Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	65×	body	640	valid
3.0ms	129×	body	80	valid
3.0ms	45×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
3.1b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite121.0ms

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))
65.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series224.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1.0 (+ x 1.0))
27.0ms	(/ 1.0 (- x 1.0))
173.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify173.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 2 (72.0ms)

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

prune685.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
0.0b	(/ 1.0 (- x 1.0))
0.2b	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
30.7b	(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ 1.0 (- x 1.0))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
42×	`times-frac`
36×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`unpow-prod-down` `cube-prod`
14×	`associate-/r*`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `sum-cubes` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`associate-+r+`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3--` `fma-def` `diff-log` `prod-diff` `flip--` `fma-udef`

Counts

4 → 123

Calls

4 calls:

7.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
5.0ms	(/ 1.0 (- x 1.0))
27.0ms	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
0.0ms	(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ 1.0 (- x 1.0))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
28.0ms	(/ 1.0 (- x 1.0))
68.0ms	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
223.0ms	(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ 1.0 (- x 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	518	949
1	2230	854
2	5001	836

prune357.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

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))
0.1b	(/ (- 2.0) (pow x 6))
0.2b	(/ 1 (pow x 2))

rewrite23.0ms

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:

0.0ms	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
4.0ms	(/ 1 (pow x 4))
6.0ms	(/ (- 2.0) (pow x 6))
4.0ms	(/ 1 (pow x 2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
26.0ms	(/ 1 (pow x 4))
51.0ms	(/ (- 2.0) (pow x 6))
16.0ms	(/ 1 (pow x 2))

simplify69.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (48.0ms)

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

prune461.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
96×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
81×	`add-cube-cbrt`
56×	`unpow-prod-down`
38×	`add-exp-log`
25×	`associate-r`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
20×	`sqr-pow`
15×	`div-exp`
14×	`associate-/r*`
13×	`add-cbrt-cube` `associate-/l*`
10×	`prod-exp`
8×	`neg-mul-1`
7×	`pow-to-exp` `pow-exp` `unswap-sqr`
6×	`pow1` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-l` `div-inv`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`neg-sub0` `pow-flip` `div-sub` `associate-r/` `distribute-frac-neg` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 230

Calls

4 calls:

14.0ms	(* 2.0 (/ 1 (pow x 4)))
0.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
4.0ms	(/ 1 (pow x 4))
6.0ms	(/ (- 2.0) (pow x 6))

series221.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 2.0 (/ 1 (pow x 4)))
109.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
26.0ms	(/ 1 (pow x 4))
51.0ms	(/ (- 2.0) (pow x 6))

simplify70.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	631	1390
1	2882	1207
2	5001	1152

prune542.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.7b

bsearch106.0ms

Steps

Iters	Range		Point
9	0.004380743253548005	488.5072251079851	210.68103720548342
10	-146662999352.95746	-3.9934486818618	-235.01839027929324

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	23
1	50	23

end0.0ms

sample442.0ms

Algorithm

intervals

Results

156.0ms	1928×	body	640	valid
91.0ms	4153×	body	80	valid
81.0ms	1279×	body	320	valid
25.0ms	640×	body	160	valid