Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	53×	body	1280	valid
6.0ms	48×	body	640	valid
4.0ms	118×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid

simplify195.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	350
14	350
13	346
12	340
11	329
10	222
9	96
8	75
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

9.0ms	(/ x (+ x 1.0))
20.0ms	(/ (+ x 1.0) (- x 1.0))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ x (+ x 1.0))
64.0ms	(/ (+ x 1.0) (- x 1.0))
144.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.0s

Counts

605 → 605

Iterations

Iter	Nodes
done	5013
2	3287
1	1251
0	523

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.2b	(/ 3.0 (* x (* x x)))
0.7b	(/ 1.0 (* x x))
7.0b	(+ (/ 3.0 (* x (* x x))) (/ 1.0 (* x x)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

22.0ms	(* x (* x x))
21.0ms	(/ 3.0 (* x (* x x)))
10.0ms	(/ 1.0 (* x x))
53.0ms	(+ (/ 3.0 (* x (* x x))) (/ 1.0 (* x x)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* x (* x x))
53.0ms	(/ 3.0 (* x (* x x)))
44.0ms	(/ 1.0 (* x x))
139.0ms	(+ (/ 3.0 (* x (* x x))) (/ 1.0 (* x x)))

simplify1.1s

Counts

109 → 109

Iterations

Iter	Nodes
done	5010
2	1308
1	340
0	136

prune305.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
32.8b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/r*` `add-exp-log`
7×	`add-cbrt-cube` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `1-exp` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

3 → 96

Calls

3 calls:

16.0ms	(/ 1 (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series235.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1 (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
160.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify2.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	3430
2	979
1	355
0	161

prune302.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (fma 1.0 x 3.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`fma-udef`
1×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 22

Calls

1 calls:

9.0ms

(* x (fma 1.0 x 3.0))

series97.0ms

Counts

1 → 3

Calls

1 calls:

97.0ms

(* x (fma 1.0 x 3.0))

simplify1.5s

Counts

25 → 25

Iterations

Iter	Nodes
done	5000
3	1046
2	239
1	92
0	43

prune106.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch109.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	11708.854968235615
10	-17239113253358.373	-4.96108325192681e-05	-10978.061542302274

simplify11.0ms

Iterations

Iter	Nodes
done	51
3	51
2	49
1	38
0	24

end0.0ms

sample1.4s

Algorithm

intervals

Results

607.0ms	4089×	body	80	valid
424.0ms	1740×	body	1280	valid
189.0ms	1239×	body	640	valid
62.0ms	624×	body	320	valid
22.0ms	308×	body	160	valid