Details

sample57.0ms

Algorithm

intervals

Results

11.0ms	291×	body	80	nan
11.0ms	57×	body	1280	valid
6.0ms	43×	body	640	valid
5.0ms	128×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 89

Calls

2 calls:

6.0ms	(sqrt (+ x 1.0))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series169.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(sqrt (+ x 1.0))
116.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1076
1	322
0	139

prune351.0ms

Pruning

6 alts after pruning (6 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	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
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 → 94

Calls

3 calls:

13.0ms	(sqrt (+ x 1.0))
32.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
84.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ x 1.0))
91.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
200.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.6s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2060
1	439
0	173

prune490.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(expm1 (log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
17×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `log1p-udef` `expm1-log1p` `clear-num` `sum-log` `frac-2neg` `div-exp` `log1p-expm1` `div-inv` `expm1-udef`

Counts

4 → 88

Calls

4 calls:

1.0ms	(log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
41.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0ms	(expm1 (log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
43.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series2.1s

Counts

4 → 12

Calls

4 calls:

629.0ms	(log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
86.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
1.2s	(expm1 (log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
211.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.5s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2723
1	612
0	229

prune508.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite550.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 324

Calls

4 calls:

60.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
57.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
59.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
345.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

424.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
204.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
205.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
192.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.3s

Counts

336 → 336

Iterations

Iter	Nodes
done	5000
2	3825
1	784
0	327

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes92.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

485.0ms	4038×	body	80	valid
384.0ms	8152×	body	80	nan
374.0ms	1768×	body	1280	valid
250.0ms	1259×	body	640	valid
66.0ms	632×	body	320	valid
57.0ms	303×	body	160	valid