Details

sample91.0ms

Algorithm

intervals

Results

20.0ms	35×	body	2560	valid
16.0ms	175×	body	80	valid
11.0ms	25×	body	1280	valid
7.0ms	256×	pre	80	true
4.0ms	12×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify127.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize38.0ms

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))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite283.0ms

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:

36.0ms	(+ (* (* 4.0 p) p) (* x x))
62.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
121.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* (* 4.0 p) p) (* x x))
121.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
143.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
108.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.6s

Counts

103 → 103

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	136	1755
1	323	1492
2	1484	1412
done	5001	1402

prune944.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (fma (* 4.0 p) p (pow x 2))))
0.2b	(* x (/ 1 (sqrt (fma (* 4.0 p) p (pow x 2)))))
3.8b	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (pow x 2))))))
14.3b	(sqrt (fma (* 4.0 p) p (pow x 2)))

rewrite106.0ms

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:

16.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (pow x 2))))
53.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (pow x 2)))))
23.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (pow x 2))))))
4.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (pow x 2))))
103.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (pow x 2)))))
140.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (pow x 2))))))
113.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

simplify1.2s

Counts

139 → 139

Iterations

Useful iterations: 2 (319.0ms)

Iter	Nodes	Cost
0	148	2235
1	344	1904
2	1314	1698
done	5000	1698

prune890.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2))))))
0.7b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2)))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2)))))))
14.3b	(sqrt (fma (* 4.0 p) p (pow x 2)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

87.0ms	(exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2))))))
28.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2)))))
96.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2)))))))
3.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2))))))
137.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2)))))
126.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (pow x 2)))))))
107.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

simplify2.0s

Counts

79 → 79

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	87	1116
1	178	1031
2	591	931
3	2863	920
done	5001	919

prune635.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))
10.1b	(+ 1.0 (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.3b	(sqrt (fma (* 4.0 p) p (pow x 2)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
31×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
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` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 102

Calls

4 calls:

13.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))
213.0ms	(+ 1.0 (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
38.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (pow x 2)))))
218.0ms	(+ 1.0 (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (pow x 2))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
86.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
92.0ms	(sqrt (fma (* 4.0 p) p (pow x 2)))

simplify1.3s

Counts

114 → 114

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	181	2270
1	403	1773
2	1621	1688
done	5000	1687

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.7b

regimes251.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	19	18
done	19	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

964.0ms	6020×	body	80	valid
462.0ms	802×	body	2560	valid
319.0ms	622×	body	1280	valid
279.0ms	8000×	pre	80	true
82.0ms	287×	body	640	valid
57.0ms	46×	body	5120	valid
33.0ms	142×	body	320	valid
12.0ms	81×	body	160	valid