Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	16	367
1	31	367
2	60	292
3	91	292
4	119	292
5	133	292
6	143	292
7	182	292
8	255	292
9	301	292
10	362	292
11	490	292
12	774	292
13	1983	292
14	4459	292
done	5000	292

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.70711 (- (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) x))
0.0b	(- (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) x)
0.1b	(fma x (fma x 0.04481 0.99229) 1.0)
16.8b	(/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

135×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
123×	`add-cube-cbrt`
117×	`prod-diff`
101×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
13×	`fma-neg`
11×	`div-inv`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-r` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `sub-neg` `associate-l` `associate-/l`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 215

Calls

4 calls:

59.0ms	(* 0.70711 (- (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) x))
25.0ms	(- (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) x)
0.0ms	(fma x (fma x 0.04481 0.99229) 1.0)
4.0ms	(/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0))

series315.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* 0.70711 (- (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) x))
80.0ms	(- (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) x)
39.0ms	(fma x (fma x 0.04481 0.99229) 1.0)
91.0ms	(/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0))

simplify4.1s

Counts

227 → 227

Iterations

Useful iterations: 3 (2.6s)

Iter	Nodes	Cost
0	300	123567
1	650	107400
2	1428	86950
3	4084	84692
done	5000	84692

prune767.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (fma 0.27061 x 2.30753) (fma 0.99229 x (fma 0.04481 (* x x) 1.0))) x)
0.0b	(fma 0.99229 x (fma 0.04481 (* x x) 1.0))
0.1b	(fma 0.04481 (* x x) 1.0)
16.8b	(/ (fma 0.27061 x 2.30753) (fma 0.99229 x (fma 0.04481 (* x x) 1.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
53×	`add-cube-cbrt`
46×	`times-frac`
39×	`prod-diff`
13×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`fma-udef` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `flip--` `distribute-lft-out--`

Counts

4 → 118

Calls

4 calls:

34.0ms	(- (/ (fma 0.27061 x 2.30753) (fma 0.99229 x (fma 0.04481 (* x x) 1.0))) x)
0.0ms	(fma 0.99229 x (fma 0.04481 (* x x) 1.0))
0.0ms	(fma 0.04481 (* x x) 1.0)
8.0ms	(/ (fma 0.27061 x 2.30753) (fma 0.99229 x (fma 0.04481 (* x x) 1.0)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (/ (fma 0.27061 x 2.30753) (fma 0.99229 x (fma 0.04481 (* x x) 1.0))) x)
41.0ms	(fma 0.99229 x (fma 0.04481 (* x x) 1.0))
97.0ms	(fma 0.04481 (* x x) 1.0)
107.0ms	(/ (fma 0.27061 x 2.30753) (fma 0.99229 x (fma 0.04481 (* x x) 1.0)))

simplify3.8s

Counts

130 → 130

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	179	57341
1	381	49831
2	912	42754
3	2970	42028
done	5026	41548

prune615.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) 0.70711) (* (- x) 0.70711))
0.1b	(fma x (fma x 0.04481 0.99229) 1.0)
0.1b	(* (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) 0.70711)
16.8b	(/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-r` `associate-/l`
2×	`distribute-lft-neg-out` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3-+` `distribute-rgt-out` `unsub-neg` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `fma-udef`

Counts

4 → 90

Calls

4 calls:

18.0ms	(+ (* (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) 0.70711) (* (- x) 0.70711))
0.0ms	(fma x (fma x 0.04481 0.99229) 1.0)
23.0ms	(* (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) 0.70711)
8.0ms	(/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0))

series472.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ (* (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) 0.70711) (* (- x) 0.70711))
50.0ms	(fma x (fma x 0.04481 0.99229) 1.0)
178.0ms	(* (/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0)) 0.70711)
117.0ms	(/ (fma 0.27061 x 2.30753) (fma x (fma x 0.04481 0.99229) 1.0))

simplify2.2s

Counts

102 → 102

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	170	36700
1	420	32189
2	1472	30672
done	5000	30572

prune589.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (fma x (fma x 0.04481 0.99229) 1.0)))
0.2b	(* (/ 1 (sqrt (fma x (fma x 0.04481 0.99229) 1.0))) (/ (fma 0.27061 x 2.30753) (sqrt (fma x (fma x 0.04481 0.99229) 1.0))))
16.8b	(sqrt (fma x (fma x 0.04481 0.99229) 1.0))
16.8b	(sqrt (fma x (fma x 0.04481 0.99229) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
30×	`add-exp-log`
22×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`pow1` `div-exp`
8×	`prod-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `associate-/l*`
2×	`rem-sqrt-square`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow`

Counts

4 → 162

Calls

4 calls:

5.0ms	(/ 1 (sqrt (fma x (fma x 0.04481 0.99229) 1.0)))
47.0ms	(* (/ 1 (sqrt (fma x (fma x 0.04481 0.99229) 1.0))) (/ (fma 0.27061 x 2.30753) (sqrt (fma x (fma x 0.04481 0.99229) 1.0))))
1.0ms	(sqrt (fma x (fma x 0.04481 0.99229) 1.0))
2.0ms	(sqrt (fma x (fma x 0.04481 0.99229) 1.0))

series423.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ 1 (sqrt (fma x (fma x 0.04481 0.99229) 1.0)))
73.0ms	(* (/ 1 (sqrt (fma x (fma x 0.04481 0.99229) 1.0))) (/ (fma 0.27061 x 2.30753) (sqrt (fma x (fma x 0.04481 0.99229) 1.0))))
96.0ms	(sqrt (fma x (fma x 0.04481 0.99229) 1.0))
101.0ms	(sqrt (fma x (fma x 0.04481 0.99229) 1.0))

simplify308.0ms

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	240	73956