Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	241×	body	80	valid
1.0ms	5×	body	1280	valid
0.0ms	5×	body	320	valid
0.0ms	2×	body	2560	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid

simplify206.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	19	7
3	29	7
4	40	7
5	45	7
6	49	7
7	58	7
8	74	7
9	90	7
10	101	7
11	103	7
12	107	7
13	108	7
done	108	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `associate-+r-` `flip3-+` `div-sub` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 18

Calls

1 calls:

28.0ms

(+ x (/ (- x y) 2.0))

series72.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

(+ x (/ (- x y) 2.0))

simplify2.5s

Counts

21 → 21

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	36	194
1	98	186
2	263	172
3	750	172
4	3556	171
done	5000	171

prune108.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (sqrt x) (sqrt x) (/ (- x y) 2.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (sqrt x) (sqrt x) (/ (- x y) 2.0))

series145.0ms

Counts

1 → 3

Calls

1 calls:

145.0ms

(fma (sqrt x) (sqrt x) (/ (- x y) 2.0))

simplify3.0s

Counts

13 → 13

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	29	170
1	59	127
2	122	108
3	271	106
4	800	106
5	4213	106
done	5000	106

prune34.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))
0.0b	(sqrt (+ x (/ (- x y) 2.0)))
0.0b	(sqrt (+ x (/ (- x y) 2.0)))
0.2b	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

rewrite532.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `hypot-def` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `times-frac` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+r-` `pow-plus` `sqrt-unprod` `div-sub` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 122

Calls

4 calls:

44.0ms	(+ x (/ (- x y) 2.0))
67.0ms	(sqrt (+ x (/ (- x y) 2.0)))
88.0ms	(sqrt (+ x (/ (- x y) 2.0)))
329.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ x (/ (- x y) 2.0))
173.0ms	(sqrt (+ x (/ (- x y) 2.0)))
124.0ms	(sqrt (+ x (/ (- x y) 2.0)))
54.0ms	(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

simplify2.2s

Counts

134 → 134

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	120	2290
1	246	1600
2	669	1490
3	2011	1431
done	5000	1399

prune435.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))
0.0b	(pow (+ x (/ (- x y) 2.0)) 1/2)
0.0b	(sqrt (+ x (/ (- x y) 2.0)))
0.2b	(* (pow (+ x (/ (- x y) 2.0)) 1/2) (sqrt (+ x (/ (- x y) 2.0))))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`sqrt-prod`
10×	`add-exp-log` `unpow-prod-down`
8×	`associate-l`
7×	`pow1` `associate-r`
6×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `pow1/2` `sqrt-div` `log1p-expm1-u` `sqr-pow`
3×	`pow-unpow` `fma-def` `flip3-+` `prod-exp` `flip-+` `unpow1/2`
2×	`pow-to-exp` `sqrt-pow1` `associate-*r/` `pow-exp` `pow-prod-up` `hypot-def`
1×	`+-commutative` `associate-+r-` `rem-sqrt-square` `pow-pow` `times-frac` `sqrt-unprod` `div-sub` `pow-prod-down` `sum-log` `rem-square-sqrt` `pow-sqr` `*-commutative` `cbrt-unprod`

Counts

4 → 102

Calls

4 calls:

37.0ms	(+ x (/ (- x y) 2.0))
54.0ms	(pow (+ x (/ (- x y) 2.0)) 1/2)
53.0ms	(sqrt (+ x (/ (- x y) 2.0)))
345.0ms	(* (pow (+ x (/ (- x y) 2.0)) 1/2) (sqrt (+ x (/ (- x y) 2.0))))

series777.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ x (/ (- x y) 2.0))
523.0ms	(pow (+ x (/ (- x y) 2.0)) 1/2)
137.0ms	(sqrt (+ x (/ (- x y) 2.0)))
61.0ms	(* (pow (+ x (/ (- x y) 2.0)) 1/2) (sqrt (+ x (/ (- x y) 2.0))))

simplify3.5s

Counts

114 → 114

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	153	1771
1	335	1352
2	900	1182
3	3402	1169
done	5001	1157

prune365.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes140.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	9	7
done	9	7

end0.0ms

sample1.2s

Algorithm

intervals

Results

786.0ms	7418×	body	80	valid
36.0ms	237×	body	1280	valid
16.0ms	90×	body	2560	valid
15.0ms	137×	body	640	valid
7.0ms	79×	body	320	valid
3.0ms	42×	body	160	valid