Details

sample340.0ms

Algorithm

intervals

Results

270.0ms

3370×

body

valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `times-frac`
63×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down` `cube-prod`
22×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `div-exp`
4×	`pow-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`sqrt-prod`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 172

Calls

4 calls:

21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
9.0ms	(pow (/ 1.0 (fabs x)) 3)
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series93.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms	(pow (/ 1.0 (fabs x)) 3)
33.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify139.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (127.0ms)

Iter	Nodes	Cost
0	584	1144
1	3655	959
2	5003	912

prune694.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

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)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
98×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
13×	`unpow-prod-down` `cube-prod`
10×	`div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
9.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series85.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify121.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	535	1298
1	3321	1112
2	5001	972

prune890.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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 (pow (fabs x) 3)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

435×	`add-exp-log`
212×	`prod-exp`
199×	`div-exp`
94×	`times-frac`
84×	`add-cbrt-cube`
83×	`add-sqr-sqrt`
70×	`add-cube-cbrt` `*-un-lft-identity`
53×	`associate-r`
48×	`pow-exp`
47×	`pow-to-exp`
34×	`cbrt-unprod`
28×	`1-exp`
26×	`cbrt-undiv`
22×	`unpow-prod-down` `cube-prod`
18×	`pow1`
14×	`associate-l`
13×	`swap-sqr`
7×	`div-inv`
6×	`frac-times` `associate-*l/`
4×	`cube-mult` `unpow3` `associate-*r/` `pow-prod-down` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-unpow` `sqrt-prod`
2×	`*-commutative` `rem-cube-cbrt`
1×	`cube-div` `pow2` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 286

Calls

4 calls:

105.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series199.0ms

Counts

4 → 10

Calls

4 calls:

136.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
39.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify65.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1406	3060
1	5001	2568

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
0.4b	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite512.0ms

Algorithm

rewrite-expression-head

Rules

929×	`add-exp-log`
505×	`prod-exp`
389×	`div-exp`
153×	`add-cbrt-cube`
94×	`pow-exp`
93×	`pow-to-exp`
78×	`frac-times`
75×	`cbrt-unprod`
56×	`1-exp`
54×	`times-frac`
50×	`associate-*l/`
44×	`add-sqr-sqrt`
43×	`cbrt-undiv` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
34×	`associate-*r/`
24×	`frac-add`
22×	`unpow-prod-down` `cube-prod`
20×	`pow1`
9×	`pow-prod-down`
8×	`flip3-+` `flip-+`
4×	`cube-mult` `unpow3` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `sqrt-prod` `div-inv`
2×	`associate-l` `*-commutative` `rem-cube-cbrt`
1×	`cube-div` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 387

Calls

4 calls:

370.0ms	(* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
101.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3)))
10.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series393.0ms

Counts

4 → 10

Calls

4 calls:

216.0ms	(* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
136.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3)))
41.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify106.0ms

Algorithm

egg-herbie

Counts

397 → 397

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2115	7226
1	5002	6712

prune974.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes444.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	33
1	42	33

end0.0ms

sample7.4s

Algorithm

intervals

Results

6.2s

78267×

body

valid