Details

sample57.0ms

Algorithm

intervals

Results

26.0ms	55×	body	1280	valid
9.0ms	143×	body	80	valid
9.0ms	32×	body	640	valid
5.0ms	21×	body	320	valid
1.0ms	5×	body	160	valid

simplify139.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.8b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

8.0ms	(/ x (+ x 1))
28.0ms	(/ (+ x 1) (- x 1))
63.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ x (+ x 1))
41.0ms	(/ (+ x 1) (- x 1))
84.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.5s

Counts

762 → 762

Iterations

Iter	Nodes
done	2001
2	2001
1	1369
0	584

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
2.8b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
2.8b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
2.8b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite846.0ms

Algorithm

rewrite-expression-head

Rules

3664×	`*-un-lft-identity`
2832×	`times-frac`
2392×	`add-sqr-sqrt`
1836×	`prod-diff`
1492×	`add-cube-cbrt`
717×	`distribute-lft-out`
444×	`difference-of-squares`
318×	`associate-/r/`
255×	`distribute-lft-out--`
216×	`difference-of-sqr-1`
159×	`div-inv`
105×	`flip3-+` `flip3--` `flip-+` `flip--`
81×	`frac-times`
63×	`cbrt-div`
54×	`fma-neg`
51×	`frac-sub`
27×	`associate-*l/`
15×	`associate-*r/`
10×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 2053

Calls

4 calls:

441.0ms	(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
91.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
85.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
108.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
117.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
109.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
114.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.6s

Counts

2065 → 2065

Iterations

Iter	Nodes
done	2003
2	2003
1	1726
0	763

prune7.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune12.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(/ 3 (* x (* x x)))
0.3b	(/ 1 (* x x))
9.5b	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
26×	`pow1`
23×	`*-un-lft-identity` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`times-frac` `prod-exp` `add-log-exp`
8×	`distribute-lft-out`
7×	`div-exp` `cbrt-unprod`
6×	`fma-def` `pow-prod-up` `div-inv` `pow-flip` `associate-/l*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `associate-l`
2×	`pow2` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `pow-plus` `distribute-rgt-out` `1-exp` `pow-sqr` `flip-+`
1×	`+-commutative` `associate-+l+` `cube-unmult` `associate-r` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

16.0ms	(* x (* x x))
22.0ms	(/ 3 (* x (* x x)))
9.0ms	(/ 1 (* x x))
148.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* x (* x x))
41.0ms	(/ 3 (* x (* x x)))
20.0ms	(/ 1 (* x x))
35.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

simplify1.2s

Counts

129 → 129

Iterations

Iter	Nodes
done	2001
2	2001
1	483
0	172

prune359.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.2b

bsearch1.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	44
3	44
2	40
1	32
0	22

end0.0ms

sample1.7s

Algorithm

intervals

Results

705.0ms	1679×	body	1280	valid
397.0ms	1288×	body	640	valid
299.0ms	4120×	body	80	valid
120.0ms	608×	body	320	valid
63.0ms	305×	body	160	valid