Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	102×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
12.0ms	(+ 1.0 (sqrt (+ x 1.0)))
25.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series319.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(sqrt (+ x 1.0))
62.0ms	(+ 1.0 (sqrt (+ x 1.0)))
219.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5002
2	1541
1	333
0	143

prune399.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) 1.0)
0.2b	(/ x (+ (sqrt (+ x 1.0)) 1.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`times-frac`
8×	`sqrt-prod`
7×	`fma-def` `distribute-lft-out`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r*`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 75

Calls

3 calls:

11.0ms	(sqrt (+ x 1.0))
25.0ms	(+ (sqrt (+ x 1.0)) 1.0)
38.0ms	(/ x (+ (sqrt (+ x 1.0)) 1.0))

series351.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(sqrt (+ x 1.0))
76.0ms	(+ (sqrt (+ x 1.0)) 1.0)
236.0ms	(/ x (+ (sqrt (+ x 1.0)) 1.0))

simplify1.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1532
1	332
0	143

prune383.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (fma (sqrt (+ 1.0 x)) (+ 1.0 x) (* (* 1.0 1.0) 1.0))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.6b	(- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))
6.1b	(/ x (fma (sqrt (+ 1.0 x)) (+ 1.0 x) (* (* 1.0 1.0) 1.0)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
45×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
38×	`frac-times`
32×	`flip3-+` `frac-add` `flip-+`
28×	`associate-*r/` `add-cube-cbrt`
26×	`sqrt-prod`
21×	`pow1`
20×	`associate-l`
19×	`times-frac`
17×	`flip3--` `flip--`
13×	`add-cbrt-cube` `add-exp-log`
11×	`swap-sqr` `associate-*l/`
10×	`associate-r`
8×	`sqrt-pow1` `pow1/2`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`associate-/r` `prod-exp` `pow-sqr` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`
1×	`pow2` `distribute-rgt-in` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `distribute-lft-in` `pow-plus` `distribute-rgt-out--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff`

Counts

4 → 182

Calls

4 calls:

171.0ms	(* (/ x (fma (sqrt (+ 1.0 x)) (+ 1.0 x) (* (* 1.0 1.0) 1.0))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))))
41.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
13.0ms	(- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))
7.0ms	(/ x (fma (sqrt (+ 1.0 x)) (+ 1.0 x) (* (* 1.0 1.0) 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

737.0ms	(* (/ x (fma (sqrt (+ 1.0 x)) (+ 1.0 x) (* (* 1.0 1.0) 1.0))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))))
23.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
112.0ms	(- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))
358.0ms	(/ x (fma (sqrt (+ 1.0 x)) (+ 1.0 x) (* (* 1.0 1.0) 1.0)))

simplify2.6s

Counts

194 → 194

Iterations

Iter	Nodes
done	5002
1	1702
0	433

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) 1.0)
0.1b	(/ (+ (sqrt (+ x 1.0)) 1.0) (sqrt x))
0.1b	(/ (sqrt x) (/ (+ (sqrt (+ x 1.0)) 1.0) (sqrt x)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
291×	`*-un-lft-identity`
194×	`sqrt-prod`
190×	`add-sqr-sqrt`
187×	`add-cube-cbrt`
52×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/l*`
9×	`div-inv`
7×	`fma-def`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def`

Counts

4 → 309

Calls

4 calls:

13.0ms	(sqrt (+ x 1.0))
31.0ms	(+ (sqrt (+ x 1.0)) 1.0)
82.0ms	(/ (+ (sqrt (+ x 1.0)) 1.0) (sqrt x))
58.0ms	(/ (sqrt x) (/ (+ (sqrt (+ x 1.0)) 1.0) (sqrt x)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
48.0ms	(+ (sqrt (+ x 1.0)) 1.0)
160.0ms	(/ (+ (sqrt (+ x 1.0)) 1.0) (sqrt x))
177.0ms	(/ (sqrt x) (/ (+ (sqrt (+ x 1.0)) 1.0) (sqrt x)))

simplify1.6s

Counts

321 → 321

Iterations

Iter	Nodes
done	5001
1	1006
0	380

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	8
1	8
0	6

end0.0ms

sample714.0ms

Algorithm

intervals

Results

348.0ms	7997×	body	80	valid
126.0ms	2708×	body	80	nan
0.0ms	3×	body	1280	valid