Details

sample345.0ms

Algorithm

intervals

Results

275.0ms

3517×

body

valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	90	61
1	406	58
2	2267	36
3	5001	35

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(pow (/ 1.0 (fabs x)) 4)
1.0b	(sqrt PI)
1.2b	(pow (/ 1.0 (fabs x)) 6)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

39×	`unpow-prod-down`
37×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `cube-prod`
9×	`pow-unpow`
8×	`pow1`
7×	`add-cbrt-cube`
6×	`pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-exp` `sqrt-prod` `sqr-pow`
2×	`rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3`

Counts

4 → 123

Calls

4 calls:

6.0ms	(pow (/ 1.0 (fabs x)) 3)
6.0ms	(pow (/ 1.0 (fabs x)) 4)
3.0ms	(sqrt PI)
6.0ms	(pow (/ 1.0 (fabs x)) 6)

series106.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(pow (/ 1.0 (fabs x)) 3)
34.0ms	(pow (/ 1.0 (fabs x)) 4)
0.0ms	(sqrt PI)
43.0ms	(pow (/ 1.0 (fabs x)) 6)

simplify75.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	545	752
1	2496	663
2	5001	647

prune634.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(pow (/ 1.0 (fabs x)) 4)
1.0b	(sqrt PI)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`times-frac`
36×	`add-cube-cbrt`
26×	`unpow-prod-down`
15×	`add-exp-log`
13×	`cube-prod` `associate-l`
12×	`add-cbrt-cube`
9×	`pow1`
6×	`pow-unpow`
4×	`expm1-log1p-u` `associate-r` `pow-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`div-exp` `sqrt-prod`
2×	`cbrt-undiv` `frac-times` `pow-to-exp` `pow-pow` `flip3-+` `associate-*r/` `prod-exp` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`cube-div` `distribute-rgt-in` `cube-mult` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out`

Counts

4 → 134

Calls

4 calls:

67.0ms	(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
8.0ms	(pow (/ 1.0 (fabs x)) 4)
1.0ms	(sqrt PI)

series215.0ms

Counts

4 → 10

Calls

4 calls:

152.0ms	(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
33.0ms	(pow (/ 1.0 (fabs x)) 3)
30.0ms	(pow (/ 1.0 (fabs x)) 4)
0.0ms	(sqrt PI)

simplify111.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	722	1344
1	3637	1199
2	5002	1192

prune756.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (pow (fabs x) 6))
0.3b	(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

207×	`times-frac`
130×	`add-sqr-sqrt`
129×	`add-cube-cbrt` `*-un-lft-identity`
77×	`unpow-prod-down`
65×	`cube-prod`
39×	`associate-/r*`
24×	`add-exp-log`
12×	`div-exp` `div-inv`
11×	`add-cbrt-cube`
9×	`sqr-pow`
7×	`pow-exp`
6×	`pow1` `associate-/l*`
5×	`cube-mult` `pow-to-exp` `unpow3`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `pow-unpow` `1-exp` `sqrt-prod`
2×	`cube-div` `frac-2neg` `clear-num` `rem-cube-cbrt`
1×	`rem-sqrt-square` `pow-flip` `pow-pow` `sqrt-pow1` `pow1/2` `associate-/r/` `inv-pow`

Counts

4 → 267

Calls

4 calls:

8.0ms	(/ 1 (pow (fabs x) 6))
18.0ms	(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series167.0ms

Counts

4 → 10

Calls

4 calls:

49.0ms	(/ 1 (pow (fabs x) 6))
89.0ms	(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
29.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify97.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	676	2145
1	3542	1768
2	5003	1746

prune1.0s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))
0.3b	(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

1089×	`times-frac`
528×	`add-sqr-sqrt`
527×	`add-cube-cbrt` `*-un-lft-identity`
221×	`unpow-prod-down` `cube-prod`
133×	`associate-/r*`
40×	`div-inv`
29×	`add-exp-log`
17×	`cube-mult` `unpow3` `sqr-pow`
16×	`div-exp`
14×	`add-cbrt-cube`
6×	`pow1` `cube-div` `pow-exp` `associate-/r/` `associate-/l*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `sqrt-prod`
2×	`frac-2neg` `clear-num` `rem-cube-cbrt`
1×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2`

Counts

4 → 639

Calls

4 calls:

35.0ms	(/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))
16.0ms	(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series195.0ms

Counts

4 → 10

Calls

4 calls:

75.0ms	(/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))
90.0ms	(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
29.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify103.0ms

Algorithm

egg-herbie

Counts

649 → 649

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1479	7275
1	5001	6557

prune2.5s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

regimes564.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	33
1	43	33

end0.0ms

sample539.0ms

Algorithm

intervals

Results

443.0ms

5665×

body

valid