Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	99×	body	80	nan

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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))))

rewrite77.0ms

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:

11.0ms	(sqrt (+ x 1.0))
14.0ms	(+ 1.0 (sqrt (+ x 1.0)))
50.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series306.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(sqrt (+ x 1.0))
54.0ms	(+ 1.0 (sqrt (+ x 1.0)))
204.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5002
2	1541
1	333
0	143

prune313.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0))
0.2b	(/ x (/ (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))) (fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0))))
3.8b	(- (sqrt (+ 1.0 x)) 1.0)
5.8b	(/ (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))) (fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
79×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
21×	`prod-diff`
17×	`sqrt-prod`
16×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
7×	`fma-neg`
6×	`div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `distribute-lft-out`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 156

Calls

4 calls:

0.0ms	(fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0))
17.0ms	(/ x (/ (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))) (fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0))))
43.0ms	(- (sqrt (+ 1.0 x)) 1.0)
4.0ms	(/ (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))) (fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

214.0ms	(fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0))
709.0ms	(/ x (/ (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))) (fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0))))
55.0ms	(- (sqrt (+ 1.0 x)) 1.0)
721.0ms	(/ (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))) (fma (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0) (* 1.0 1.0)))

simplify1.7s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
1	1030
0	388

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
40×	`add-cube-cbrt`
39×	`sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `hypot-def`

Counts

4 → 144

Calls

4 calls:

53.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
12.0ms	(sqrt (+ x 1.0))
27.0ms	(+ 1.0 (sqrt (+ x 1.0)))
94.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

371.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
33.0ms	(sqrt (+ x 1.0))
68.0ms	(+ 1.0 (sqrt (+ x 1.0)))
240.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.3s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	3982
1	572
0	221

prune536.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
1	8
0	6

end0.0ms

sample663.0ms

Algorithm

intervals

Results

391.0ms	7997×	body	80	valid
77.0ms	2657×	body	80	nan
1.0ms	3×	body	1280	valid