Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	123×	body	80	valid
10.0ms	312×	body	80	nan
8.0ms	49×	body	1280	valid
6.0ms	48×	body	640	valid
3.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize13.0ms

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:

9.0ms	(sqrt (+ x 1.0))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series127.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
96.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify858.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1076
1	322
0	139

prune258.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
28×	`distribute-lft-out`
24×	`times-frac` `sqrt-prod`
18×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
3×	`pow1` `flip3-+` `flip-+`
2×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

2 → 71

Calls

2 calls:

9.0ms	(sqrt (+ x 1.0))
53.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series187.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt (+ x 1.0))
155.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1874
1	394
0	157

prune337.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
20×	`sqrt-prod`
19×	`add-sqr-sqrt`
18×	`times-frac`
17×	`distribute-lft-out`
16×	`add-cube-cbrt`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u` `pow1`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `log1p-expm1` `hypot-def` `div-inv` `expm1-udef`

Counts

4 → 84

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 x))
1.0ms	(log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.0ms	(expm1 (log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
58.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series1.9s

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ 1.0 x))
631.0ms	(log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
1.1s	(expm1 (log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
145.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	2883
1	625
0	239

prune546.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
0.3b	(cbrt (+ 1.0 x))
0.3b	(cbrt (+ 1.0 x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

27.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
35.0ms	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
7.0ms	(cbrt (+ 1.0 x))
7.0ms	(cbrt (+ 1.0 x))

series577.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
137.0ms	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
115.0ms	(cbrt (+ 1.0 x))
94.0ms	(cbrt (+ 1.0 x))

simplify3.5s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	4504
1	920
0	334

prune867.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes106.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

673.0ms	1266×	body	640	valid
382.0ms	7998×	body	80	nan
259.0ms	1648×	body	1280	valid
137.0ms	4138×	body	80	valid
61.0ms	668×	body	320	valid
17.0ms	280×	body	160	valid