Details

sample116.0ms

Algorithm

intervals

Results

45.0ms	805×	body	80	nan
12.0ms	187×	body	80	valid
8.0ms	24×	body	640	valid
8.0ms	12×	body	1280	valid
7.0ms	23×	body	320	valid
2.0ms	12×	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

prune7.0ms

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: 9.8b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.1b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
7.1b	(log (- 1.0 y))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

6.0ms	(* z (log (- 1.0 y)))
1.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
5.0ms	(log (- 1.0 y))

series227.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* z (log (- 1.0 y)))
114.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
47.0ms	(log (- 1.0 y))

simplify106.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	332	427
1	1128	376
2	4553	369
3	5001	366

prune184.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Merged error: 0.1b

Counts

69 → 3

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b

(* 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)))))) t)

0.1b

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

51×	`prod-diff`
46×	`associate--l+`
42×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
38×	`add-cube-cbrt`
34×	`distribute-rgt-in` `distribute-lft-in`
18×	`pow1`
13×	`log-pow`
12×	`log-prod`
6×	`associate-r`
5×	`add-exp-log` `sub-neg` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `difference-of-squares` `unswap-sqr`

Counts

3 → 121

Calls

3 calls:

10.0ms

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

12.0ms

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

1.0ms

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

series386.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms

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

120.0ms

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

162.0ms

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

simplify70.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	428	2727
1	1620	1650
2	5001	1591

prune398.0ms

Filtered

130 candidates to 79 candidates (60.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	127	6	133

Merged error: 0.1b

Counts

133 → 6

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

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

series280.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
165.0ms	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify141.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	102	342
1	272	291
2	951	291
3	4792	291
4	5001	291

prune128.0ms

Filtered

26 candidates to 24 candidates (92.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	26	6	32

Merged error: 0.1b

Counts

32 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.1b	(fma (log y) x (- (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
0.2b	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.2b	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

192×	`sqrt-prod`
171×	`prod-diff`
122×	`add-sqr-sqrt` `*-un-lft-identity`
112×	`add-cube-cbrt`
89×	`distribute-rgt-in` `distribute-lft-in`
88×	`associate--l+`
37×	`pow1`
26×	`log-pow`
16×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
6×	`add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `frac-times` `flip3--` `flip3-+` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-lft-out` `distribute-lft-out--`
2×	`associate-l/` `-commutative`
1×	`fma-neg` `diff-log` `fma-udef` `unswap-sqr`

Counts

4 → 266

Calls

4 calls:

32.0ms	(- (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
1.0ms	(fma (log y) x (- (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
10.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
23.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series957.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
179.0ms	(fma (log y) x (- (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
190.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
463.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	948	12403
1	5001	8471

prune888.0ms

Filtered

278 candidates to 141 candidates (50.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	278	6	284

Merged error: 0.1b

Counts

284 → 6

regimes154.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	24046×	body	80	nan
344.0ms	5537×	body	80	valid
300.0ms	880×	body	640	valid
248.0ms	383×	body	1280	valid
159.0ms	756×	body	320	valid
62.0ms	468×	body	160	valid

Details

sample116.0ms

simplify26.0ms

prune7.0ms

localize11.0ms

rewrite13.0ms

series227.0ms

simplify106.0ms

prune184.0ms

localize18.0ms

rewrite29.0ms

series386.0ms

simplify70.0ms

prune398.0ms

localize21.0ms

rewrite2.0ms

series280.0ms

simplify141.0ms

prune128.0ms

localize21.0ms

rewrite83.0ms

series957.0ms

simplify121.0ms

prune888.0ms

regimes154.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.3s

Profiling