Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	201×	body	80	valid
6.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	39	16
3	46	16
4	48	16
5	50	16
6	51	16
done	51	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.0b	(fma (* 4.0 p) p (* x x))
0.7b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
14.1b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`fma-def`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`div-inv`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `clear-num` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 102

Calls

4 calls:

3.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.0ms	(fma (* 4.0 p) p (* x x))
16.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
43.0ms	(fma (* 4.0 p) p (* x x))
81.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
64.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.1s

Counts

114 → 114

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	117	1452
1	221	1334
2	616	1244
3	2240	1244
done	5000	1244

prune359.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
0.7b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
14.1b	(sqrt (fma (* 4.0 p) p (* x x)))
14.1b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

44×	`fma-def`
36×	`*-un-lft-identity` `times-frac`
34×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
24×	`sqrt-prod`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 102

Calls

4 calls:

16.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
16.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
81.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
65.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
64.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.5s

Counts

114 → 114

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	56	984
1	119	926
2	242	860
3	524	816
4	1273	816
5	3614	816
done	5000	816

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
6.8b	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
14.1b	(sqrt (fma (* 4.0 p) p (* x x)))
14.1b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
52×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
7×	`fma-def`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 128

Calls

4 calls:

12.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
19.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
82.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
63.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
72.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify4.3s

Counts

140 → 140

Iterations

Useful iterations: 3 (819.0ms)

Iter	Nodes	Cost
0	116	3008
1	222	1719
2	735	1576
3	4002	1512
done	5000	1512

prune363.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

14.1b	(sqrt (* (* (cbrt (fma (* 4.0 p) p (* x x))) (cbrt (fma (* 4.0 p) p (* x x)))) (cbrt (fma (* 4.0 p) p (* x x)))))
14.8b	(cbrt (fma (* 4.0 p) p (* x x)))
14.8b	(cbrt (fma (* 4.0 p) p (* x x)))
14.8b	(cbrt (fma (* 4.0 p) p (* x x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 65

Calls

4 calls:

11.0ms	(sqrt (* (* (cbrt (fma (* 4.0 p) p (* x x))) (cbrt (fma (* 4.0 p) p (* x x)))) (cbrt (fma (* 4.0 p) p (* x x)))))
0.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
0.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
1.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (* (* (cbrt (fma (* 4.0 p) p (* x x))) (cbrt (fma (* 4.0 p) p (* x x)))) (cbrt (fma (* 4.0 p) p (* x x)))))
148.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
144.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
144.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

simplify4.1s

Counts

77 → 77

Iterations

Useful iterations: 3 (565.0ms)

Iter	Nodes	Cost
0	80	1160
1	142	1062
2	483	777
3	2762	723
done	5001	723

prune234.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.3b

regimes96.0ms

Accuracy

0% (1.3b remaining)

Error of 13.9b against oracle of 12.7b and baseline of 13.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	18	28
done	18	28

end0.0ms

sample835.0ms

Algorithm

intervals

Results

215.0ms	6089×	body	80	valid
181.0ms	795×	body	2560	valid
109.0ms	8000×	pre	80	true
108.0ms	604×	body	1280	valid
41.0ms	292×	body	640	valid
17.0ms	143×	body	320	valid
5.0ms	77×	body	160	valid