Details

sample55.0ms

Algorithm

intervals

Results

34.0ms

644×

body

valid

simplify81.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	53	14
1	173	13
2	532	12
3	1681	12
4	4278	12
5	5001	12
done	5001	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(* (* b b) (+ 3.0 a))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

26×	`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`
9×	`associate-r`
7×	`fma-def`
6×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

61.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
33.0ms	(* (* a a) (- 1.0 a))
14.0ms	(pow (+ (* a a) (* b b)) 2.0)
30.0ms	(* (* b b) (+ 3.0 a))

series321.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
51.0ms	(* (* a a) (- 1.0 a))
112.0ms	(pow (+ (* a a) (* b b)) 2.0)
39.0ms	(* (* b b) (+ 3.0 a))

simplify95.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	646	990
1	3454	779
2	5001	776
done	5001	776

prune345.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
0.1b	(* (* a a) (- 1.0 a))
0.2b	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.4b	(* (* b b) (+ 3.0 a))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
34×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+l+`
14×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-*r/`
9×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`associate-+r+` `associate-l` `*-commutative` `unswap-sqr`
1×	`+-commutative` `fma-def` `sum-log` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 125

Calls

4 calls:

247.0ms	(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
37.0ms	(* (* a a) (- 1.0 a))
0.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
31.0ms	(* (* b b) (+ 3.0 a))

series269.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
56.0ms	(* (* a a) (- 1.0 a))
125.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
34.0ms	(* (* b b) (+ 3.0 a))

simplify109.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	705	1308
1	3861	1011
2	5001	1006
done	5001	1006

prune446.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (fma a a (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.4b	(pow (fma a a (* b b)) 2.0)
0.4b	(* (* b b) (+ 3.0 a))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

26×	`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`
9×	`associate-r`
7×	`fma-def`
6×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

15.0ms	(+ (pow (fma a a (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
36.0ms	(* (* a a) (- 1.0 a))
3.0ms	(pow (fma a a (* b b)) 2.0)
31.0ms	(* (* b b) (+ 3.0 a))

series318.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (pow (fma a a (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
52.0ms	(* (* a a) (- 1.0 a))
119.0ms	(pow (fma a a (* b b)) 2.0)
35.0ms	(* (* b b) (+ 3.0 a))

simplify89.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	644	950
1	3442	745
2	5002	742
done	5002	742

prune337.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (+ 3.0 a))
18.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-l` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

33.0ms	(* (* b b) (+ 3.0 a))
8.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series509.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* b b) (+ 3.0 a))
156.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
160.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
154.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify38.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	270	642
1	1138	585
2	5001	579
done	5001	579

prune334.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	20
1	26	20
done	26	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

979.0ms

20599×

body

valid