Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	5

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize6.0ms

Local error

Found 1 expressions with local error:

16.7b

(/ x (+ (* x x) 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
2×	`associate-/r/`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

12.0ms

(/ x (+ (* x x) 1.0))

series77.0ms

Counts

1 → 3

Calls

1 calls:

77.0ms

(/ x (+ (* x x) 1.0))

simplify633.0ms

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
2	808
1	189
0	76

prune137.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (fma x x 1.0)))
0.0b	(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
16.6b	(sqrt (fma x x 1.0))
16.6b	(sqrt (fma x x 1.0))

rewrite63.0ms

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:

6.0ms	(/ 1 (sqrt (fma x x 1.0)))
46.0ms	(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
2.0ms	(sqrt (fma x x 1.0))
3.0ms	(sqrt (fma x x 1.0))

series356.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1 (sqrt (fma x x 1.0)))
100.0ms	(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
79.0ms	(sqrt (fma x x 1.0))
80.0ms	(sqrt (fma x x 1.0))

simplify2.0s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	4147
1	621
0	208

prune622.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (/ (fma x x 1.0) x))
16.6b	(/ (fma x x 1.0) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
52×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`pow1`
2×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `1-exp` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

2 → 107

Calls

2 calls:

16.0ms	(/ 1 (/ (fma x x 1.0) x))
7.0ms	(/ (fma x x 1.0) x)

series209.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(/ 1 (/ (fma x x 1.0) x))
131.0ms	(/ (fma x x 1.0) x)

simplify991.0ms

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1803
1	408
0	168

prune305.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (/ 1.0 (pow x 3)))
0.0b	(/ 1.0 (pow x 5))
0.1b	(/ 1.0 (pow x 3))
15.8b	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

1770×	`times-frac`
1242×	`add-sqr-sqrt`
1223×	`*-un-lft-identity`
1198×	`add-cube-cbrt`
1040×	`prod-diff`
522×	`associate-+r+`
270×	`unpow-prod-down`
249×	`cube-prod`
112×	`div-inv`
92×	`sqr-pow`
82×	`cube-mult` `unpow3`
25×	`fma-def`
19×	`associate-/r*`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`fma-neg`
11×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `associate-/l*` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `distribute-lft-out`
3×	`frac-add`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `pow-exp` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 1249

Calls

4 calls:

84.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
6.0ms	(/ 1.0 (pow x 5))
8.0ms	(/ 1.0 (pow x 3))
308.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
79.0ms	(/ 1.0 (pow x 5))
86.0ms	(/ 1.0 (pow x 3))
63.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

simplify1.3s

Counts

1261 → 1261

Iterations

Iter	Nodes
done	5000
1	2518
0	1137

prune2.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch112.0ms

Steps

Iters	Range		Point
8	5.1212688054922095	257785.57693934403	726.4607531112061
8	-346749.28651926527	-205.8624528279525	-3116.202715780454

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample539.0ms

Algorithm

intervals

Results

354.0ms

8000×

body

valid