Details

sample1.8s

Algorithm

intervals

Results

1.7s

3576×

body

valid

simplify6.7s

Counts

1 → 1

Iterations

Iter	Nodes
4	8828
3	1935
2	407
1	93
0	31

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize95.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b	(sqrt PI)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
144×	`times-frac`
124×	`add-exp-log`
113×	`*-un-lft-identity`
89×	`add-cube-cbrt`
50×	`pow1`
48×	`div-exp` `prod-exp`
45×	`swap-sqr`
40×	`add-cbrt-cube`
39×	`associate-r` `associate-l`
27×	`unswap-sqr`
24×	`rec-exp` `1-exp` `pow-flip` `inv-pow`
18×	`div-inv`
15×	`pow-prod-up`
12×	`cbrt-undiv` `cbrt-unprod`
9×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 306

Calls

4 calls:

12.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
20.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
26.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms	(sqrt PI)

series86.0ms

Counts

4 → 10

Calls

4 calls:

27.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
28.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
31.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms	(sqrt PI)

simplify3.4s

Counts

316 → 316

Iterations

Iter	Nodes
3	2654
2	991
1	478
0	166

prune7.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

462×	`add-exp-log`
352×	`pow1`
240×	`div-exp`
194×	`times-frac`
192×	`pow-div`
161×	`prod-exp`
158×	`add-cbrt-cube`
117×	`pow-prod-up`
106×	`add-sqr-sqrt`
96×	`pow-flip` `inv-pow`
75×	`*-un-lft-identity`
72×	`cbrt-undiv`
65×	`add-cube-cbrt`
57×	`pow-sqr`
53×	`pow-plus`
49×	`cbrt-unprod`
45×	`pow2`
40×	`rec-exp` `1-exp`
26×	`associate-/l*`
19×	`swap-sqr`
17×	`associate-r` `associate-l`
16×	`div-inv` `unswap-sqr`
13×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `associate-/r*` `frac-2neg` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 416

Calls

4 calls:

18.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
18.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
57.0ms	(* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))))
1.0ms	(sqrt PI)

series153.0ms

Counts

4 → 10

Calls

4 calls:

51.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
39.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
63.0ms	(* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))))
0.0ms	(sqrt PI)

simplify1.3s

Counts

426 → 426

Iterations

Iter	Nodes
2	2753
1	966
0	367

prune7.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.3b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (/ 15/8 (fabs x)) (pow (fabs x) -6) (fma 3/4 (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (/ (exp (* (fabs x) (fabs x))) (sqrt PI)))
0.4b	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.4b	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
1.0b	(sqrt PI)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

82×	`times-frac`
56×	`add-sqr-sqrt`
52×	`add-exp-log`
47×	`*-un-lft-identity` `add-cube-cbrt`
35×	`pow1`
33×	`add-cbrt-cube`
26×	`associate-/l*`
25×	`div-exp`
22×	`associate-r`
16×	`pow-div`
13×	`cbrt-undiv` `sqrt-prod`
10×	`prod-exp`
8×	`pow-flip` `inv-pow`
7×	`div-inv`
6×	`cbrt-unprod`
4×	`pow2` `expm1-log1p-u` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`clear-num` `associate-/r*` `frac-2neg` `associate-/l/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 179

Calls

4 calls:

13.0ms	(* (fma (/ 15/8 (fabs x)) (pow (fabs x) -6) (fma 3/4 (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (/ (exp (* (fabs x) (fabs x))) (sqrt PI)))
17.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
28.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
2.0ms	(sqrt PI)

series522.0ms

Counts

4 → 10

Calls

4 calls:

414.0ms	(* (fma (/ 15/8 (fabs x)) (pow (fabs x) -6) (fma 3/4 (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (/ (exp (* (fabs x) (fabs x))) (sqrt PI)))
60.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
47.0ms	(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.0ms	(sqrt PI)

simplify7.4s

Counts

189 → 189

Iterations

Iter	Nodes
3	7996
2	1792
1	586
0	236

prune3.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 3/4 (pow (fabs x) 5))
0.2b	(/ 15/8 (pow (fabs x) 7))
0.3b	(* (* (exp (* (fabs x) (fabs x))) (+ (/ 1 (fabs x)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))) (sqrt (/ 1 PI)))
0.4b	(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

82×	`times-frac`
58×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
30×	`add-exp-log`
25×	`add-cbrt-cube`
24×	`unpow-prod-down`
19×	`associate-/l*`
18×	`frac-add`
16×	`associate-r`
15×	`associate-/r` `associate-r/`
13×	`sqrt-prod`
12×	`div-exp`
9×	`pow1`
8×	`cbrt-undiv` `sqrt-div` `sqr-pow`
7×	`frac-times` `associate-*l/`
6×	`flip3-+` `flip-+` `div-inv`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
2×	`pow-to-exp` `pow-exp`
1×	`associate-l` `*-commutative` `associate-/l/`

Counts

4 → 190

Calls

4 calls:

9.0ms	(/ 3/4 (pow (fabs x) 5))
9.0ms	(/ 15/8 (pow (fabs x) 7))
1.4s	(* (* (exp (* (fabs x) (fabs x))) (+ (/ 1 (fabs x)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))) (sqrt (/ 1 PI)))
25.0ms	(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 3/4 (pow (fabs x) 5))
61.0ms	(/ 15/8 (pow (fabs x) 7))
505.0ms	(* (* (exp (* (fabs x) (fabs x))) (+ (/ 1 (fabs x)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))) (sqrt (/ 1 PI)))
57.0ms	(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))

simplify4.4s

Counts

202 → 202

Iterations

Iter	Nodes
2	4625
1	1207
0	444

prune3.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes344.0ms

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	30
1	30
0	25

end0.0ms

sample11.2s

Algorithm

intervals

Results

10.7s

25476×

body

valid