Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	58×	body	640	valid
3.0ms	146×	body	80	valid
2.0ms	34×	body	320	valid
1.0ms	18×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
2.9b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite91.0ms

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:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
36.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
172.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify168.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 2 (71.0ms)

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

prune665.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(pow (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) 3)
0.0b	(cbrt (pow (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) 3))
2.9b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

835×	`*-un-lft-identity`
686×	`times-frac`
565×	`add-sqr-sqrt`
397×	`add-cube-cbrt`
378×	`prod-diff`
159×	`distribute-lft-out--`
100×	`distribute-lft-out`
92×	`associate-/r/`
74×	`difference-of-squares`
51×	`div-inv`
50×	`cbrt-prod`
44×	`unpow-prod-down` `cube-prod`
28×	`flip-+`
26×	`flip--`
23×	`flip3-+`
21×	`flip3--`
18×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `cbrt-div` `frac-sub` `associate-/l*`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 595

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(pow (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) 3)
28.0ms	(cbrt (pow (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) 3))
36.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series802.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ x 1.0))
235.0ms	(pow (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) 3)
362.0ms	(cbrt (pow (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) 3))
178.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify142.0ms

Algorithm

egg-herbie

Counts

607 → 607

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1442	14472
1	5001	10713

prune861.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

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	(/ (- 2.0) (pow x 6))
0.1b	(/ 1 (pow x 4))
0.7b	(/ 1 (pow x 2))

rewrite24.0ms

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))))
6.0ms	(/ (- 2.0) (pow x 6))
5.0ms	(/ 1 (pow x 4))
5.0ms	(/ 1 (pow x 2))

series186.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
48.0ms	(/ (- 2.0) (pow x 6))
33.0ms	(/ 1 (pow x 4))
17.0ms	(/ 1 (pow x 2))

simplify71.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	584	1345
1	2344	1132
2	5002	1058

prune457.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

374×	`times-frac`
318×	`add-sqr-sqrt`
310×	`*-un-lft-identity`
308×	`add-cube-cbrt`
222×	`prod-diff`
166×	`unpow-prod-down`
108×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
74×	`fma-neg`
56×	`sqr-pow`
36×	`neg-mul-1`
18×	`add-exp-log`
14×	`associate-/r*`
13×	`associate-/l*`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `difference-of-squares`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 487

Calls

4 calls:

32.0ms	(- (/ (- 2.0) (pow x 6)) (fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4)))))
1.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
6.0ms	(/ (- 2.0) (pow x 6))
5.0ms	(/ 1 (pow x 4))

series264.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (/ (- 2.0) (pow x 6)) (fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4)))))
108.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
55.0ms	(/ (- 2.0) (pow x 6))
28.0ms	(/ 1 (pow x 4))

simplify168.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	1046	12714
1	3327	7433
2	5002	7316

prune949.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes51.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch95.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	261.4892299688821
8	-1816.595590764893	-1.0806682141483241	-297.81446535009724

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	27
1	42	27

end0.0ms

sample447.0ms

Algorithm

intervals

Results

158.0ms	1913×	body	640	valid
91.0ms	4180×	body	80	valid
79.0ms	1266×	body	320	valid
26.0ms	641×	body	160	valid