Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
6.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	16×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify32.0ms

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: 12.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b	(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:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
13.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
60.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: 3 (433.0ms)

Iter	Nodes	Cost
0	136	1755
1	296	1489
2	854	1391
3	2975	1379
done	5001	1379

prune379.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma 4.0 (pow p 2) (* x x))))
0.4b	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))))
0.4b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
14.9b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

3.0ms	(/ x (sqrt (fma 4.0 (pow p 2) (* x x))))
39.0ms	(log (exp (+ 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)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ x (sqrt (fma 4.0 (pow p 2) (* x x))))
80.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))))
79.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))))
62.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.2s

Counts

104 → 104

Iterations

Useful iterations: 4 (400.0ms)

Iter	Nodes	Cost
0	130	1688
1	228	1514
2	431	1419
3	881	1419
4	1999	1418
done	5000	1418

prune401.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (fma 4.0 (pow p 2) (* x x))))
0.2b	(* x (/ 1 (sqrt (fma 4.0 (pow p 2) (* x x)))))
3.0b	(+ 1.0 (* x (/ 1 (sqrt (fma 4.0 (pow p 2) (* x x))))))
14.9b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
26×	`sqrt-prod`
22×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 127

Calls

4 calls:

3.0ms	(/ 1 (sqrt (fma 4.0 (pow p 2) (* x x))))
12.0ms	(* x (/ 1 (sqrt (fma 4.0 (pow p 2) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma 4.0 (pow p 2) (* x x))))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 1 (sqrt (fma 4.0 (pow p 2) (* x x))))
60.0ms	(* x (/ 1 (sqrt (fma 4.0 (pow p 2) (* x x)))))
74.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma 4.0 (pow p 2) (* x x))))))
62.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify2.1s

Counts

139 → 139

Iterations

Useful iterations: 3 (285.0ms)

Iter	Nodes	Cost
0	147	2235
1	319	1821
2	618	1689
3	1397	1686
4	3606	1686
done	5000	1686

prune379.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))) 1.0)
14.9b	(sqrt (fma 4.0 (pow p 2) (* x x)))
14.9b	(sqrt (fma 4.0 (pow p 2) (* x x)))
14.9b	(sqrt (fma 4.0 (pow p 2) (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
74×	`times-frac`
66×	`prod-diff`
46×	`sqrt-prod`
22×	`fma-neg`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 151

Calls

4 calls:

24.0ms	(- (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))) 1.0)
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:

78.0ms	(- (/ x (sqrt (fma 4.0 (pow p 2) (* x x)))) 1.0)
59.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
60.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))
56.0ms	(sqrt (fma 4.0 (pow p 2) (* x x)))

simplify1.0s

Counts

163 → 163

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	165	3975
1	303	3167
2	617	2862
3	1617	2522
done	5000	2321

prune522.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

regimes171.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	51
1	27	51
done	27	51

end0.0ms

sample843.0ms

Algorithm

intervals

Results

218.0ms	5999×	body	80	valid
177.0ms	801×	body	2560	valid
114.0ms	642×	body	1280	valid
106.0ms	8000×	pre	80	true
46.0ms	317×	body	640	valid
16.0ms	156×	body	320	valid
6.0ms	85×	body	160	valid