Details

sample125.0ms

Algorithm

intervals

Results

35.0ms	58×	body	640	valid
27.0ms	278×	body	80	nan
22.0ms	36×	body	1280	valid
16.0ms	134×	body	80	valid
6.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	15
2	15
1	11
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.8b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
902×	`*-un-lft-identity`
788×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
74×	`distribute-lft-out`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 793

Calls

4 calls:

10.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
58.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1))
38.0ms	(/ 1 (sqrt (+ x 1)))
40.0ms	(/ 1 (sqrt x))
83.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify3.3s

Counts

805 → 805

Iterations

Iter	Nodes
2	2418
1	1414
0	651

prune9.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 18.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
2.8b	(- (sqrt (+ x 1)) (sqrt x))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
79×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
42×	`prod-diff`
39×	`add-cube-cbrt`
12×	`distribute-lft-out` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `hypot-def` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 171

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
109.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
17.0ms	(* (sqrt x) (sqrt (+ x 1)))
33.0ms	(- (sqrt (+ x 1)) (sqrt x))

series479.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ x 1))
238.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
99.0ms	(* (sqrt x) (sqrt (+ x 1)))
91.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify16.4s

Counts

183 → 183

Iterations

Iter	Nodes
3	8508
2	1660
1	522
0	216

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

115×	`*-un-lft-identity`
78×	`times-frac`
55×	`sqrt-prod`
52×	`add-sqr-sqrt`
42×	`distribute-lft-out`
40×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
14×	`div-exp`
10×	`pow1`
8×	`associate-/r/`
7×	`cbrt-undiv` `associate-/r` `associate-r*`
6×	`flip3-+` `sqrt-div` `associate-l` `flip-+`
5×	`prod-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `hypot-def`
1×	`rem-sqrt-square` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 182

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
48.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
20.0ms	(* (sqrt x) (sqrt (+ x 1)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (+ x 1))
70.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
190.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
58.0ms	(* (sqrt x) (sqrt (+ x 1)))

simplify1.2m

Counts

194 → 194

Iterations

Iter	Nodes
3	7851
2	1793
1	591
0	243

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(fma (+ x 1) (sqrt x) (* (sqrt (+ x 1)) x))
0.1b	(* (sqrt (+ x 1)) x)
0.3b	(/ 1 (fma (+ x 1) (sqrt x) (* (sqrt (+ x 1)) x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac` `sqrt-prod`
8×	`pow1` `add-cbrt-cube`
7×	`associate-l`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-/l`
2×	`flip3-+` `div-exp` `associate-*l/` `flip-+` `hypot-def` `distribute-lft-out` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 94

Calls

4 calls:

4.0ms	(sqrt (+ x 1))
0.0ms	(fma (+ x 1) (sqrt x) (* (sqrt (+ x 1)) x))
14.0ms	(* (sqrt (+ x 1)) x)
4.0ms	(/ 1 (fma (+ x 1) (sqrt x) (* (sqrt (+ x 1)) x)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ x 1))
97.0ms	(fma (+ x 1) (sqrt x) (* (sqrt (+ x 1)) x))
45.0ms	(* (sqrt (+ x 1)) x)
133.0ms	(/ 1 (fma (+ x 1) (sqrt x) (* (sqrt (+ x 1)) x)))

simplify5.7s

Counts

106 → 106

Iterations

Iter	Nodes
4	5975
3	1878
2	695
1	305
0	153

prune606.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

651.0ms	1118×	body	1280	valid
575.0ms	8086×	body	80	nan
441.0ms	1853×	body	640	valid
301.0ms	4080×	body	80	valid
109.0ms	649×	body	320	valid
34.0ms	300×	body	160	valid