Details

sample126.0ms

Algorithm

intervals

Results

104.0ms

667×

body

valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
4	2005
3	726
2	183
1	56
0	18

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
0.1b	(* (* a a) (- 1 a))
0.3b	(* (* b b) (+ 3 a))
0.3b	(pow (+ (* a a) (* b b)) 2)

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-r`
8×	`fma-def`
6×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `difference-of-squares` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 121

Calls

4 calls:

64.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
49.0ms	(* (* a a) (- 1 a))
41.0ms	(* (* b b) (+ 3 a))
14.0ms	(pow (+ (* a a) (* b b)) 2)

series349.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
76.0ms	(* (* a a) (- 1 a))
59.0ms	(* (* b b) (+ 3 a))
50.0ms	(pow (+ (* a a) (* b b)) 2)

simplify1.1s

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
2	2000
1	735
0	229

prune640.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* b b) (* b b) (fma (* 2 (* a a)) (* b b) (* (* a a) (* a a))))
0.2b	(* (* a a) (* a a))
0.3b	(* (* b b) (+ 3 a))
1.0b	(fma (* 2 (* a a)) (* b b) (* (* a a) (* a a)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
36×	`pow-prod-up`
26×	`pow-prod-down`
22×	`pow-sqr`
21×	`add-cbrt-cube` `add-exp-log`
18×	`pow-plus`
13×	`pow2`
11×	`prod-exp` `cbrt-unprod`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`associate-r` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-l` `associate-r/` `-commutative` `fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `swap-sqr` `flip-+` `distribute-lft-out`

Counts

4 → 115

Calls

4 calls:

0.0ms	(fma (* b b) (* b b) (fma (* 2 (* a a)) (* b b) (* (* a a) (* a a))))
26.0ms	(* (* a a) (* a a))
56.0ms	(* (* b b) (+ 3 a))
1.0ms	(fma (* 2 (* a a)) (* b b) (* (* a a) (* a a)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(fma (* b b) (* b b) (fma (* 2 (* a a)) (* b b) (* (* a a) (* a a))))
66.0ms	(* (* a a) (* a a))
64.0ms	(* (* b b) (+ 3 a))
86.0ms	(fma (* 2 (* a a)) (* b b) (* (* a a) (* a a)))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	2002
3	2002
2	1414
1	391
0	130

prune460.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a a) (- 1 a))
0.1b	(fma (* b b) (* b b) (fma (* 2 (* a a)) (* b b) (pow a 4)))
0.3b	(* (* b b) (+ 3 a))
1.0b	(fma (* 2 (* a a)) (* b b) (pow a 4))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
14×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `associate-l` `*-commutative` `fma-udef` `difference-of-squares` `unswap-sqr`
1×	`flip3-+` `flip3--` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 98

Calls

4 calls:

45.0ms	(* (* a a) (- 1 a))
0.0ms	(fma (* b b) (* b b) (fma (* 2 (* a a)) (* b b) (pow a 4)))
44.0ms	(* (* b b) (+ 3 a))
1.0ms	(fma (* 2 (* a a)) (* b b) (pow a 4))

series264.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* a a) (- 1 a))
76.0ms	(fma (* b b) (* b b) (fma (* 2 (* a a)) (* b b) (pow a 4)))
63.0ms	(* (* b b) (+ 3 a))
66.0ms	(fma (* 2 (* a a)) (* b b) (pow a 4))

simplify1.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	2008
3	2008
2	1930
1	584
0	189

prune508.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2)
0.3b	(* (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))) (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`sqrt-prod`
22×	`pow1`
16×	`*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`flip3-+` `swap-sqr` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube` `associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `unpow-prod-down` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `pow-to-exp` `rem-square-sqrt` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unpow2` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

9.0ms	(pow (+ (* a a) (* b b)) 2)
219.0ms	(* (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))) (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))))
76.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
80.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

series902.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (+ (* a a) (* b b)) 2)
137.0ms	(* (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))) (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))))
195.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
511.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

simplify1.2s

Counts

129 → 129

Iterations

Iter	Nodes
done	2000
3	2000
2	1285
1	409
0	161

prune826.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes339.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	29
1	29
0	20

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.8s

20540×

body

valid