Details

sample55.0ms

Algorithm

intervals

Results

34.0ms

646×

body

valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (+ 3.0 a))

rewrite146.0ms

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:

65.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
35.0ms	(* (* a a) (- 1.0 a))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)
33.0ms	(* (* b b) (+ 3.0 a))

series304.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (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))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)
36.0ms	(* (* b b) (+ 3.0 a))

simplify87.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (77.0ms)

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

prune339.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (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))))) 1.0)
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)))))
0.5b	(* (* b b) (+ 3.0 a))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

7.0ms	(- (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))))) 1.0)
35.0ms	(* (* 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)))))
34.0ms	(* (* b b) (+ 3.0 a))

series321.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (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))))) 1.0)
54.0ms	(* (* a a) (- 1.0 a))
120.0ms	(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)))))
37.0ms	(* (* b b) (+ 3.0 a))

simplify79.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	595	1735
1	2941	1313
2	5001	1286
done	5001	1286

prune337.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (fma a a (* b b)) (* 2 (/ 2.0 2))) (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- 1.0)))
0.1b	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b	(pow (fma a a (* b b)) (* 2 (/ 2.0 2)))
0.5b	(* (* b b) (+ 3.0 a))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`add-sqr-sqrt` `add-cbrt-cube`
8×	`add-cube-cbrt`
7×	`fma-def`
6×	`unpow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `associate-*r/` `flip-+` `fma-udef` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `pow-unpow` `associate-+r+` `pow-pow` `distribute-lft-in` `associate-l` `pow-exp` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

17.0ms	(+ (pow (fma a a (* b b)) (* 2 (/ 2.0 2))) (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- 1.0)))
0.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
3.0ms	(pow (fma a a (* b b)) (* 2 (/ 2.0 2)))
33.0ms	(* (* b b) (+ 3.0 a))

series319.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (pow (fma a a (* b b)) (* 2 (/ 2.0 2))) (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- 1.0)))
46.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
120.0ms	(pow (fma a a (* b b)) (* 2 (/ 2.0 2)))
54.0ms	(* (* b b) (+ 3.0 a))

simplify49.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	382	700
1	1799	630
2	5002	622
done	5002	622

prune342.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (+ 3.0 a))
11.4b	(cbrt (+ (* a a) (* b b)))
11.4b	(cbrt (+ (* a a) (* b b)))
11.4b	(cbrt (+ (* a a) (* b b)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

30.0ms	(* (* b b) (+ 3.0 a))
8.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* b b) (+ 3.0 a))
96.0ms	(cbrt (+ (* a a) (* b b)))
95.0ms	(cbrt (+ (* a a) (* b b)))
94.0ms	(cbrt (+ (* a a) (* b b)))

simplify44.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	284	519
1	1396	477
2	5002	465
done	5002	465

prune351.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes153.0ms

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	29	14
1	31	14
2	31	14
done	31	14

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s

20589×

body

valid