Details

sample121.0ms

Algorithm

intervals

Results

83.0ms

653×

body

valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	18	29
1	53	27
2	172	26
3	509	26
4	1497	26
5	3573	26
done	5000	26

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)))
0.3b	(pow (fma a a (* b b)) 2.0)
1.0b	(* (* b b) (+ 3.0 a))

rewrite75.0ms

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:

1.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
1.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
5.0ms	(pow (fma a a (* b b)) 2.0)
66.0ms	(* (* b b) (+ 3.0 a))

series442.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
58.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
169.0ms	(pow (fma a a (* b b)) 2.0)
59.0ms	(* (* b b) (+ 3.0 a))

simplify4.0s

Counts

77 → 77

Iterations

Useful iterations: 3 (2.4s)

Iter	Nodes	Cost
0	136	1157
1	320	1101
2	1101	970
3	4265	962
done	5000	962

prune311.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* b b) (+ 3.0 a))
1.0b	(* (* b b) (+ 3.0 a))
12.0b	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.0b	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `associate-r`
6×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

36.0ms	(* (* b b) (+ 3.0 a))
38.0ms	(* (* b b) (+ 3.0 a))
2.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* b b) (+ 3.0 a))
42.0ms	(* (* b b) (+ 3.0 a))
239.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
235.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify2.4s

Counts

94 → 94

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	108	1666
1	275	1504
2	951	1360
3	3540	1352
done	5001	1352

prune391.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* b b) (+ 3.0 a))
12.0b	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.5b	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.5b	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

33.0ms	(* (* b b) (+ 3.0 a))
2.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* b b) (+ 3.0 a))
222.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
260.0ms	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
264.0ms	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify2.9s

Counts

79 → 79

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	160	2057
1	390	1962
2	1239	1766
3	4382	1658
done	5000	1658

prune512.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

12.0b	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.0b	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.0b	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.5b	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

261.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
253.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
240.0ms	(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
305.0ms	(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify2.8s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	116	2217
1	256	2024
2	611	1872
3	1660	1808
4	4640	1781
done	5000	1781

prune401.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes173.0ms

Accuracy

0% (0.2b 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	18	53
1	20	53
done	20	53

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.8s

20825×

body

valid