Details

sample114.0ms

Algorithm

intervals

Results

44.0ms	261×	body	160	nan
31.0ms	513×	body	80	nan
19.0ms	256×	body	80	valid

simplify21.0s

Counts

1 → 1

Iterations

Iter	Nodes
9	4745
8	1502
7	489
6	252
5	117
4	66
3	35
2	19
1	15
0	7

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (fma x x -1)))
31.9b	(sqrt (fma x x -1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `fma-def` `sqrt-prod`
2×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

5.0ms	(+ x (sqrt (fma x x -1)))
1.0ms	(sqrt (fma x x -1))

series118.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ x (sqrt (fma x x -1)))
51.0ms	(sqrt (fma x x -1))

simplify1.7s

Counts

40 → 40

Iterations

Iter	Nodes
4	2637
3	1022
2	408
1	170
0	73

prune426.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- (fma 2 x (/ -1/8 (* (* x x) x))) (/ 1/2 x)))
0.0b	(- (fma 2 x (/ -1/8 (* (* x x) x))) (/ 1/2 x))
0.1b	(* (* x x) x)
0.4b	(/ -1/8 (* (* x x) x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
43×	`add-cube-cbrt`
39×	`prod-diff`
32×	`times-frac`
24×	`pow1`
19×	`add-exp-log`
18×	`add-cbrt-cube`
6×	`log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`cbrt-undiv` `fma-neg` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `flip3--` `pow-sqr` `flip--` `distribute-lft-out--`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `associate-l` `pow3` `associate--l+` `log-pow` `-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

8.0ms	(log (- (fma 2 x (/ -1/8 (* (* x x) x))) (/ 1/2 x)))
7.0ms	(- (fma 2 x (/ -1/8 (* (* x x) x))) (/ 1/2 x))
16.0ms	(* (* x x) x)
14.0ms	(/ -1/8 (* (* x x) x))

series361.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(log (- (fma 2 x (/ -1/8 (* (* x x) x))) (/ 1/2 x)))
64.0ms	(- (fma 2 x (/ -1/8 (* (* x x) x))) (/ 1/2 x))
54.0ms	(* (* x x) x)
79.0ms	(/ -1/8 (* (* x x) x))

simplify2.5s

Counts

150 → 150

Iterations

Iter	Nodes
3	5063
2	1689
1	644
0	279

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (fma x x -1)))
31.9b	(sqrt (fma x x -1))
31.9b	(sqrt (fma x x -1))
31.9b	(sqrt (fma x x -1))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

2.0ms	(cbrt (sqrt (fma x x -1)))
2.0ms	(sqrt (fma x x -1))
3.0ms	(sqrt (fma x x -1))
3.0ms	(sqrt (fma x x -1))

series347.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (sqrt (fma x x -1)))
72.0ms	(sqrt (fma x x -1))
65.0ms	(sqrt (fma x x -1))
58.0ms	(sqrt (fma x x -1))

simplify2.0s

Counts

77 → 77

Iterations

Iter	Nodes
4	4341
3	1353
2	481
1	199
0	92

prune861.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	7723×	body	160	nan
1.3s	16421×	body	80	nan
821.0ms	8000×	body	80	valid