Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	5	7
1	7	6
done	7	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize7.0ms

Local error

Found 1 expressions with local error:

13.2b

(/ x (fma x x 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

9.0ms

(/ x (fma x x 1.0))

series93.0ms

Counts

1 → 3

Calls

1 calls:

93.0ms

(/ x (fma x x 1.0))

simplify3.6s

Counts

32 → 32

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	68	377
1	442	356
done	5000	332

prune81.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
0.0b	(/ x (sqrt (fma x x 1.0)))
13.1b	(sqrt (fma x x 1.0))
13.1b	(sqrt (fma x x 1.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`add-cube-cbrt` `*-un-lft-identity`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 248

Calls

4 calls:

18.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
7.0ms	(/ x (sqrt (fma x x 1.0)))
2.0ms	(sqrt (fma x x 1.0))
2.0ms	(sqrt (fma x x 1.0))

series432.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
165.0ms	(/ x (sqrt (fma x x 1.0)))
89.0ms	(sqrt (fma x x 1.0))
77.0ms	(sqrt (fma x x 1.0))

simplify3.7s

Counts

260 → 260

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	304	5985
1	1815	5150
done	5001	4854

prune669.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (sqrt (fma x x 1.0))))
13.1b	(sqrt (fma x x 1.0))
13.1b	(sqrt (fma x x 1.0))
13.1b	(sqrt (fma x x 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 98

Calls

4 calls:

15.0ms	(/ x (sqrt (sqrt (fma x x 1.0))))
3.0ms	(sqrt (fma x x 1.0))
3.0ms	(sqrt (fma x x 1.0))
3.0ms	(sqrt (fma x x 1.0))

series654.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(/ x (sqrt (sqrt (fma x x 1.0))))
80.0ms	(sqrt (fma x x 1.0))
96.0ms	(sqrt (fma x x 1.0))
99.0ms	(sqrt (fma x x 1.0))

simplify2.2s

Counts

110 → 110

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	159	1417
1	929	1243
done	5001	1193

prune383.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (/ 1.0 (pow x 3)))
0.3b	(/ 1.0 (pow x 3))
0.5b	(/ 1.0 (pow x 5))
21.0b	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

rewrite651.0ms

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×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out`
3×	`frac-add`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 1249

Calls

4 calls:

136.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
13.0ms	(/ 1.0 (pow x 3))
8.0ms	(/ 1.0 (pow x 5))
299.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
50.0ms	(/ 1.0 (pow x 3))
101.0ms	(/ 1.0 (pow x 5))
61.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

simplify2.0s

Counts

1261 → 1261

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1137	49036
done	5001	36090

prune3.5s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch105.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	529.597454464039
10	-6045414056204.408	-123.41774798665298	-853997951174.7607

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	20	44
1	26	30
done	26	30

end0.0ms

sample502.0ms

Algorithm

intervals

Results

320.0ms

8000×

body

valid