Details

sample324.0ms

Algorithm

intervals

Results

90.0ms	67×	body	10240	exit
89.0ms	54×	body	640	valid
56.0ms	52×	body	1280	valid
54.0ms	311×	body	80	valid
11.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1436
3	398
2	124
1	49
0	19

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma eps x x))
0.0b	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps))))
0.0b	(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
4.7b	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

403×	`add-sqr-sqrt`
327×	`times-frac`
298×	`*-un-lft-identity`
180×	`prod-diff`
143×	`add-cube-cbrt`
104×	`difference-of-squares`
60×	`fma-udef`
58×	`exp-sum`
51×	`difference-of-sqr-1`
35×	`distribute-lft-out--`
21×	`div-inv`
14×	`associate-/l*`
7×	`add-log-exp`
6×	`add-cbrt-cube`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `fma-neg`
2×	`flip3--` `div-sub` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `associate--l+` `associate--r-` `rem-exp-log`

Counts

4 → 321

Calls

4 calls:

2.0ms	(exp (fma eps x x))
0.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps))))
26.0ms	(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
56.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(exp (fma eps x x))
44.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps))))
48.0ms	(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
159.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

simplify2.8s

Counts

333 → 333

Iterations

Iter	Nodes
done	5000
2	3327
1	1310
0	511

prune2.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 2 (* x x))
0.4b	(* x 2/3)
7.0b	(fma (* x x) (* x 2/3) (- 2 (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `prod-diff` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

9.0ms	(- 2 (* x x))
11.0ms	(* x 2/3)
1.0ms	(fma (* x x) (* x 2/3) (- 2 (* x x)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(- 2 (* x x))
34.0ms	(* x 2/3)
61.0ms	(fma (* x x) (* x 2/3) (- 2 (* x x)))

simplify2.0s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	1733
2	555
1	216
0	89

prune320.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 2 (* x x))
0.4b	(* x 2/3)
7.0b	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) (- 2 (* x x)))
60.3b	(posit16->real (real->posit16 (* x 2/3)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `remove-posit16` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

9.0ms	(- 2 (* x x))
10.0ms	(* x 2/3)
0.0ms	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) (- 2 (* x x)))
1.0ms	(posit16->real (real->posit16 (* x 2/3)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- 2 (* x x))
26.0ms	(* x 2/3)
54.0ms	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) (- 2 (* x x)))
20.0ms	(posit16->real (real->posit16 (* x 2/3)))

simplify3.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	5009
3	2524
2	644
1	227
0	100

prune659.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
7.0b	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) (fma (* (cbrt 2) (cbrt 2)) (cbrt 2) (- (* x x))))
60.3b	(posit16->real (real->posit16 (* x 2/3)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`
1×	`fma-udef` `remove-posit16`

Counts

4 → 50

Calls

4 calls:

6.0ms	(cbrt 2)
1.0ms	(cbrt 2)
0.0ms	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) (fma (* (cbrt 2) (cbrt 2)) (cbrt 2) (- (* x x))))
0.0ms	(posit16->real (real->posit16 (* x 2/3)))

series117.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
96.0ms	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) (fma (* (cbrt 2) (cbrt 2)) (cbrt 2) (- (* x x))))
20.0ms	(posit16->real (real->posit16 (* x 2/3)))

simplify3.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
4	3133
3	599
2	188
1	82
0	54

prune519.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes121.0ms

Accuracy

96% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.2b

bsearch232.0ms

Steps

Iters	Range		Point
8	0.003724545156938161	2.2608459371195293	2.224816812712469

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample11.9s

Algorithm

intervals

Results

3.9s	1987×	body	10240	exit
3.4s	9884×	body	80	valid
2.4s	1758×	body	1280	valid
1.2s	1276×	body	640	valid
443.0ms	637×	body	320	valid
142.0ms	333×	body	160	valid