Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	244×	body	80	valid
1.0ms	4×	body	1280	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	10	8
2	11	8
done	11	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

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` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

22.0ms

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

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify4.0s

Counts

20 → 20

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	33	213
1	89	204
2	226	185
3	515	185
4	1428	185
5	3947	185
done	5000	185

prune70.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.3b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite209.0ms

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` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 121

Calls

4 calls:

11.0ms	(+ x (/ (fabs (- y x)) 2.0))
33.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
20.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
141.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ x (/ (fabs (- y x)) 2.0))
70.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
62.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
28.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify2.4s

Counts

133 → 133

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	135	2667
1	284	1909
2	787	1765
3	2441	1708
done	5000	1674

prune336.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.3b	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`associate-r`
16×	`add-sqr-sqrt`
14×	`sqrt-div`
12×	`cbrt-prod` `add-cube-cbrt` `sqrt-prod`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`cbrt-div` `associate-*r/`
9×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`pow1/3` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

44.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
123.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
9.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
10.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
90.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
62.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
59.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.5s

Counts

106 → 106

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	260	3520
1	657	3271
2	2027	2997
done	5001	2867

prune619.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.2b	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
0.6b	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

121×	`sqrt-prod`
74×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
36×	`sqrt-div`
29×	`unpow-prod-down` `cube-prod`
26×	`associate-r`
25×	`add-cube-cbrt`
24×	`unswap-sqr`
12×	`pow1` `sqrt-pow1`
10×	`add-exp-log` `associate-l`
9×	`flip3-+` `flip-+`
8×	`cube-div`
7×	`add-cbrt-cube` `distribute-lft-out`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate-r/` `associate-l/` `pow-exp`
1×	`*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 177

Calls

4 calls:

19.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
21.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
195.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
34.0ms	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

series292.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
60.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
28.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
142.0ms	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

simplify1.0s

Counts

189 → 189

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	237	5011
1	591	4380
2	1997	3410
done	5000	3243

prune528.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes139.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8
done	8	8

end0.0ms

sample760.0ms

Algorithm

intervals

Results

354.0ms	7722×	body	80	valid
49.0ms	56×	body	2560	valid
18.0ms	101×	body	1280	valid
10.0ms	66×	body	640	valid
4.0ms	35×	body	320	valid
2.0ms	21×	body	160	valid