Details

sample62.0ms

Algorithm

intervals

Results

14.0ms	195×	body	80	valid
12.0ms	26×	body	2560	valid
7.0ms	256×	pre	80	true
5.0ms	16×	body	1280	valid
2.0ms	10×	body	320	valid
1.0ms	5×	body	640	valid
1.0ms	4×	body	160	valid

simplify95.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 p) p (* x x))
0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.9b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
14.7b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite68.0ms

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:

0.0ms	(fma (* 4.0 p) p (* x x))
6.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
54.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (* 4.0 p) p (* x x))
92.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
117.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
112.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.3s

Counts

114 → 114

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	117	1452
1	216	1326
2	467	1244
3	1041	1244
4	3137	1244
done	5000	1244

prune619.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.9b	(+ (log (exp (/ x (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
2.5b	(log (exp (/ x (sqrt (fma (* 4.0 p) p (* x x))))))
14.7b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
52×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
49×	`add-cube-cbrt`
47×	`log-pow`
44×	`exp-prod`
33×	`sqrt-prod`
26×	`fma-def`
8×	`pow1`
6×	`add-exp-log` `log-prod` `associate-/r*` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-+l+` `div-inv` `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` `clear-num` `sum-log` `flip-+`

Counts

4 → 136

Calls

4 calls:

6.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
138.0ms	(+ (log (exp (/ x (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
14.0ms	(log (exp (/ x (sqrt (fma (* 4.0 p) p (* x x))))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
124.0ms	(+ (log (exp (/ x (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
68.0ms	(log (exp (/ x (sqrt (fma (* 4.0 p) p (* x x))))))
112.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify5.5s

Counts

148 → 148

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	162	2024
1	256	1717
2	475	1639
3	852	1639
4	1973	1639
5	4898	1639
done	5000	1639

prune820.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.4b

localize33.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (* (cbrt (fma (* 4.0 p) p (* x x))) (cbrt (fma (* 4.0 p) p (* x x)))))
15.5b	(cbrt (fma (* 4.0 p) p (* x x)))
15.5b	(cbrt (fma (* 4.0 p) p (* x x)))
15.5b	(cbrt (fma (* 4.0 p) p (* x x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 60

Calls

4 calls:

12.0ms	(sqrt (* (cbrt (fma (* 4.0 p) p (* x x))) (cbrt (fma (* 4.0 p) p (* x x)))))
1.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
1.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
2.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

series976.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(sqrt (* (cbrt (fma (* 4.0 p) p (* x x))) (cbrt (fma (* 4.0 p) p (* x x)))))
224.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
270.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
210.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

simplify3.7s

Counts

72 → 72

Iterations

Useful iterations: 5 (1.7s)

Iter	Nodes	Cost
0	69	1016
1	120	855
2	216	779
3	455	750
4	1078	734
5	2975	726
done	5000	726

prune661.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize37.0ms

Local error

Found 4 expressions with local error:

8.2b	(+ (log (exp (/ (/ x (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))))) 1.0)
14.7b	(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)))

rewrite404.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
71×	`fma-def`
69×	`log-pow`
67×	`exp-prod`
52×	`add-sqr-sqrt` `*-un-lft-identity`
49×	`add-cube-cbrt`
42×	`cbrt-prod`
30×	`sqrt-prod`
10×	`div-inv`
9×	`pow1`
5×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `associate-+l+` `log-prod` `sqrt-pow1` `pow1/2`
2×	`distribute-lft-out`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 134

Calls

4 calls:

391.0ms	(+ (log (exp (/ (/ x (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))))) 1.0)
2.0ms	(sqrt (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)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (log (exp (/ (/ x (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))))) 1.0)
103.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
115.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
113.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.7s

Counts

146 → 146

Iterations

Useful iterations: 4 (954.0ms)

Iter	Nodes	Cost
0	64	1559
1	128	1436
2	288	883
3	798	804
4	2863	792
done	5000	792

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.4b

regimes240.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	5977×	body	80	valid
450.0ms	850×	body	2560	valid
385.0ms	638×	body	1280	valid
202.0ms	8000×	pre	80	true
85.0ms	284×	body	640	valid
55.0ms	86×	body	160	valid
34.0ms	165×	body	320	valid