Details

sample83.0ms

Algorithm

intervals

Results

58.0ms

665×

body

valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	18	29
1	53	27
2	172	26
3	554	26
4	2113	26
done	5001	26

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
0.1b	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.4b	(pow (fma a a (* b b)) 2.0)
1.1b	(* (* b b) (+ 3.0 a))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
0.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
3.0ms	(pow (fma a a (* b b)) 2.0)
51.0ms	(* (* b b) (+ 3.0 a))

series421.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
84.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
175.0ms	(pow (fma a a (* b b)) 2.0)
50.0ms	(* (* b b) (+ 3.0 a))

simplify2.3s

Counts

77 → 77

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	136	1157
1	366	1105
2	2153	971
done	5004	969

prune431.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma 1.0 (pow a 2) (* 3.0 (pow b 2))) (pow a 3))
0.1b	(fma (- (fma 1.0 (pow a 2) (* 3.0 (pow b 2))) (pow a 3)) 4.0 (pow (fma a a (* b b)) 2.0))
0.2b	(* 3.0 (pow b 2))
0.4b	(pow (fma a a (* b b)) 2.0)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
36×	`prod-diff`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
17×	`unpow-prod-down`
10×	`add-exp-log` `cube-prod`
8×	`associate-r`
7×	`sqr-pow`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
3×	`cube-mult` `pow-unpow` `fma-neg` `unpow3` `associate-l` `prod-exp`
2×	`pow-to-exp` `pow-exp` `fma-udef` `unpow2`
1×	`sub-neg` `flip3--` `pow-pow` `diff-log` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 117

Calls

4 calls:

14.0ms	(- (fma 1.0 (pow a 2) (* 3.0 (pow b 2))) (pow a 3))
0.0ms	(fma (- (fma 1.0 (pow a 2) (* 3.0 (pow b 2))) (pow a 3)) 4.0 (pow (fma a a (* b b)) 2.0))
22.0ms	(* 3.0 (pow b 2))
5.0ms	(pow (fma a a (* b b)) 2.0)

series340.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (fma 1.0 (pow a 2) (* 3.0 (pow b 2))) (pow a 3))
125.0ms	(fma (- (fma 1.0 (pow a 2) (* 3.0 (pow b 2))) (pow a 3)) 4.0 (pow (fma a a (* b b)) 2.0))
32.0ms	(* 3.0 (pow b 2))
130.0ms	(pow (fma a a (* b b)) 2.0)

simplify3.6s

Counts

129 → 129

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	230	3243
1	548	2662
2	2524	2256
done	5002	1901

prune531.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (fma a a (* b b)) 2.0)
16.4b	(cbrt (pow (fma a a (* b b)) 2.0))
16.4b	(cbrt (pow (fma a a (* b b)) 2.0))
16.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `pow1/3`
1×	`pow-to-exp` `pow-pow` `pow-exp`

Counts

4 → 70

Calls

4 calls:

4.0ms	(pow (fma a a (* b b)) 2.0)
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
3.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series825.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(pow (fma a a (* b b)) 2.0)
206.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
207.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
226.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	82	1147
1	177	1122
2	486	1023
3	1827	1014
done	5001	1011

prune558.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

16.4b	(cbrt (pow (fma a a (* b b)) 2.0))
16.4b	(cbrt (pow (fma a a (* b b)) 2.0))
16.4b	(cbrt (pow (fma a a (* b b)) 2.0))
16.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series872.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
243.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
189.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
188.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.8s

Counts

80 → 80

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	58	1188
1	105	1172
2	228	1064
3	656	1052
4	2741	1052
done	5000	1052

prune745.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes183.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	20	26
done	20	26

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.9s

20473×

body

valid