Details

sample341.0ms

Algorithm

intervals

Results

281.0ms

3541×

body

valid

simplify65.0ms

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

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite46.0ms

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:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series72.0ms

Counts

4 → 10

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
27.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify71.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (54.0ms)

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

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

3341×	`add-exp-log`
1930×	`prod-exp`
1241×	`div-exp`
1117×	`add-cbrt-cube`
618×	`cbrt-unprod`
361×	`cbrt-undiv`
131×	`frac-times` `associate-*l/`
112×	`1-exp`
96×	`pow-to-exp` `pow-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`pow1` `associate-r`
33×	`associate-*r/`
27×	`associate-l`
26×	`swap-sqr`
17×	`pow-prod-down`
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 → 729

Calls

4 calls:

48.0ms	(* (* (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series196.0ms

Counts

4 → 10

Calls

4 calls:

139.0ms	(* (* (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 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)))
34.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify185.0ms

Algorithm

egg-herbie

Counts

739 → 739

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	4399	16237
1	5002	15801

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-exp-log` `add-cbrt-cube`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
66×	`prod-exp` `cbrt-unprod`
65×	`pow1`
45×	`cbrt-undiv` `div-exp`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
23×	`pow-plus` `pow-prod-up`
19×	`frac-times` `associate-*l/`
9×	`associate-*r/` `div-inv`
8×	`pow-prod-down` `unswap-sqr`
6×	`pow2` `pow-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 249

Calls

4 calls:

18.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series87.0ms

Counts

4 → 10

Calls

4 calls:

41.0ms	(* (* (* (/ 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)

simplify108.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	848	2581
1	3913	1673
2	5001	1400

prune961.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (* (/ 3.0 4.0) (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

1217×	`frac-times`
937×	`associate-*r/`
679×	`associate-*l/`
434×	`frac-add`
99×	`add-sqr-sqrt`
90×	`times-frac`
69×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-l`
33×	`add-exp-log` `add-cbrt-cube`
29×	`associate-r`
26×	`swap-sqr`
21×	`pow1`
10×	`prod-exp` `cbrt-unprod` `unswap-sqr`
9×	`cbrt-undiv` `div-exp` `div-inv`
4×	`add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`pow2` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 619

Calls

4 calls:

57.0ms	(* (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (* (/ 3.0 4.0) (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series186.0ms

Counts

4 → 10

Calls

4 calls:

141.0ms	(* (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (* (/ 3.0 4.0) (* (* (* (/ 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)

simplify135.0ms

Algorithm

egg-herbie

Counts

629 → 629

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5001	13378

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

regimes216.0ms

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	45
1	46	45

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

20720×

body

valid