Details

sample88.0ms

Algorithm

intervals

Results

25.0ms	185×	body	80	valid
17.0ms	26×	body	2560	valid
16.0ms	28×	body	1280	valid
10.0ms	256×	pre	80	true
3.0ms	7×	body	640	valid
2.0ms	6×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify78.0ms

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize31.0ms

Local error

Found 3 expressions with local error:

12.4b	(sqrt (fma p (* 4 p) (* x x)))
0.4b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0b	(fma p (* 4 p) (* x x))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 38

Calls

3 calls:

Slowest

1.0ms	(sqrt (fma p (* 4 p) (* x x)))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0ms	(fma p (* 4 p) (* x x))

series213.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

91.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
74.0ms	(sqrt (fma p (* 4 p) (* x x)))
47.0ms	(fma p (* 4 p) (* x x))

simplify544.0ms

Counts: 47 → 47

prune464.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize32.0ms

Local error

Found 4 expressions with local error:

12.4b	(sqrt (fma p (* 4 p) (* x x)))
0.4b	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
0.4b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0b	(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `exp-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-prod` `fma-udef`
2×	`exp-sum`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

Slowest

3.0ms	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
2.0ms	(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series333.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
80.0ms	(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
80.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
50.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify748.0ms

Counts: 73 → 73

prune687.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize41.0ms

Local error

Found 4 expressions with local error:

12.4b	(sqrt (fma p (* 4 p) (* x x)))
12.4b	(sqrt (fma p (* 4 p) (* x x)))
12.4b	(sqrt (fma p (* 4 p) (* x x)))
0.5b	(* (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`cbrt-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
9×	`sqrt-prod`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

Slowest

9.0ms	(* (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

340.0ms	(* (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
61.0ms	(sqrt (fma p (* 4 p) (* x x)))
56.0ms	(sqrt (fma p (* 4 p) (* x x)))
56.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify949.0ms

Counts: 103 → 103

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize29.0ms

Local error

Found 4 expressions with local error:

12.4b	(sqrt (fma p (* 4 p) (* x x)))
12.4b	(sqrt (fma p (* 4 p) (* x x)))
8.6b	(fma (/ x (* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)
0.6b	(* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 121

Calls

4 calls:

Slowest

18.0ms	(* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
0.0ms	(fma (/ x (* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)

series239.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

81.0ms	(fma (/ x (* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)
55.0ms	(sqrt (fma p (* 4 p) (* x x)))
52.0ms	(sqrt (fma p (* 4 p) (* x x)))
51.0ms	(* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))

simplify1.4s

Counts: 133 → 133

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.1b

regimes156.0ms

Accuracy

0% (1.2b remaining)

Error of 14.1b against oracle of 12.9b and baseline of 14.1b

bsearch3.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

993.0ms	6032×	body	80	valid
536.0ms	766×	body	2560	valid
370.0ms	605×	body	1280	valid
271.0ms	8000×	pre	80	true
179.0ms	309×	body	640	valid
48.0ms	156×	body	320	valid
43.0ms	56×	body	5120	valid
15.0ms	76×	body	160	valid