Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	35×	body	1280	valid
7.0ms	178×	body	80	valid
4.0ms	27×	body	640	valid
3.0ms	128×	body	80	nan
2.0ms	12×	body	1280	nan
1.0ms	12×	body	320	valid
1.0ms	11×	body	320	nan
1.0ms	6×	body	640	nan
0.0ms	4×	body	160	valid
0.0ms	3×	body	160	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 19.3b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 227

Calls

4 calls:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(/ (- x y) (- 1.0 y))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify107.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	986	4621
1	3240	3344
2	5001	3134

prune412.0ms

Filtered

239 candidates to 126 candidates (52.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	237	3	240

Merged error: 0.0b

Counts

240 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 248

Calls

4 calls:

15.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
127.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify115.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	1074	4812
1	3721	3718
2	5001	3710

prune556.0ms

Filtered

260 candidates to 157 candidates (60.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	259	4	263

Merged error: 0b

Counts

263 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0))))
0.2b	(fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

1.0ms	(log (fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0))))
1.0ms	(fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0)))

series246.0ms

Counts

2 → 6

Calls

2 calls:

165.0ms	(log (fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0))))
81.0ms	(fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	135	299
1	355	245
2	1721	235
3	5002	224

prune78.0ms

Filtered

30 candidates to 26 candidates (86.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	30	4	34

Merged error: 0b

Counts

34 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
1.5b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
12.1b	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
12.8b	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

1072×	`add-sqr-sqrt`
1012×	`*-un-lft-identity`
828×	`prod-diff`
616×	`times-frac`
615×	`unpow-prod-down` `cube-prod`
498×	`add-cube-cbrt`
289×	`difference-of-squares`
256×	`distribute-lft-out--`
101×	`sqr-pow`
81×	`cube-mult` `unpow3`
48×	`associate-/r/`
39×	`log-prod`
27×	`flip3--` `flip--`
24×	`div-inv`
16×	`associate-+l+`
15×	`pow1`
12×	`fma-neg`
11×	`log-pow`
8×	`log-div` `add-log-exp`
6×	`add-exp-log` `fma-def` `distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate-+r+` `flip3-+` `flip-+`
2×	`difference-cubes` `associate-+r-` `sub-neg` `diff-log` `rem-log-exp` `sum-log` `associate--r-`
1×	`+-commutative` `associate-+l-`

Counts

4 → 982

Calls

4 calls:

25.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
62.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
17.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
79.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

series975.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
175.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
162.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
330.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

simplify331.0ms

Algorithm

egg-herbie

Counts

994 → 994

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1816	33637
1	5001	25708

prune685.0ms

Filtered

994 candidates to 138 candidates (13.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	994	0	994
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	994	4	998

Merged error: 0b

Counts

998 → 4

regimes120.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 18.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	19
1	25	19

end0.0ms

sample1.0s

Algorithm

intervals

Results

221.0ms	5669×	body	80	valid
169.0ms	873×	body	1280	valid
110.0ms	797×	body	640	valid
101.0ms	3793×	body	80	nan
60.0ms	399×	body	1280	nan
46.0ms	411×	body	640	nan
41.0ms	430×	body	320	valid
18.0ms	221×	body	320	nan
15.0ms	231×	body	160	valid
5.0ms	102×	body	160	nan