Details

sample102.0ms

Algorithm

intervals

Results

39.0ms	760×	body	80	nan
10.0ms	186×	body	80	valid
9.0ms	29×	body	640	valid
5.0ms	7×	body	1280	valid
3.0ms	18×	body	320	valid
2.0ms	16×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 5.8b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(* (- x 1.0) (log y))
4.0b	(log (- 1.0 y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
9.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
4.0ms	(log (- 1.0 y))

series271.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
47.0ms	(* (- z 1.0) (log (- 1.0 y)))
55.0ms	(* (- x 1.0) (log y))
46.0ms	(log (- 1.0 y))

simplify72.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	682	971
1	2728	901
2	5001	884

prune385.0ms

Filtered

130 candidates to 100 candidates (76.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	123	7	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	7	131

Merged error: 0.0b

Counts

131 → 7

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`prod-diff`
43×	`add-cube-cbrt`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
27×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/`
21×	`pow1`
16×	`frac-add`
14×	`log-pow`
12×	`frac-times` `associate--l+`
10×	`associate-r` `associate-l`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-*r/`
5×	`add-log-exp`
4×	`sub-neg` `distribute-lft-out--`
3×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 168

Calls

3 calls:

14.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
15.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
7.0ms	(* (- x 1.0) (log y))

series418.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
152.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
202.0ms	(* (- x 1.0) (log y))

simplify66.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1020	3793
1	5001	2864

prune602.0ms

Filtered

177 candidates to 115 candidates (65.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	177	7	184

Merged error: 0.0b

Counts

184 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log y))
7.2b	(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
9.5b	(log (- (sqrt 1.0) (sqrt y)))
9.6b	(log (+ (sqrt 1.0) (sqrt y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

7.0ms	(* (- x 1.0) (log y))
14.0ms	(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
10.0ms	(log (- (sqrt 1.0) (sqrt y)))
6.0ms	(log (+ (sqrt 1.0) (sqrt y)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- x 1.0) (log y))
295.0ms	(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
143.0ms	(log (- (sqrt 1.0) (sqrt y)))
142.0ms	(log (+ (sqrt 1.0) (sqrt y)))

simplify48.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	454	1089
1	1487	993
2	5001	943

prune385.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	122	7	129

Merged error: 0.0b

Counts

129 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)
4.0b	(log (- 1.0 y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

41×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`cbrt-prod` `associate-+l+`
21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`associate-+r+`
8×	`associate-*l/`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `flip3--` `flip--`
4×	`expm1-log1p-u` `frac-add` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `pow1/3`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `sum-log` `log-pow` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 99

Calls

4 calls:

14.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
4.0ms	(log (- 1.0 y))

series545.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
170.0ms	(cbrt y)
167.0ms	(cbrt y)
44.0ms	(log (- 1.0 y))

simplify75.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	624	855
1	2426	720
2	5003	688

prune452.0ms

Filtered

111 candidates to 102 candidates (91.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	112	6	118

Merged error: 0.0b

Counts

118 → 6

regimes213.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	28	15

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	24311×	body	80	nan
340.0ms	5842×	body	80	valid
244.0ms	768×	body	640	valid
162.0ms	257×	body	1280	valid
143.0ms	738×	body	320	valid
52.0ms	423×	body	160	valid