Details

sample82.0ms

Algorithm

intervals

Results

21.0ms	57×	body	1280	valid
19.0ms	298×	body	80	nan
10.0ms	135×	body	80	valid
9.0ms	31×	body	640	valid
6.0ms	26×	body	320	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.7b	(- (sqrt (+ x 1)) (sqrt x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
42×	`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` `hypot-def` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 92

Calls

2 calls:

5.0ms	(sqrt (+ x 1))
63.0ms	(- (sqrt (+ x 1)) (sqrt x))

series86.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(sqrt (+ x 1))
62.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify3.7s

Counts

98 → 98

Iterations

Iter	Nodes
4	3956
3	1441
2	597
1	283
0	134

prune493.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
28×	`sqrt-prod`
22×	`distribute-lft-out`
21×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
7×	`fma-def` `add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 93

Calls

3 calls:

5.0ms	(sqrt (+ x 1))
30.0ms	(+ (sqrt (+ x 1)) (sqrt x))
27.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(sqrt (+ x 1))
65.0ms	(+ (sqrt (+ x 1)) (sqrt x))
110.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
4	2673
3	1160
2	569
1	256
0	126

prune692.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (fabs (sqrt (+ x 1))) (sqrt x))
0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (+ (fabs (sqrt (+ x 1))) (sqrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
7×	`add-exp-log`
6×	`distribute-lft-out`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 79

Calls

3 calls:

5.0ms	(+ (fabs (sqrt (+ x 1))) (sqrt x))
8.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (+ (fabs (sqrt (+ x 1))) (sqrt x)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (fabs (sqrt (+ x 1))) (sqrt x))
41.0ms	(sqrt (+ x 1))
50.0ms	(/ 1 (+ (fabs (sqrt (+ x 1))) (sqrt x)))

simplify2.0s

Counts

88 → 88

Iterations

Iter	Nodes
3	2521
2	916
1	353
0	158

prune678.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.2b	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 177

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ x 1)))
5.0ms	(sqrt (sqrt (+ x 1)))
45.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
61.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series247.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (sqrt (+ x 1)))
48.0ms	(sqrt (sqrt (+ x 1)))
115.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
44.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify2.3s

Counts

189 → 189

Iterations

Iter	Nodes
3	2255
2	1017
1	448
0	217

prune936.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

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
2	10
1	10
0	8

end0.0ms

sample2.2s

Algorithm

intervals

Results

597.0ms	1228×	body	640	valid
574.0ms	1712×	body	1280	valid
473.0ms	8131×	body	80	nan
228.0ms	4144×	body	80	valid
84.0ms	608×	body	320	valid
30.0ms	308×	body	160	valid