Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	58×	body	1280	valid
4.0ms	226×	body	80	nan
3.0ms	42×	body	640	valid
2.0ms	123×	body	80	valid
1.0ms	23×	body	320	valid
0.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize5.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

30.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series73.0ms

Counts

1 → 3

Calls

1 calls:

73.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.5s

Counts

73 → 73

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	117	1805
1	259	1303
2	747	970
3	3669	800
done	5000	793

prune91.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

13.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
27.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series214.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
145.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify637.0ms

Counts

80 → 80

Iterations

Useful iterations: done (635.0ms)

Iter	Nodes	Cost
0	143	1265
1	359	1038
2	1300	936
done	5001	932

prune159.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`sqrt-prod`
17×	`add-cube-cbrt`
12×	`times-frac`
8×	`pow1` `sqrt-pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `log1p-expm1-u` `distribute-lft-out` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0)))
1.0ms	(sqrt (sqrt x))
1.0ms	(sqrt (sqrt x))
8.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0)))
148.0ms	(sqrt (sqrt x))
145.0ms	(sqrt (sqrt x))
217.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0))))

simplify885.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	209	1590
1	514	1161
2	2199	1032
done	5000	1032

prune262.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (fma (* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x)))) (sqrt (sqrt x)) (sqrt (+ x 1.0))))
0.3b	(* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

8.0ms	(/ (+ 1.0 0) (fma (* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x)))) (sqrt (sqrt x)) (sqrt (+ x 1.0))))
11.0ms	(* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x))))
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series952.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (+ 1.0 0) (fma (* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x)))) (sqrt (sqrt x)) (sqrt (+ x 1.0))))
293.0ms	(* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x))))
189.0ms	(cbrt x)
186.0ms	(cbrt x)

simplify1.1s

Counts

115 → 115

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	280	2515
1	669	2288
2	2791	2139
done	5000	2136

prune468.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 2 (2.0ms)

Iter	Nodes	Cost
0	16	21
1	19	21
2	23	19
done	23	19

end0.0ms

sample665.0ms

Algorithm

intervals

Results

146.0ms	1746×	body	1280	valid
139.0ms	7984×	body	80	nan
89.0ms	1276×	body	640	valid
77.0ms	4049×	body	80	valid
30.0ms	615×	body	320	valid
10.0ms	314×	body	160	valid