Details

sample142.0ms

Algorithm

intervals

Results

68.0ms	72×	body	1280	valid
27.0ms	54×	body	640	valid
18.0ms	27×	body	2560	valid
9.0ms	25×	body	320	valid
4.0ms	57×	body	80	valid
4.0ms	21×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.6b

localize18.0ms

Local error

Found 2 expressions with local error:

1.0b	(+ x (hypot 1 x))
4.3b	(log (+ x (hypot 1 x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 36

Calls

2 calls:

8.0ms	(+ x (hypot 1 x))
7.0ms	(log (+ x (hypot 1 x)))

series280.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(+ x (hypot 1 x))
205.0ms	(log (+ x (hypot 1 x)))

simplify1.7s

Counts

42 → 42

Iterations

Iter	Nodes
done	5000
3	1585
2	577
1	215
0	93

prune230.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.3b	(* x -1/6)
11.8b	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
5.0ms	(* x -1/6)
0.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))

series315.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms	(fma 3/40 (pow x 5) x)
28.0ms	(* x -1/6)
88.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))

simplify2.9s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
4	3874
3	1071
2	330
1	130
0	67

prune210.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1/8 x) (* x x))
0.2b	(/ 1/16 (pow x 5))
13.6b	(log (+ (- (/ -1/2 x) (/ 1/16 (pow x 5))) (/ (/ 1/8 x) (* x x))))
19.3b	(+ (- (/ -1/2 x) (/ 1/16 (pow x 5))) (/ (/ 1/8 x) (* x x)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

562×	`times-frac`
417×	`add-sqr-sqrt`
409×	`*-un-lft-identity`
393×	`add-cube-cbrt`
327×	`associate-+l+`
325×	`prod-diff`
131×	`unpow-prod-down`
45×	`sqr-pow`
42×	`div-inv`
22×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-/l*`
13×	`fma-def`
9×	`div-exp` `add-log-exp`
8×	`associate-/r*` `difference-of-squares`
7×	`cbrt-undiv`
6×	`frac-add`
5×	`pow1` `log-div` `log-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--`
2×	`clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip-+` `flip--`
1×	`pow-to-exp` `+-commutative` `sub-neg` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `associate-+l-` `associate-/l/`

Counts

4 → 480

Calls

4 calls:

21.0ms	(/ (/ 1/8 x) (* x x))
6.0ms	(/ 1/16 (pow x 5))
49.0ms	(log (+ (- (/ -1/2 x) (/ 1/16 (pow x 5))) (/ (/ 1/8 x) (* x x))))
114.0ms	(+ (- (/ -1/2 x) (/ 1/16 (pow x 5))) (/ (/ 1/8 x) (* x x)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (/ 1/8 x) (* x x))
70.0ms	(/ 1/16 (pow x 5))
129.0ms	(log (+ (- (/ -1/2 x) (/ 1/16 (pow x 5))) (/ (/ 1/8 x) (* x x))))
58.0ms	(+ (- (/ -1/2 x) (/ 1/16 (pow x 5))) (/ (/ 1/8 x) (* x x)))

simplify2.6s

Counts

492 → 492

Iterations

Iter	Nodes
done	5008
2	3441
1	1025
0	397

prune3.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.3b	(* x -1/6)
4.6b	(log (exp (fma 3/40 (pow x 5) x)))
11.9b	(fma (* x -1/6) (* x x) (log (exp (fma 3/40 (pow x 5) x))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log-prod` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `associate-r` `associate-l` `fma-udef`
1×	`rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

0.0ms	(fma 3/40 (pow x 5) x)
5.0ms	(* x -1/6)
4.0ms	(log (exp (fma 3/40 (pow x 5) x)))
1.0ms	(fma (* x -1/6) (* x x) (log (exp (fma 3/40 (pow x 5) x))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(fma 3/40 (pow x 5) x)
21.0ms	(* x -1/6)
219.0ms	(log (exp (fma 3/40 (pow x 5) x)))
91.0ms	(fma (* x -1/6) (* x x) (log (exp (fma 3/40 (pow x 5) x))))

simplify2.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
4	3997
3	1050
2	357
1	167
0	95

prune342.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch71.0ms

Steps

Iters	Range		Point
8	0.006928851504795399	68.55102067575892	0.007871312528259618
9	-17438.246738609338	-0.0018335887134067947	-1.0481361170547778

simplify4.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.7s	2305×	body	1280	valid
705.0ms	1560×	body	640	valid
628.0ms	2088×	body	80	valid
442.0ms	824×	body	2560	valid
188.0ms	807×	body	320	valid
61.0ms	416×	body	160	valid