Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
8.0ms	251×	body	80	nan

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	7
1	41	6
2	69	6
3	95	6
4	125	6
5	140	6
6	142	6
7	142	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
95×	`add-sqr-sqrt` `*-un-lft-identity`
67×	`add-cube-cbrt`
16×	`associate-/r*`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--` `fma-udef`

Counts

3 → 142

Calls

3 calls:

0.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
25.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
5.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

series155.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
76.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
44.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	627	1691
1	2379	1609
2	5002	1609

prune620.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) (/ 1 6.0))
0.1b	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

652×	`times-frac`
371×	`add-sqr-sqrt` `*-un-lft-identity`
279×	`add-cube-cbrt`
46×	`distribute-lft-out--` `difference-of-squares`
36×	`div-inv`
27×	`add-exp-log`
24×	`associate-/l*`
17×	`div-exp` `add-cbrt-cube`
16×	`associate-/r*`
9×	`cbrt-undiv`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`flip3--` `associate-/r/` `flip--` `fma-udef`

Counts

3 → 356

Calls

3 calls:

0.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
32.0ms	(/ (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) (/ 1 6.0))
17.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series185.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
78.0ms	(/ (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) (/ 1 6.0))
73.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

365 → 365

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1624	5786
1	5001	5326

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
0.0b	(/ (/ 1 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))) (/ 1 6.0))
0.1b	(/ 1 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

3155×	`times-frac`
1525×	`add-sqr-sqrt` `*-un-lft-identity`
1241×	`add-cube-cbrt`
142×	`distribute-lft-out--` `difference-of-squares`
132×	`div-inv`
110×	`associate-/r/`
100×	`add-exp-log`
78×	`div-exp`
74×	`associate-/l*`
47×	`flip3--` `flip--`
39×	`associate-/r*`
32×	`add-cbrt-cube`
19×	`cbrt-undiv`
17×	`rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 1172

Calls

4 calls:

0.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
12.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
63.0ms	(/ (/ 1 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))) (/ 1 6.0))
19.0ms	(/ 1 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
74.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
82.0ms	(/ (/ 1 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))) (/ 1 6.0))
338.0ms	(/ 1 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify247.0ms

Algorithm

egg-herbie

Counts

1184 → 1184

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5001	22630

prune5.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.2b	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
0.2b	(/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

417×	`times-frac`
399×	`add-sqr-sqrt`
286×	`*-un-lft-identity`
174×	`add-cube-cbrt`
164×	`sqrt-prod`
122×	`associate-r`
108×	`difference-of-squares`
54×	`distribute-lft-out--`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
12×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-*l/` `clear-num` `associate-/r/` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`flip3--` `div-sub` `associate-r/` `pow-prod-down` `-commutative` `flip--` `fma-udef`

Counts

4 → 350

Calls

4 calls:

0.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
5.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
108.0ms	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
39.0ms	(/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

series718.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
56.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
440.0ms	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
183.0ms	(/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

simplify88.0ms

Algorithm

egg-herbie

Counts

362 → 362

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1211	5565
1	5001	5285

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample736.0ms

Algorithm

intervals

Results

283.0ms	8000×	body	80	valid
255.0ms	8056×	body	80	nan