Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	201×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
2.0ms	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 (+ (* (* 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)))

rewrite60.0ms

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:

15.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
37.0ms	(+ (* (* 4.0 p) p) (* x x))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: 3 (512.0ms)

Iter	Nodes	Cost
0	136	1755
1	296	1489
2	854	1391
3	2981	1379
done	5000	1379

prune362.0ms

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)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
75.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
60.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
60.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.8s

Counts

76 → 76

Iterations

Useful iterations: 4 (220.0ms)

Iter	Nodes	Cost
0	56	984
1	122	906
2	255	840
3	558	818
4	1372	816
5	3819	816
done	5001	816

prune360.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize20.0ms

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)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
57.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
61.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
58.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.8s

Counts

74 → 74

Iterations

Useful iterations: 4 (210.0ms)

Iter	Nodes	Cost
0	56	882
1	122	793
2	255	746
3	558	735
4	1372	734
5	3819	734
done	5001	734

prune343.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (+ 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×	`pow1` `add-cube-cbrt`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

9.0ms	(log (+ 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)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(log (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x))))))
59.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
59.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
57.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.4s

Counts

74 → 74

Iterations

Useful iterations: 5 (523.0ms)

Iter	Nodes	Cost
0	74	1008
1	141	916
2	268	852
3	509	840
4	1065	839
5	2483	837
done	5000	837

prune353.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

regimes165.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample810.0ms

Algorithm

intervals

Results

211.0ms	6089×	body	80	valid
171.0ms	795×	body	2560	valid
108.0ms	604×	body	1280	valid
106.0ms	8000×	pre	80	true
39.0ms	292×	body	640	valid
14.0ms	143×	body	320	valid
5.0ms	77×	body	160	valid