Details

sample128.0ms

Algorithm

intervals

Results

54.0ms	802×	body	80	nan
13.0ms	183×	body	80	valid
10.0ms	27×	body	640	valid
6.0ms	25×	body	320	valid
5.0ms	7×	body	1280	valid
2.0ms	15×	body	160	valid

simplify71.0ms

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

prune7.0ms

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: 7.1b

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))
6.7b	(log (- 1.0 y))

rewrite38.0ms

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:

14.0ms	(+ (* (- 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))

series278.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
43.0ms	(* (- z 1.0) (log (- 1.0 y)))
62.0ms	(* (- x 1.0) (log y))
44.0ms	(log (- 1.0 y))

simplify74.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (62.0ms)

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

prune541.0ms

Filtered

130 candidates to 100 candidates (76.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	122	8	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Merged error: 0.1b

Counts

131 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
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))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
80×	`times-frac`
78×	`add-cube-cbrt` `associate-r`
56×	`unpow-prod-down`
48×	`prod-diff`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`pow1` `log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`frac-add`
14×	`log-pow`
13×	`associate-l` `add-cbrt-cube`
12×	`frac-times` `prod-exp` `associate--l+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 280

Calls

4 calls:

20.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(* (- 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)))))))
10.0ms	(* (- x 1.0) (log y))

series331.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
65.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
151.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
61.0ms	(* (- x 1.0) (log y))

simplify84.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1523	4441
1	5002	3593

prune925.0ms

Filtered

292 candidates to 186 candidates (63.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	291	9	300

Merged error: 0.1b

Counts

300 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`log-prod` `prod-diff`
23×	`distribute-rgt-in` `distribute-lft-in`
19×	`pow1`
13×	`log-pow`
12×	`associate-r`
10×	`associate-l`
9×	`add-exp-log` `sqrt-prod`
8×	`add-cbrt-cube`
7×	`flip3--` `flip--`
6×	`associate--l+`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`difference-of-squares`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-log-exp` `fma-udef`

Counts

4 → 135

Calls

4 calls:

2.0ms	(log (sqrt y))
14.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma (log (sqrt y)) (- x 1.0) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
8.0ms	(* (- x 1.0) (log (sqrt y)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(log (sqrt y))
70.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
136.0ms	(fma (log (sqrt y)) (- x 1.0) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
65.0ms	(* (- x 1.0) (log (sqrt y)))

simplify86.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	630	2396
1	2758	1671
2	5001	1651

prune502.0ms

Filtered

147 candidates to 86 candidates (58.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	147	9	156

Merged error: 0.0b

Counts

156 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

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

series1.0s

Counts

4 → 12

Calls

4 calls:

312.0ms	(* (cbrt (log (sqrt y))) (cbrt (log (sqrt y))))
232.0ms	(cbrt (log (sqrt y)))
238.0ms	(cbrt (log (sqrt y)))
238.0ms	(cbrt (log (sqrt y)))

simplify60.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	445	1134
1	1825	1014
2	5001	950

prune495.0ms

Filtered

113 candidates to 75 candidates (66.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Merged error: 0.0b

Counts

122 → 9

regimes279.0ms

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

sample3.5s

Algorithm

intervals

Results

1.5s	23982×	body	80	nan
407.0ms	5822×	body	80	valid
297.0ms	810×	body	640	valid
174.0ms	255×	body	1280	valid
169.0ms	734×	body	320	valid
62.0ms	425×	body	160	valid