Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	215×	body	80	valid
6.0ms	18×	body	2560	valid
5.0ms	256×	pre	80	true
2.0ms	9×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	40	16
3	47	16
4	49	16
5	51	16
6	52	16
done	52	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.8b

localize22.0ms

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)
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite46.0ms

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:

7.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.0ms	(fma (* 4.0 p) p (* x x))
33.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
66.0ms	(fma (* 4.0 p) p (* x x))
140.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
94.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.4s

Counts

114 → 114

Iterations

Useful iterations: 3 (533.0ms)

Iter	Nodes	Cost
0	117	1452
1	225	1328
2	665	1266
3	2837	1244
done	5001	1244

prune561.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize28.0ms

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)
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite86.0ms

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:

47.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
29.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
120.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
92.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
86.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: 3 (147.0ms)

Iter	Nodes	Cost
0	56	984
1	120	926
2	275	860
3	682	816
4	1927	816
done	5000	816

prune718.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))) (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))))
5.1b	(+ (/ x (* (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))) (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))))) 1.0)
15.2b	(sqrt (fma (pow p 2) 4.0 (* x x)))
15.2b	(sqrt (fma (pow p 2) 4.0 (* x x)))

rewrite80.0ms

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:

23.0ms	(* (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))) (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))))
47.0ms	(+ (/ x (* (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))) (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))))) 1.0)
2.0ms	(sqrt (fma (pow p 2) 4.0 (* x x)))
2.0ms	(sqrt (fma (pow p 2) 4.0 (* x x)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))) (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))))
128.0ms	(+ (/ x (* (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))) (sqrt (sqrt (fma (pow p 2) 4.0 (* x x)))))) 1.0)
96.0ms	(sqrt (fma (pow p 2) 4.0 (* x x)))
89.0ms	(sqrt (fma (pow p 2) 4.0 (* x x)))

simplify1.4s

Counts

140 → 140

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	116	3008
1	255	1718
2	1222	1576
done	5001	1544

prune593.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
0.0b	(fma (* 4.0 p) p (* x x))
9.9b	(fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

8.0ms	(sqrt (* (fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
0.0ms	(fma (* 4.0 p) p (* x x))
0.0ms	(fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

374.0ms	(sqrt (* (fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
57.0ms	(fma (* 4.0 p) p (* x x))
131.0ms	(fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
99.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.1s

Counts

60 → 60

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	72	781
1	105	732
2	258	641
3	988	641
done	5000	641

prune261.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.7b

regimes77.0ms

Accuracy

0% (0.2b remaining)

Error of 12.7b against oracle of 12.5b and baseline of 12.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	18	32
done	18	32

end0.0ms

sample2.1s

Algorithm

intervals

Results

510.0ms	8000×	pre	80	true
410.0ms	6085×	body	80	valid
338.0ms	746×	body	2560	valid
313.0ms	591×	body	1280	valid
121.0ms	298×	body	640	valid
33.0ms	58×	body	5120	valid
28.0ms	155×	body	320	valid
8.0ms	67×	body	160	valid