Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	249×	body	80	valid
0.0ms	3×	body	1280	valid
0.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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:

6.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify1.5s

Counts

20 → 20

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	33	213
1	89	204
2	199	185
3	464	185
4	1210	185
5	3513	185
done	5000	185

prune49.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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)))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite87.0ms

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:

8.0ms	(+ x (/ (fabs (- y x)) 2.0))
12.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
12.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
51.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ x (/ (fabs (- y x)) 2.0))
51.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
47.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify730.0ms

Counts

133 → 133

Iterations

Useful iterations: done (726.0ms)

Iter	Nodes	Cost
0	135	2667
1	284	1909
2	913	1765
done	5000	1753

prune266.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

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))))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
0.4b	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-div`
112×	`sqrt-prod`
91×	`sqrt-pow1`
69×	`pow1`
60×	`add-sqr-sqrt`
47×	`pow1/2`
42×	`*-un-lft-identity`
39×	`pow-prod-up`
35×	`flip3-+` `flip-+`
32×	`frac-times`
22×	`add-cube-cbrt`
20×	`swap-sqr`
17×	`associate-l`
16×	`associate-*r/`
12×	`pow-prod-down`
11×	`add-exp-log` `associate-r` `pow-sqr` `add-cbrt-cube` `unswap-sqr`
10×	`associate-*l/`
9×	`distribute-lft-out`
4×	`expm1-log1p-u` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`pow2` `pow-plus` `rem-square-sqrt`

Counts

4 → 213

Calls

4 calls:

11.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
11.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
88.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
57.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
50.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
17.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
52.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify958.0ms

Counts

225 → 225

Iterations

Useful iterations: done (951.0ms)

Iter	Nodes	Cost
0	277	7004
1	646	4371
2	1971	3968
done	5000	3964

prune455.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.4b	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
17×	`associate-r`
14×	`sqrt-div`
13×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`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`
3×	`unswap-sqr`
2×	`pow1/3` `associate-l/` `-commutative`

Counts

4 → 95

Calls

4 calls:

27.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
53.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
6.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
71.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
56.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
57.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify658.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	272	3563
1	684	3320
2	2272	3053
done	5000	3053

prune368.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes66.0ms

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

sample296.0ms

Algorithm

intervals

Results

150.0ms	7713×	body	80	valid
8.0ms	94×	body	1280	valid
5.0ms	74×	body	640	valid
5.0ms	46×	body	2560	valid
3.0ms	49×	body	320	valid
1.0ms	27×	body	160	valid