Details

sample106.0ms

Algorithm

intervals

Results

35.0ms	513×	body	80	nan
35.0ms	261×	body	160	nan
18.0ms	256×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
8	2004
7	1307
6	580
5	196
4	68
3	37
2	21
1	17
0	7

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

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:

6.0ms	(+ x (sqrt (fma x x -1)))
2.0ms	(sqrt (fma x x -1))

series139.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(+ x (sqrt (fma x x -1)))
66.0ms	(sqrt (fma x x -1))

simplify889.0ms

Counts

40 → 40

Iterations

Iter	Nodes
done	2003
4	2003
3	1250
2	461
1	172
0	73

prune272.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `flip3-+` `pow-sqr` `flip-+` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `clear-num` `associate-/r` `sum-log` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

29.0ms	(log (+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* (* x x) x))))
15.0ms	(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* (* x x) x)))
19.0ms	(* (* x x) x)
14.0ms	(/ -1/8 (* (* x x) x))

series273.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(log (+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* (* x x) x))))
71.0ms	(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* (* x x) x)))
36.0ms	(* (* x x) x)
75.0ms	(/ -1/8 (* (* x x) x))

simplify890.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	2018
3	2018
2	1195
1	366
0	155

prune807.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize37.0ms

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))

rewrite5.0ms

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:

1.0ms	(cbrt (sqrt (fma x x -1)))
1.0ms	(sqrt (fma x x -1))
1.0ms	(sqrt (fma x x -1))
1.0ms	(sqrt (fma x x -1))

series260.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (sqrt (fma x x -1)))
47.0ms	(sqrt (fma x x -1))
50.0ms	(sqrt (fma x x -1))
48.0ms	(sqrt (fma x x -1))

simplify1.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	2002
4	2002
3	1521
2	507
1	201
0	92

prune655.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	7723×	body	160	nan
1.1s	16421×	body	80	nan
896.0ms	8000×	body	80	valid