Details

sample71.0ms

Algorithm

intervals

Results

17.0ms	202×	body	80	valid
12.0ms	9×	body	640	valid
12.0ms	21×	body	2560	valid
8.0ms	256×	pre	80	true
7.0ms	16×	body	1280	valid
1.0ms	5×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	50
4	50
3	48
2	42
1	30
0	14

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma p (* 4 p) (* x x))
0.0b	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.4b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
17.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`fma-udef`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 80

Calls

4 calls:

0.0ms	(fma p (* 4 p) (* x x))
7.0ms	(/ 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)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma p (* 4 p) (* x x))
86.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
107.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
80.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify830.0ms

Counts

92 → 92

Iterations

Iter	Nodes
4	2387
3	769
2	311
1	167
0	108

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.7b

localize34.0ms

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)))))
2.1b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
17.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite32.0ms

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` `insert-posit16` `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 → 93

Calls

4 calls:

1.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
27.0ms	(* 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)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
75.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
89.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
66.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify1.3s

Counts

105 → 105

Iterations

Iter	Nodes
4	2792
3	1170
2	532
1	263
0	132

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma p (* p 4) (* x x))))
0.2b	(log (exp (sqrt (fma 0.5 (/ x (sqrt (fma p (* p 4) (* x x)))) 0.5))))
0.4b	(fma 0.5 (/ x (sqrt (fma p (* p 4) (* x x)))) 0.5)
17.0b	(sqrt (fma p (* p 4) (* x x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
7×	`log-pow`
6×	`pow1` `exp-prod` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-/l*`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `fma-udef` `div-inv`

Counts

4 → 90

Calls

4 calls:

5.0ms	(/ x (sqrt (fma p (* p 4) (* x x))))
3.0ms	(log (exp (sqrt (fma 0.5 (/ x (sqrt (fma p (* p 4) (* x x)))) 0.5))))
0.0ms	(fma 0.5 (/ x (sqrt (fma p (* p 4) (* x x)))) 0.5)
1.0ms	(sqrt (fma p (* p 4) (* x x)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ x (sqrt (fma p (* p 4) (* x x))))
239.0ms	(log (exp (sqrt (fma 0.5 (/ x (sqrt (fma p (* p 4) (* x x)))) 0.5))))
107.0ms	(fma 0.5 (/ x (sqrt (fma p (* p 4) (* x x)))) 0.5)
52.0ms	(sqrt (fma p (* p 4) (* x x)))

simplify690.0ms

Counts

102 → 102

Iterations

Iter	Nodes
4	2140
3	665
2	303
1	187
0	131

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.7b

localize49.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (exp (sqrt (fma 0.5 (/ x (* (sqrt (sqrt (fma p (* p 4) (* x x)))) (sqrt (sqrt (fma p (* p 4) (* x x)))))) 0.5))))
6.2b	(fma 0.5 (/ x (* (sqrt (sqrt (fma p (* p 4) (* x x)))) (sqrt (sqrt (fma p (* p 4) (* x x)))))) 0.5)
17.0b	(sqrt (fma p (* p 4) (* x x)))
17.0b	(sqrt (fma p (* p 4) (* x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series545.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(log (exp (sqrt (fma 0.5 (/ x (* (sqrt (sqrt (fma p (* p 4) (* x x)))) (sqrt (sqrt (fma p (* p 4) (* x x)))))) 0.5))))
112.0ms	(fma 0.5 (/ x (* (sqrt (sqrt (fma p (* p 4) (* x x)))) (sqrt (sqrt (fma p (* p 4) (* x x)))))) 0.5)
76.0ms	(sqrt (fma p (* p 4) (* x x)))
74.0ms	(sqrt (fma p (* p 4) (* x x)))

simplify6.2s

Counts

76 → 76

Iterations

Iter	Nodes
5	8400
4	1497
3	390
2	167
1	106
0	80

prune869.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.7b

regimes243.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	15
1	15
0	13

end0.0ms

sample2.7s

Algorithm

intervals

Results

707.0ms	5992×	body	80	valid
595.0ms	8000×	pre	80	true
573.0ms	738×	body	2560	valid
378.0ms	672×	body	1280	valid
138.0ms	293×	body	640	valid
53.0ms	174×	body	320	valid
39.0ms	54×	body	5120	valid
16.0ms	77×	body	160	valid