Details

sample28.0ms

Algorithm

intervals

Results

5.0ms	334×	body	80	nan
5.0ms	63×	body	1280	valid
2.0ms	130×	body	80	valid
2.0ms	32×	body	640	valid
1.0ms	17×	body	320	valid
0.0ms	14×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 29.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite65.0ms

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))
53.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(sqrt (+ x 1.0))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify47.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

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

prune134.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite107.0ms

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))
36.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
60.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series438.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
270.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (42.0ms)

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

prune214.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite423.0ms

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-exp-log` `add-cbrt-cube`
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` `associate-/l/` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 324

Calls

4 calls:

51.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
56.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
232.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series784.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
139.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
158.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify123.0ms

Counts

336 → 336

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	723	3905
1	3885	3364
2	5002	3360
done	5002	3360

prune611.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

142×	`*-un-lft-identity`
100×	`sqrt-prod`
61×	`distribute-lft-out`
58×	`times-frac`
44×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `sqrt-div` `associate-/r/`
5×	`flip3-+` `flip-+` `associate-/l*`
4×	`expm1-log1p-u` `hypot-def` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `div-inv` `associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`sqrt-undiv` `sqrt-unprod` `associate-*l/` `prod-exp` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

42.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
49.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
56.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
81.0ms	(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series818.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
349.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
168.0ms	(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify94.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	780	2162
1	3564	1966
2	5001	1955
done	5001	1955

prune494.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6
done	16	6

end0.0ms

sample719.0ms

Algorithm

intervals

Results

142.0ms	8104×	body	80	nan
137.0ms	1713×	body	1280	valid
82.0ms	1318×	body	640	valid
75.0ms	4060×	body	80	valid
28.0ms	605×	body	320	valid
10.0ms	304×	body	160	valid