Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	64×	body	640	valid
3.0ms	134×	body	80	valid
3.0ms	41×	body	320	valid
1.0ms	17×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	15	5

prune1.0ms

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: 14.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
3.2b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

662×	`*-un-lft-identity`
589×	`times-frac`
496×	`add-sqr-sqrt`
378×	`prod-diff`
368×	`add-cube-cbrt`
86×	`associate-/r/`
79×	`distribute-lft-out--`
76×	`distribute-lft-out`
62×	`difference-of-squares`
44×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 504

Calls

3 calls:

6.0ms	(/ 1.0 (- x 1.0))
6.0ms	(/ 1.0 (+ x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series235.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
182.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify183.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1200	13350
1	3593	9620
2	5001	9568

prune789.0ms

Filtered

513 candidates to 209 candidates (40.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	511	2	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	512	2	514

Merged error: 0.4b

Counts

514 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) (* 1.0 1.0))
0.0b	(/ (* 1.0 (- (- x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
2.4b	(- (- x 1.0) (+ x 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
30×	`prod-diff`
21×	`add-cube-cbrt`
17×	`add-log-exp`
11×	`associate--l+` `distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `flip3--` `frac-sub` `add-cbrt-cube` `flip--`
7×	`diff-log` `distribute-lft-out`
6×	`fma-neg` `associate-*r/` `associate-/l/`
4×	`flip3-+` `times-frac` `associate-/r*` `flip-+`
3×	`pow1` `expm1-log1p-u` `sub-neg` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `sum-log` `associate-/r/`
1×	`associate--l-` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `associate--r+`

Counts

3 → 114

Calls

3 calls:

4.0ms	(- (* x x) (* 1.0 1.0))
25.0ms	(/ (* 1.0 (- (- x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
13.0ms	(- (- x 1.0) (+ x 1.0))

series104.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(- (* x x) (* 1.0 1.0))
51.0ms	(/ (* 1.0 (- (- x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
7.0ms	(- (- x 1.0) (+ x 1.0))

simplify114.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	593	1128
1	3665	844
2	5001	841

prune186.0ms

Filtered

123 candidates to 82 candidates (66.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	123	2	125

Merged error: 0.4b

Counts

125 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
0.1b	(/ 1 (pow x 4))
0.2b	(/ (- 2.0) (pow x 6))
0.4b	(/ 1 (pow x 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
83×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
57×	`unpow-prod-down`
27×	`add-exp-log`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
22×	`associate-/r*`
19×	`sqr-pow`
16×	`associate-/l*`
15×	`div-exp`
10×	`add-cbrt-cube`
8×	`neg-mul-1`
7×	`pow-to-exp` `pow-exp`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-flip` `inv-pow`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `fma-udef`

Counts

4 → 229

Calls

4 calls:

1.0ms	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
5.0ms	(/ 1 (pow x 4))
7.0ms	(/ (- 2.0) (pow x 6))
6.0ms	(/ 1 (pow x 2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
29.0ms	(/ 1 (pow x 4))
48.0ms	(/ (- 2.0) (pow x 6))
20.0ms	(/ 1 (pow x 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	584	1345
1	2346	1132
2	5001	1048

prune397.0ms

Filtered

241 candidates to 121 candidates (50.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	240	3	243

Merged error: 0b

Counts

243 → 3

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
0.1b	(/ 1 (pow x 4))
0.2b	(/ (- 2.0) (pow x 6))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
65×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
45×	`unpow-prod-down`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
17×	`add-exp-log`
15×	`sqr-pow`
14×	`associate-/r*`
13×	`associate-/l*`
9×	`div-exp`
8×	`neg-mul-1`
7×	`add-cbrt-cube`
4×	`pow-to-exp` `pow-exp`
3×	`pow1` `expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `fma-udef` `inv-pow`

Counts

3 → 170

Calls

3 calls:

1.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
5.0ms	(/ 1 (pow x 4))
7.0ms	(/ (- 2.0) (pow x 6))

series186.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
27.0ms	(/ 1 (pow x 4))
51.0ms	(/ (- 2.0) (pow x 6))

simplify58.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	472	1086
1	1887	982
2	5002	931

prune339.0ms

Filtered

179 candidates to 106 candidates (59.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	179	3	182

Merged error: 0b

Counts

182 → 3

regimes25.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 13.9b

bsearch75.0ms

Steps

Iters	Range		Point
9	0.06406876111163662	2027774.326345067	1434.7656270328541
8	-2.277385665595032e+17	-464914908895680.06	-2101387514886478.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	18
1	41	18

end0.0ms

sample465.0ms

Algorithm

intervals

Results

160.0ms	1895×	body	640	valid
102.0ms	4241×	body	80	valid
78.0ms	1263×	body	320	valid
29.0ms	601×	body	160	valid