Details

sample99.0ms

Algorithm

intervals

Results

78.0ms

632×

body

valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
6	4855
5	1985
4	584
3	159
2	60
1	27
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma b b (* a a))
0.0b	(fma b b (* a a))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

3 → 30

Calls

3 calls:

0.0ms	(fma b b (* a a))
0.0ms	(fma b b (* a a))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

series208.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(fma b b (* a a))
45.0ms	(fma b b (* a a))
122.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) (fma (* b b) 4 -1))

simplify1.3s

Counts

39 → 39

Iterations

Iter	Nodes
4	2645
3	668
2	187
1	68
0	40

prune398.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a))))
0.2b	(fma (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (fma b b (* a a)) (fma (* b b) 4 -1))
8.7b	(sqrt (fma b b (* a a)))
8.7b	(sqrt (fma b b (* a a)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `fma-udef`
2×	`rem-sqrt-square` `hypot-def`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

13.0ms	(* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a))))
0.0ms	(fma (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (fma b b (* a a)) (fma (* b b) 4 -1))
2.0ms	(sqrt (fma b b (* a a)))
2.0ms	(sqrt (fma b b (* a a)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a))))
107.0ms	(fma (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (fma b b (* a a)) (fma (* b b) 4 -1))
70.0ms	(sqrt (fma b b (* a a)))
65.0ms	(sqrt (fma b b (* a a)))

simplify4.0s

Counts

105 → 105

Iterations

Iter	Nodes
4	8147
3	1411
2	379
1	142
0	84

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a))))
0.2b	(fma (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (fma b b (* a a)) (fma (* b b) 4 -1))
8.7b	(sqrt (fma b b (* a a)))
8.7b	(sqrt (fma b b (* a a)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `fma-udef`
2×	`rem-sqrt-square` `hypot-def`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

12.0ms	(* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a))))
0.0ms	(fma (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (fma b b (* a a)) (fma (* b b) 4 -1))
1.0ms	(sqrt (fma b b (* a a)))
1.0ms	(sqrt (fma b b (* a a)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a))))
141.0ms	(fma (* (sqrt (fma b b (* a a))) (sqrt (fma b b (* a a)))) (fma b b (* a a)) (fma (* b b) 4 -1))
376.0ms	(sqrt (fma b b (* a a)))
52.0ms	(sqrt (fma b b (* a a)))

simplify4.1s

Counts

105 → 105

Iterations

Iter	Nodes
4	8147
3	1411
2	379
1	142
0	84

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt (fma b b (* a a)))) (* (sqrt (sqrt (fma b b (* a a)))) (sqrt (fma b b (* a a)))))
8.7b	(sqrt (fma b b (* a a)))
8.7b	(sqrt (fma b b (* a a)))
8.7b	(sqrt (fma b b (* a a)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-pow1`
41×	`pow1`
30×	`pow-prod-up`
26×	`pow1/2`
19×	`sqrt-prod`
15×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-cbrt-cube` `associate-l` `add-exp-log`
7×	`pow-prod-down`
4×	`expm1-log1p-u` `pow-plus` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod` `fma-udef` `hypot-def`
2×	`sqrt-unprod` `cube-unmult`
1×	`associate-r` `*-commutative`

Counts

4 → 95

Calls

4 calls:

30.0ms	(* (sqrt (sqrt (fma b b (* a a)))) (* (sqrt (sqrt (fma b b (* a a)))) (sqrt (fma b b (* a a)))))
1.0ms	(sqrt (fma b b (* a a)))
2.0ms	(sqrt (fma b b (* a a)))
2.0ms	(sqrt (fma b b (* a a)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt (sqrt (fma b b (* a a)))) (* (sqrt (sqrt (fma b b (* a a)))) (sqrt (fma b b (* a a)))))
69.0ms	(sqrt (fma b b (* a a)))
81.0ms	(sqrt (fma b b (* a a)))
78.0ms	(sqrt (fma b b (* a a)))

simplify943.0ms

Counts

107 → 107

Iterations

Iter	Nodes
4	2178
3	627
2	349
1	200
0	83

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
1	11
0	11

end0.0ms

sample3.5s

Algorithm

intervals

Results

3.1s

20616×

body

valid