Details

sample128.0ms

Algorithm

intervals

Results

66.0ms	78×	body	1280	valid
24.0ms	48×	body	640	valid
10.0ms	31×	body	320	valid
8.0ms	15×	body	2560	valid
5.0ms	70×	body	80	valid
2.0ms	14×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
0.7b	(+ x (hypot 1 x))
4.0b	(log (+ x (hypot 1 x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

0.0ms	(hypot 1 x)
6.0ms	(+ x (hypot 1 x))
5.0ms	(log (+ x (hypot 1 x)))

series366.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(hypot 1 x)
75.0ms	(+ x (hypot 1 x))
208.0ms	(log (+ x (hypot 1 x)))

simplify1.8s

Counts

56 → 56

Iterations

Iter	Nodes
done	5010
3	2035
2	666
1	244
0	108

prune299.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* (* x x) x) -1/6 x)
0.1b	(* (* x x) x)
17.6b	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma (* (* x x) x) -1/6 x)
25.0ms	(* (* x x) x)
1.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

series239.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(fma (* (* x x) x) -1/6 x)
42.0ms	(* (* x x) x)
86.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

simplify1.8s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
3	1430
2	359
1	134
0	71

prune231.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1/16 (pow x 5))
0.5b	(/ 1/8 (* x x))
14.6b	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
21.0b	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

1355×	`times-frac`
775×	`add-sqr-sqrt`
754×	`*-un-lft-identity`
737×	`add-cube-cbrt`
625×	`prod-diff`
240×	`unpow-prod-down`
131×	`div-inv`
82×	`sqr-pow`
25×	`fma-neg`
15×	`add-exp-log`
12×	`difference-of-squares`
11×	`add-cbrt-cube`
8×	`associate-/r*`
6×	`log-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-div` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`cbrt-undiv` `frac-add` `distribute-lft-out`
2×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `flip--`
1×	`pow-to-exp` `sub-neg` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `prod-exp` `log-pow` `cbrt-unprod` `flip-+`

Counts

4 → 775

Calls

4 calls:

7.0ms	(/ 1/16 (pow x 5))
8.0ms	(/ 1/8 (* x x))
198.0ms	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
114.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1/16 (pow x 5))
28.0ms	(/ 1/8 (* x x))
127.0ms	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
171.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

simplify2.1s

Counts

787 → 787

Iterations

Iter	Nodes
done	5000
1	2323
0	1032

prune4.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch104.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	0.00749865384513097
10	-26711381.42537418	-6.803810524357175e-07	-1.0467443314953524

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	2363×	body	1280	valid
567.0ms	1540×	body	640	valid
451.0ms	774×	body	2560	valid
235.0ms	785×	body	320	valid
106.0ms	2145×	body	80	valid
78.0ms	393×	body	160	valid