Details

sample33.0ms

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

simplify38.0ms

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

16.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
7.0ms	(+ (* (* 4.0 p) p) (* x x))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
40.0ms	(+ (* (* 4.0 p) p) (* x x))
82.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts

103 → 103

Iterations

Useful iterations: 3 (508.0ms)

Iter	Nodes	Cost
0	136	1755
1	296	1489
2	917	1391
3	4072	1379
done	5000	1379

prune363.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
0.7b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `fma-def` `sqrt-prod`
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-+` `distribute-lft-out`

Counts

4 → 64

Calls

4 calls:

9.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
9.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
80.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
61.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
59.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify2.2s

Counts

76 → 76

Iterations

Useful iterations: 4 (241.0ms)

Iter	Nodes	Cost
0	56	984
1	122	906
2	258	840
3	586	818
4	1507	816
5	4560	816
done	5000	816

prune343.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

9.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
54.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
60.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
58.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: 4 (241.0ms)

Iter	Nodes	Cost
0	56	882
1	122	793
2	258	746
3	586	735
4	1507	734
5	4560	734
done	5000	734

prune335.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))
14.1b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

16.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
56.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
54.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
60.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: 4 (229.0ms)

Iter	Nodes	Cost
0	56	882
1	122	793
2	258	746
3	586	735
4	1507	734
5	4560	734
done	5000	734

prune341.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.3b

regimes150.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	18	32
done	18	32

end0.0ms

sample785.0ms

Algorithm

intervals

Results

206.0ms	6089×	body	80	valid
172.0ms	795×	body	2560	valid
102.0ms	604×	body	1280	valid
101.0ms	8000×	pre	80	true
39.0ms	292×	body	640	valid
14.0ms	143×	body	320	valid
5.0ms	77×	body	160	valid