Details

sample339.0ms

Algorithm

intervals

Results

280.0ms

3513×

body

valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
120×	`times-frac`
89×	`add-cube-cbrt` `*-un-lft-identity`
40×	`add-exp-log` `add-cbrt-cube`
39×	`swap-sqr` `associate-r` `associate-l`
26×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 214

Calls

4 calls:

13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series69.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify77.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	426	1780
1	2077	1524
2	5002	1377

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

749×	`add-exp-log`
477×	`add-cbrt-cube`
426×	`prod-exp`
266×	`cbrt-unprod`
233×	`div-exp`
137×	`cbrt-undiv`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
51×	`frac-times` `associate-*l/`
39×	`pow1` `associate-r`
33×	`associate-*r/`
27×	`associate-l`
26×	`swap-sqr`
17×	`pow-prod-down`
16×	`pow-to-exp` `pow-exp`
9×	`div-inv`
8×	`unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 361

Calls

4 calls:

1.1s	(* (* (* (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series108.0ms

Counts

4 → 10

Calls

4 calls:

52.0ms	(* (* (* (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
32.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify89.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1944	6412
1	5002	4251

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite367.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

315.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series104.0ms

Counts

4 → 10

Calls

4 calls:

57.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify130.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1312	4435
1	4821	2405
2	5001	2405

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (* (* 1.0 1.0) (pow 1.0 3)) (/ 1.0 (fabs x))) (pow (fabs x) 5))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

208×	`add-exp-log`
104×	`prod-exp`
90×	`add-sqr-sqrt`
87×	`times-frac`
74×	`div-exp`
65×	`add-cube-cbrt` `*-un-lft-identity`
57×	`add-cbrt-cube`
27×	`pow-to-exp` `pow-exp`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`cbrt-unprod`
19×	`pow1`
18×	`cbrt-undiv`
9×	`div-inv`
8×	`unswap-sqr`
7×	`associate-/r*`
6×	`unpow-prod-down`
4×	`add-log-exp`
3×	`associate-*r/` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `pow-sqr` `-commutative` `pow-prod-up` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/` `associate-/l*`

Counts

4 → 225

Calls

4 calls:

32.0ms	(/ (* (* (* 1.0 1.0) (pow 1.0 3)) (/ 1.0 (fabs x))) (pow (fabs x) 5))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series150.0ms

Counts

4 → 10

Calls

4 calls:

98.0ms	(/ (* (* (* 1.0 1.0) (pow 1.0 3)) (/ 1.0 (fabs x))) (pow (fabs x) 5))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify132.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	835	2092
1	4584	1785
2	5002	1590

prune1.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.3b

regimes275.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	47
1	45	47

end0.0ms

sample9.4s

Algorithm

intervals

Results

8.2s

103451×

body

valid