Details

sample49.0ms

Algorithm

intervals

Results

32.0ms

620×

body

valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	158	28
3	443	28
4	1206	28
5	3442	28
done	5000	28

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.1b	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.3b	(pow (fma a a (* b b)) 2.0)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
1.0ms	(pow (fma a a (* b b)) 2.0)
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
94.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
116.0ms	(pow (fma a a (* b b)) 2.0)
50.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify641.0ms

Counts

84 → 84

Iterations

Useful iterations: done (639.0ms)

Iter	Nodes	Cost
0	160	1452
1	383	1411
2	1371	1221
done	5000	1218

prune289.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
24.8b	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
24.8b	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
24.8b	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
7.0ms	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
8.0ms	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
176.0ms	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
176.0ms	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
173.0ms	(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

simplify620.0ms

Counts

84 → 84

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	162	1874
1	413	1809
2	1496	1622
done	5000	1487

prune416.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
10.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
0.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
0.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
255.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
250.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
250.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify2.9s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	144	2483
1	352	2463
2	1225	2202
3	4955	2028
done	5000	2028

prune389.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
9.6b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

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

series919.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
212.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
249.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
247.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify694.0ms

Counts

68 → 68

Iterations

Useful iterations: done (692.0ms)

Iter	Nodes	Cost
0	116	2438
1	252	2296
2	657	2112
3	2020	1994
done	5001	1990

prune360.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes151.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	51
1	24	51
done	24	51

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

20313×

body

valid