Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	34×	body	2560	valid
7.0ms	185×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	20×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

100.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
47.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
71.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
43.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

453.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
98.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
94.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
92.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts

104 → 104

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	145	1890
1	298	1592
2	764	1504
3	1877	1491
done	5000	1484

prune474.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize32.0ms

Local error

Found 4 expressions with local error:

1.1b	(- 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
2.8b	(/ x (fma (* 4.0 p) p (* x x)))
14.7b	(sqrt (fma (* 4.0 p) p (* x x)))
14.7b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
76×	`add-cube-cbrt`
66×	`prod-diff`
65×	`times-frac`
34×	`sqrt-prod`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-/r` `associate-/l` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

4 → 146

Calls

4 calls:

31.0ms	(- 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
5.0ms	(/ x (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
63.0ms	(/ x (fma (* 4.0 p) p (* x x)))
89.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
84.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify3.4s

Counts

158 → 158

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	258	7107
1	572	6242
2	1352	4654
3	4339	3768
done	5000	3768

prune504.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
3.3b	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
14.7b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`times-frac` `associate-r`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
12×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp` `unswap-sqr`
4×	`prod-exp`
3×	`expm1-log1p-u` `fma-def` `associate-l` `log1p-expm1-u`
2×	`div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `div-inv`

Counts

3 → 80

Calls

3 calls:

21.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
7.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series222.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
85.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
73.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.6s

Counts

89 → 89

Iterations

Useful iterations: 3 (357.0ms)

Iter	Nodes	Cost
0	127	1384
1	290	1107
2	615	1004
3	1452	1001
4	3595	1001
done	5000	1001

prune265.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 14.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
8.2b	(+ 1.0 (* (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (/ 1 (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
14.7b	(sqrt (fma (* 4.0 p) p (* x x)))
14.7b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
31×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv`

Counts

4 → 99

Calls

4 calls:

14.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
10.0ms	(+ 1.0 (* (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (/ 1 (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
109.0ms	(+ 1.0 (* (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (/ 1 (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))))
91.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
94.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.7s

Counts

111 → 111

Iterations

Useful iterations: 3 (744.0ms)

Iter	Nodes	Cost
0	150	2172
1	296	1957
2	819	1803
3	2713	1605
done	5000	1605

prune358.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 14.7b

regimes208.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	48
1	25	48
done	25	48

end0.0ms

sample984.0ms

Algorithm

intervals

Results

228.0ms	6050×	body	80	valid
201.0ms	835×	body	2560	valid
120.0ms	8000×	pre	80	true
112.0ms	568×	body	1280	valid
50.0ms	316×	body	640	valid
18.0ms	161×	body	320	valid
5.0ms	70×	body	160	valid