Details

sample92.0ms

Algorithm

intervals

Results

16.0ms	279×	body	80	nan
16.0ms	256×	body	80	valid

simplify79.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	11	14
1	22	12
2	44	11
3	63	11
4	67	11
5	68	11
done	68	11

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ (* x y) (* x z))
1.2b	(+ (+ (* x y) (* x z)) (* y z))
16.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
4×	`pow1` `sum-log`
3×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

3 → 51

Calls

3 calls:

14.0ms	(+ (* x y) (* x z))
41.0ms	(+ (+ (* x y) (* x z)) (* y z))
36.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ (* x y) (* x z))
31.0ms	(+ (+ (* x y) (* x z)) (* y z))
167.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify3.4s

Counts

60 → 60

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	92	853
1	271	652
2	970	584
3	4050	573
done	5000	572

prune333.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (+ z x))
0.5b	(fma z x (* y (+ z x)))
16.6b	(sqrt (fma z x (* y (+ z x))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cube-cbrt`
5×	`add-exp-log` `add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
2×	`associate-*r/`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

20.0ms	(* y (+ z x))
0.0ms	(fma z x (* y (+ z x)))
2.0ms	(sqrt (fma z x (* y (+ z x))))

series195.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* y (+ z x))
26.0ms	(fma z x (* y (+ z x)))
125.0ms	(sqrt (fma z x (* y (+ z x))))

simplify1.6s

Counts

59 → 59

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	90	581
1	214	532
2	637	483
3	2279	479
done	5000	476

prune262.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 17.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
16.6b	(sqrt (fma z x (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

2.0ms	(cbrt y)
2.0ms	(cbrt y)
2.0ms	(cbrt y)
13.0ms	(sqrt (fma z x (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

335.0ms	(cbrt y)
328.0ms	(cbrt y)
300.0ms	(cbrt y)
171.0ms	(sqrt (fma z x (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

simplify4.0s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	65	570
1	133	515
2	329	417
3	940	359
4	3271	356
done	5000	356

prune409.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 17.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma z x (* y (+ z x)))
0.5b	(* (sqrt (sqrt (fma z x (* y (+ z x))))) (sqrt (sqrt (fma z x (* y (+ z x))))))
16.6b	(sqrt (fma z x (* y (+ z x))))
16.6b	(sqrt (fma z x (* y (+ z x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma z x (* y (+ z x)))
24.0ms	(* (sqrt (sqrt (fma z x (* y (+ z x))))) (sqrt (sqrt (fma z x (* y (+ z x))))))
2.0ms	(sqrt (fma z x (* y (+ z x))))
2.0ms	(sqrt (fma z x (* y (+ z x))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma z x (* y (+ z x)))
148.0ms	(* (sqrt (sqrt (fma z x (* y (+ z x))))) (sqrt (sqrt (fma z x (* y (+ z x))))))
165.0ms	(sqrt (fma z x (* y (+ z x))))
203.0ms	(sqrt (fma z x (* y (+ z x))))

simplify1.9s

Counts

129 → 129

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	110	2711
1	199	1644
2	511	1519
3	1942	1452
done	5000	1401

prune466.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.4b

regimes175.0ms

Accuracy

0% (0.1b remaining)

Error of 19.8b against oracle of 19.7b and baseline of 19.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	13
1	17	11
done	17	11

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	7961×	body	80	nan
651.0ms	8000×	body	80	valid