Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	99×	body	80	nan

simplify5.0ms

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

localize20.0ms

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))))

rewrite98.0ms

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))
23.0ms	(+ 1.0 (sqrt (+ x 1.0)))
61.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series360.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(sqrt (+ x 1.0))
69.0ms	(+ 1.0 (sqrt (+ x 1.0)))
233.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5003
2	1162
1	333
0	143

prune368.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.9b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.8b	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
45×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`flip3-+` `flip-+`
30×	`associate-*r/`
28×	`add-cube-cbrt`
26×	`sqrt-prod`
21×	`pow1`
20×	`associate-l`
19×	`times-frac`
16×	`frac-sub`
14×	`frac-times`
13×	`add-cbrt-cube` `add-exp-log`
11×	`swap-sqr`
10×	`associate-r`
9×	`associate-*l/`
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` `sub-div`
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` `flip3--` `distribute-rgt-out--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `flip--`

Counts

4 → 170

Calls

4 calls:

167.0ms	(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
39.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
44.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0ms	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

710.0ms	(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
33.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
78.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
333.0ms	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

simplify3.9s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
2	4848
1	1243
0	392

prune887.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

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)))))

rewrite126.0ms

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:

32.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(sqrt (+ x 1.0))
12.0ms	(+ 1.0 (sqrt (+ x 1.0)))
67.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series725.0ms

Counts

4 → 12

Calls

4 calls:

395.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
34.0ms	(sqrt (+ x 1.0))
77.0ms	(+ 1.0 (sqrt (+ x 1.0)))
219.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify2.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	1984
1	572
0	221

prune620.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes105.0ms

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

sample654.0ms

Algorithm

intervals

Results

395.0ms	7997×	body	80	valid
71.0ms	2657×	body	80	nan
1.0ms	3×	body	1280	valid