Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	57×	body	1280	valid
4.0ms	239×	body	80	nan
2.0ms	128×	body	80	valid
2.0ms	38×	body	640	valid
1.0ms	21×	body	320	valid
0.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite63.0ms

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×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
51.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series96.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(sqrt (+ x 1.0))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify40.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	299	1161
1	921	822
2	5001	744
done	5001	744

prune127.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

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)))

rewrite103.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 94

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
35.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
57.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series223.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
131.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify47.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	409	789
1	1675	716
2	5001	675
done	5001	675

prune213.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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 1.0) (* 0 0)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
35.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
43.0ms	(/ (- (* 1.0 1.0) (* 0 0)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))

series238.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ x 1.0))
73.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
133.0ms	(/ (- (* 1.0 1.0) (* 0 0)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify85.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	492	602
1	2727	486
2	5002	475
done	5002	475

prune213.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

1122×	`*-un-lft-identity`
908×	`sqrt-prod`
774×	`times-frac`
460×	`distribute-lft-out`
310×	`add-sqr-sqrt`
292×	`add-cube-cbrt`
46×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
8×	`hypot-def`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 563

Calls

4 calls:

42.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
137.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
151.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
306.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
130.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify156.0ms

Counts

575 → 575

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1107	11444
1	4551	9783
2	5001	9783
done	5001	9783

prune602.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	16	8
2	16	8
done	16	8

end0.0ms

sample706.0ms

Algorithm

intervals

Results

136.0ms	1694×	body	1280	valid
132.0ms	7837×	body	80	nan
78.0ms	4137×	body	80	valid
74.0ms	1228×	body	640	valid
28.0ms	618×	body	320	valid
10.0ms	323×	body	160	valid