Details

sample352.0ms

Algorithm

intervals

Results

292.0ms

3682×

body

valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune13.0ms

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

rewrite30.0ms

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:

15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms	(pow (/ 1.0 (fabs x)) 3)
4.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series89.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms	(pow (/ 1.0 (fabs x)) 3)
32.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify122.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (108.0ms)

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

prune656.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

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

rewrite41.0ms

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:

13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series81.0ms

Counts

4 → 10

Calls

4 calls:

27.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify105.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	535	1295
1	3321	1109
2	5001	969

prune845.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x))))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

1543×	`add-exp-log`
920×	`prod-exp`
523×	`div-exp`
498×	`add-cbrt-cube`
280×	`cbrt-unprod`
138×	`cbrt-undiv`
70×	`1-exp`
62×	`add-sqr-sqrt` `pow-exp`
61×	`pow-to-exp`
59×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1` `associate-r`
14×	`associate-l`
13×	`unpow-prod-down` `cube-prod` `swap-sqr`
7×	`div-inv`
6×	`frac-times` `associate-*l/`
4×	`associate-*r/` `pow-prod-down` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `sqrt-prod`
2×	`*-commutative` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `unpow3` `pow-sqr` `pow-prod-up` `sqr-pow`

Counts

4 → 439

Calls

4 calls:

91.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x))))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series196.0ms

Counts

4 → 10

Calls

4 calls:

135.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x))))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify97.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1946	7390
1	5001	4293

prune845.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (+ (+ (* (/ (* 1.0 1.0) (pow (fabs x) 5)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite896.0ms

Algorithm

rewrite-expression-head

Rules

116×	`times-frac`
87×	`add-sqr-sqrt`
74×	`add-cube-cbrt` `*-un-lft-identity`
54×	`frac-add`
35×	`associate-*l/`
31×	`add-cbrt-cube`
29×	`add-exp-log`
23×	`associate-/l/`
22×	`associate-/r*`
21×	`sqrt-prod`
20×	`frac-times`
16×	`associate-*r/`
13×	`pow1` `unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
11×	`cbrt-undiv` `div-exp`
9×	`div-inv`
6×	`prod-exp` `cbrt-unprod`
4×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `unpow3` `pow-prod-down` `clear-num` `associate-/r/` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l` `sqr-pow`

Counts

4 → 213

Calls

4 calls:

865.0ms	(/ (* (+ (+ (* (/ (* 1.0 1.0) (pow (fabs x) 5)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series473.0ms

Counts

4 → 10

Calls

4 calls:

414.0ms	(/ (* (+ (+ (* (/ (* 1.0 1.0) (pow (fabs x) 5)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify64.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1351	4004
1	5002	3584

prune916.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.0b

regimes286.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	43	25

end0.0ms

sample912.0ms

Algorithm

intervals

Results

780.0ms

9964×

body

valid