Details

sample115.0ms

Algorithm

intervals

Results

46.0ms	764×	body	80	nan
12.0ms	182×	body	80	valid
8.0ms	22×	body	640	valid
6.0ms	10×	body	1280	valid
6.0ms	25×	body	320	valid
2.0ms	18×	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: 10.0b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (log y)) (* z (log (- 1.0 y))))
0.0b	(* z (log (- 1.0 y)))
0.2b	(* x (log y))
5.7b	(log (- 1.0 y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

7.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
6.0ms	(* z (log (- 1.0 y)))
4.0ms	(* x (log y))
4.0ms	(log (- 1.0 y))

series227.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (* x (log y)) (* z (log (- 1.0 y))))
66.0ms	(* z (log (- 1.0 y)))
41.0ms	(* x (log y))
43.0ms	(log (- 1.0 y))

simplify59.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	496	683
1	1771	625
2	5001	600

prune306.0ms

Filtered

118 candidates to 85 candidates (72.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	6	120

Merged error: 0.1b

Counts

120 → 6

localize17.0ms

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))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`prod-diff`
56×	`*-un-lft-identity`
51×	`add-cube-cbrt`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
24×	`log-prod`
22×	`pow1`
14×	`log-pow`
13×	`associate--l+`
11×	`add-log-exp`
10×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-l`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `distribute-lft-out--`
2×	`flip3--` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `flip-+`

Counts

4 → 170

Calls

4 calls:

7.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
10.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* x (log y))

series446.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
122.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
100.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
41.0ms	(* x (log y))

simplify98.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	644	3156
1	2391	2185
2	5003	2156

prune520.0ms

Filtered

182 candidates to 107 candidates (58.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Merged error: 0.1b

Counts

188 → 9

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
77×	`add-sqr-sqrt`
72×	`associate-r`
56×	`unpow-prod-down`
41×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log`
24×	`unpow2` `sqr-pow`
18×	`unswap-sqr`
11×	`prod-exp`
10×	`add-cbrt-cube`
9×	`div-exp`
8×	`pow1`
6×	`pow-to-exp` `log-prod` `associate-l` `pow-exp`
3×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `associate-*r/` `log-pow` `fma-udef` `div-inv`

Counts

3 → 149

Calls

3 calls:

19.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
1.0ms	(fma (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- (* x (log y)) t))
5.0ms	(* x (log y))

series267.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
175.0ms	(fma (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- (* x (log y)) t))
42.0ms	(* x (log y))

simplify78.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	683	943
1	2833	789
2	5002	788

prune514.0ms

Filtered

158 candidates to 102 candidates (64.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	158	9	167

Merged error: 0.1b

Counts

167 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 210

Calls

4 calls:

24.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
4.0ms	(- (fma x (log y) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma x (log y) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
190.0ms	(- (fma x (log y) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
112.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
136.0ms	(fma x (log y) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	910	2946
1	3815	2058
2	5002	2049

prune579.0ms

Filtered

222 candidates to 128 candidates (57.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	223	8	231

Merged error: 0.1b

Counts

231 → 8

regimes171.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	27	11
2	27	11

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	24440×	body	80	nan
376.0ms	5555×	body	80	valid
330.0ms	902×	body	640	valid
278.0ms	411×	body	1280	valid
152.0ms	684×	body	320	valid
69.0ms	479×	body	160	valid