Details

sample106.0ms

Algorithm

intervals

Results

31.0ms	195×	body	80	valid
18.0ms	20×	body	2560	valid
15.0ms	21×	body	1280	valid
12.0ms	256×	pre	80	true
7.0ms	12×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	2×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	48
4	48
3	46
2	40
1	28
0	14

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0b	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
15.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 81

Calls

4 calls:

1.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
4.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
2.0ms	(sqrt (fma p (* 4 p) (* x x)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
68.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
100.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
69.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify767.0ms

Counts

93 → 93

Iterations

Iter	Nodes
4	2334
3	722
2	286
1	157
0	106

prune939.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
0.2b	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
2.4b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
15.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 89

Calls

4 calls:

1.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
10.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
0.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
56.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
82.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
77.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify4.1s

Counts

101 → 101

Iterations

Iter	Nodes
4	3457
3	1324
2	546
1	258
0	128

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0b	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
15.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 81

Calls

4 calls:

2.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
4.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
55.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
101.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
73.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify682.0ms

Counts

93 → 93

Iterations

Iter	Nodes
4	2334
3	722
2	286
1	157
0	106

prune847.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
7.8b	(fma (* (* x (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)
15.0b	(sqrt (fma p (* 4 p) (* x x)))
15.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

37×	`sqrt-prod`
25×	`associate-r`
22×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
11×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `associate-l` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 85

Calls

4 calls:

38.0ms	(* (* x (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
0.0ms	(fma (* (* x (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) (sqrt (/ 1 (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)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* x (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
81.0ms	(fma (* (* x (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)
53.0ms	(sqrt (fma p (* 4 p) (* x x)))
52.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify3.2s

Counts

97 → 97

Iterations

Iter	Nodes
4	5331
3	1959
2	696
1	281
0	130

prune881.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.4b

regimes137.0ms

Accuracy

0% (0.2b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample2.7s

Algorithm

intervals

Results

999.0ms	6035×	body	80	valid
619.0ms	741×	body	2560	valid
339.0ms	605×	body	1280	valid
316.0ms	8000×	pre	80	true
144.0ms	308×	body	640	valid
69.0ms	67×	body	5120	valid
44.0ms	155×	body	320	valid
18.0ms	89×	body	160	valid