Details

sample76.0ms

Algorithm

intervals

Results

22.0ms	17×	body	1280	valid
13.0ms	196×	body	80	valid
11.0ms	27×	body	2560	valid
7.0ms	256×	pre	80	true
2.0ms	8×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify94.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 p) p (* x x))
0.2b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
1.0b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
14.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite57.0ms

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:

1.0ms	(fma (* 4.0 p) p (* x x))
13.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
35.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma (* 4.0 p) p (* x x))
112.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
91.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
101.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.5s

Counts

114 → 114

Iterations

Useful iterations: 3 (577.0ms)

Iter	Nodes	Cost
0	117	1452
1	225	1328
2	672	1266
3	2914	1244
done	5001	1244

prune652.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
1.0b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
3.3b	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
14.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

13.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
59.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
18.0ms	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
103.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
255.0ms	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
115.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.3s

Counts

121 → 121

Iterations

Useful iterations: 3 (464.0ms)

Iter	Nodes	Cost
0	132	1735
1	244	1605
2	626	1518
3	2089	1473
done	5000	1473

prune639.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
8.2b	(+ (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
14.0b	(sqrt (fma (* 4.0 p) p (* x x)))
14.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

564×	`sqrt-prod`
549×	`times-frac`
295×	`add-sqr-sqrt` `*-un-lft-identity`
293×	`add-cube-cbrt`
283×	`fma-def`
11×	`div-inv`
9×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `div-exp` `clear-num` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 380

Calls

4 calls:

9.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
275.0ms	(+ (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (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)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
107.0ms	(+ (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
88.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
79.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.3s

Counts

392 → 392

Iterations

Useful iterations: 3 (995.0ms)

Iter	Nodes	Cost
0	150	2157
1	300	1714
2	925	1634
3	4758	1618
done	5000	1618

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (pow 1.0 3) (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3))
14.0b	(sqrt (fma (* 4.0 p) p (* x x)))
14.0b	(sqrt (fma (* 4.0 p) p (* x x)))
14.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`fma-def`
10×	`add-cube-cbrt`
9×	`sqrt-prod`
7×	`pow1` `unpow-prod-down` `cube-prod`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `cube-mult` `flip3-+` `unpow3` `sum-log` `sum-cubes` `flip-+` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

98.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 3))
92.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
89.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
81.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.0s

Counts

88 → 88

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	64	1088
1	151	963
2	561	905
3	3185	905
done	5000	905

prune522.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.4b

regimes181.0ms

Accuracy

0% (3.9b remaining)

Error of 13.4b against oracle of 9.5b and baseline of 13.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	51
1	26	51
done	26	51

end0.0ms

sample2.1s

Algorithm

intervals

Results

675.0ms	719×	body	2560	valid
462.0ms	6025×	body	80	valid
309.0ms	638×	body	1280	valid
211.0ms	8000×	pre	80	true
78.0ms	322×	body	640	valid
36.0ms	169×	body	320	valid
22.0ms	50×	body	5120	valid
9.0ms	77×	body	160	valid