b	(+ (* x (log y)) (* z (log (- 1.0 y))))
0.2b	(* x (log y))
7.4b	(log (- 1.0 y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
37×	`log-prod`
36×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
16×	`distribute-rgt-in` `distribute-lft-in`
13×	`fma-def` `associate-l`
12×	`pow1` `associate-r`
10×	`associate-+r+`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`associate-+l+` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `distribute-lft-out`
3×	`*-commutative` `unswap-sqr`
2×	`log-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3--` `flip3-+` `rem-log-exp` `sum-log` `flip--` `flip-+`

Counts

4 → 122

Calls

4 calls:

6.0ms	(* z (log (- 1.0 y)))
18.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
4.0ms	(* x (log y))
4.0ms	(log (- 1.0 y))

series227.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* z (log (- 1.0 y)))
79.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
41.0ms	(* x (log y))
43.0ms	(log (- 1.0 y))

simplify58.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	488	703
1	1743	645
2	5001	620

prune283.0ms

Filtered

134 candidates to 96 candidates (71.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	126	8	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 0.0b

Counts

136 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

369×	`*-un-lft-identity`
189×	`prod-diff`
137×	`associate-l`
132×	`associate-+r+`
128×	`distribute-lft-out`
110×	`add-sqr-sqrt`
108×	`distribute-rgt-in` `distribute-lft-in`
100×	`add-cube-cbrt`
92×	`associate--l+`
57×	`pow1`
49×	`log-pow`
36×	`log-prod`
22×	`associate-r`
15×	`distribute-lft-out--`
13×	`fma-def`
12×	`associate-+l+`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`sub-neg` `fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative` `unswap-sqr`
2×	`+-commutative` `flip3--` `diff-log` `associate-*r/` `pow-prod-down` `prod-exp` `sum-log` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`flip3-+` `flip-+`

Counts

4 → 351

Calls

4 calls:

101.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
89.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
72.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* x (log y))

series461.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
131.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
105.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
38.0ms	(* x (log y))

simplify125.0ms

Algorithm

egg-herbie

Counts

363 → 363

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	691	6337
1	2458	4352
2	5003	4295

prune671.0ms

Filtered

363 candidates to 151 candidates (41.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	354	9	363
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	362	9	371

Merged error: 0.0b

Counts

371 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (log (sqrt y))) (fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.2b	(fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.2b	(* x (log (sqrt y)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
56×	`prod-diff`
51×	`add-sqr-sqrt`
50×	`associate-l`
45×	`distribute-rgt-in` `distribute-lft-in`
43×	`add-cube-cbrt`
42×	`distribute-lft-out`
31×	`pow1`
30×	`log-prod`
26×	`associate-r`
25×	`log-pow`
15×	`fma-def`
12×	`associate-+l+` `sqrt-prod`
10×	`distribute-lft-out--`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate--l+` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative` `unswap-sqr`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`+-commutative` `associate-+r+` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `difference-of-squares`

Counts

4 → 187

Calls

4 calls:

11.0ms	(+ (* x (log (sqrt y))) (fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
72.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
6.0ms	(* x (log (sqrt y)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(+ (* x (log (sqrt y))) (fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
107.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
176.0ms	(fma (log (sqrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
97.0ms	(* x (log (sqrt y)))

simplify91.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	545	3402
1	2094	2401
2	5001	2356

prune491.0ms

Filtered

199 candidates to 98 candidates (49.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	201	7	208

Merged error: 0b

Counts

208 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt y)) (cbrt (sqrt y)))
0.7b	(cbrt (sqrt y))
0.7b	(cbrt (sqrt y))
0.7b	(cbrt (sqrt y))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cbrt-prod`
44×	`add-sqr-sqrt`
29×	`sqrt-prod`
22×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `swap-sqr`
9×	`pow1/3` `associate-r` `associate-l` `unswap-sqr`
8×	`add-cbrt-cube`
6×	`add-exp-log`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 109

Calls

4 calls:

8.0ms	(* (cbrt (sqrt y)) (cbrt (sqrt y)))
2.0ms	(cbrt (sqrt y))
2.0ms	(cbrt (sqrt y))
2.0ms	(cbrt (sqrt y))

series616.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (cbrt (sqrt y)) (cbrt (sqrt y)))
154.0ms	(cbrt (sqrt y))
153.0ms	(cbrt (sqrt y))
150.0ms	(cbrt (sqrt y))

simplify108.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	161	756
1	598	698
2	3221	615
3	5001	584

prune522.0ms

Filtered

121 candidates to 78 candidates (64.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	121	7	128

Merged error: 0b

Counts

128 → 7

regimes207.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	25
1	33	25

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	24607×	body	80	nan
292.0ms	5511×	body	80	valid
271.0ms	904×	body	640	valid
243.0ms	410×	body	1280	valid
128.0ms	715×	body	320	valid
53.0ms	491×	body	160	valid