Details

sample121.0ms

Algorithm

intervals

Results

45.0ms	822×	body	80	nan
14.0ms	189×	body	80	valid
11.0ms	14×	body	1280	valid
7.0ms	21×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify67.0ms

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 9.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.2b	(log (- 1.0 y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `add-cbrt-cube`
4×	`associate-r` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3--` `associate-*l/` `log-pow` `flip--`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
1.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series306.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* (- z 1.0) (log (- 1.0 y)))
219.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
44.0ms	(log (- 1.0 y))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	364	521
1	1204	461
2	5001	449

prune227.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 0.1b

Counts

73 → 6

localize24.0ms

Local error

Found 3 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))))))

0.1b

(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
60×	`*-un-lft-identity`
56×	`unpow-prod-down`
55×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`prod-diff` `unpow2` `sqr-pow`
18×	`unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
11×	`prod-exp`
10×	`add-cbrt-cube`
9×	`div-exp`
8×	`associate-l`
7×	`log-pow`
6×	`pow-to-exp` `log-prod` `flip3--` `pow-exp` `associate--l+` `flip--`
4×	`frac-times`
3×	`expm1-log1p-u` `associate-*r/` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`sub-neg` `pow-prod-down` `associate-l/` `-commutative` `difference-of-squares`
1×	`cbrt-undiv` `fma-udef` `div-inv`

Counts

3 → 189

Calls

3 calls:

20.0ms

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

14.0ms

(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

1.0ms

(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series334.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms

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

63.0ms

(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

221.0ms

(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify129.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	933	2642
1	4282	1844
2	5001	1841

prune634.0ms

Filtered

198 candidates to 114 candidates (57.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	193	5	198
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	197	7	204

Merged error: 0.1b

Counts

204 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
99×	`add-cube-cbrt`
87×	`prod-diff`
80×	`times-frac`
79×	`associate-r`
56×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
46×	`associate--l+`
39×	`associate-+r+`
31×	`add-exp-log`
24×	`pow1` `unpow2` `sqr-pow`
22×	`associate-+l+`
19×	`unswap-sqr`
14×	`log-pow`
13×	`add-cbrt-cube`
12×	`log-prod` `associate-l` `prod-exp`
11×	`flip3--` `flip--`
9×	`sub-neg` `associate-*r/` `div-exp` `add-log-exp`
6×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `frac-times` `frac-add` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`associate-*l/` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `fma-def` `flip3-+` `diff-log` `flip-+` `div-inv`

Counts

4 → 307

Calls

4 calls:

23.0ms	(+ (* (log y) (- x 1.0)) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
19.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
15.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
8.0ms	(* (log y) (- x 1.0))

series434.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(+ (* (log y) (- x 1.0)) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
62.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
91.0ms	(* (log y) (- x 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

319 → 319

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1492	4543
1	5001	3426

prune1.1s

Filtered

319 candidates to 190 candidates (59.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	310	9	319
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	316	10	326

Merged error: 0.0b

Counts

326 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
80×	`times-frac`
77×	`associate-r`
63×	`*-un-lft-identity`
58×	`add-cube-cbrt`
56×	`unpow-prod-down`
31×	`add-exp-log`
24×	`prod-diff` `unpow2` `sqr-pow`
19×	`unswap-sqr`
18×	`pow1`
17×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-cbrt-cube`
12×	`associate-l` `prod-exp`
9×	`div-exp`
8×	`log-pow`
6×	`pow-to-exp` `log-prod` `flip3--` `pow-exp` `associate--l+` `flip--`
4×	`expm1-log1p-u` `frac-times` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `-commutative` `distribute-lft-out--`
2×	`sub-neg` `associate-*l/` `difference-of-squares`
1×	`cbrt-undiv` `fma-udef` `div-inv`

Counts

4 → 210

Calls

4 calls:

1.0ms	(fma (- 1.0) (log y) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
23.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
14.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* (log y) x)

series324.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(fma (- 1.0) (log y) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
52.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
64.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
64.0ms	(* (log y) x)

simplify122.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1004	2727
1	4567	1919
2	5001	1919

prune768.0ms

Filtered

222 candidates to 132 candidates (59.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	217	5	222
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	223	9	232

Merged error: 0.0b

Counts

232 → 9

regimes377.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	30
1	35	30

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	23996×	body	80	nan
328.0ms	5894×	body	80	valid
240.0ms	770×	body	640	valid
160.0ms	251×	body	1280	valid
130.0ms	693×	body	320	valid
49.0ms	424×	body	160	valid