Details

sample16.0ms

Algorithm

intervals

Results

5.0ms	240×	body	80	valid
1.0ms	7×	body	1280	valid
0.0ms	4×	body	2560	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	640	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

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

rewrite12.0ms

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:

11.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify3.8s

Counts

20 → 20

Iterations

Useful iterations: 2 (44.0ms)

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

prune68.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

26.0ms	(* (cbrt x) (cbrt x))
2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (cbrt x) (cbrt x))
295.0ms	(cbrt x)
203.0ms	(cbrt x)
287.0ms	(cbrt x)

simplify5.3s

Counts

93 → 93

Iterations

Useful iterations: done (5.3s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	327	423
3	1104	405
4	4523	400
done	5001	390

prune377.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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))))

rewrite178.0ms

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:

19.0ms	(+ x (/ (fabs (- y x)) 2.0))
19.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
29.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
103.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ x (/ (fabs (- y x)) 2.0))
59.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
54.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
28.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify2.5s

Counts

133 → 133

Iterations

Useful iterations: done (2.5s)

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

prune394.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

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))))
0.2b	(* (* (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)))

rewrite256.0ms

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:

67.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
161.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
12.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
12.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
122.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
90.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
82.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.4s

Counts

106 → 106

Iterations

Useful iterations: done (1.4s)

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

prune498.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes157.0ms

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

sample463.0ms

Algorithm

intervals

Results

191.0ms	7725×	body	80	valid
11.0ms	101×	body	1280	valid
10.0ms	48×	body	2560	valid
6.0ms	74×	body	640	valid
3.0ms	40×	body	320	valid
1.0ms	15×	body	160	valid