Details

sample143.0ms

Algorithm

intervals

Results

76.0ms	81×	body	1280	valid
24.0ms	46×	body	640	valid
17.0ms	26×	body	2560	valid
6.0ms	20×	body	320	valid
6.0ms	66×	body	80	valid
3.0ms	17×	body	160	valid

simplify7.0ms

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: 44.6b

localize14.0ms

Local error

Found 2 expressions with local error:

1.1b	(+ x (hypot 1 x))
3.2b	(log (+ x (hypot 1 x)))

rewrite12.0ms

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:

7.0ms	(+ x (hypot 1 x))
5.0ms	(log (+ x (hypot 1 x)))

series268.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(+ x (hypot 1 x))
186.0ms	(log (+ x (hypot 1 x)))

simplify945.0ms

Counts

42 → 42

Iterations

Iter	Nodes
done	2001
4	2001
3	1585
2	577
1	215
0	93

prune240.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.1b	(* x (* x x))
21.0b	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
14.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

series237.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(fma 3/40 (pow x 5) x)
35.0ms	(* x (* x x))
60.0ms	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

simplify942.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	2003
4	2003
3	1342
2	341
1	119
0	70

prune506.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/8 x) (* x x))
0.1b	(/ -1/16 (pow x 5))
11.7b	(log (+ (+ (/ -1/16 (pow x 5)) (/ (/ 1/8 x) (* x x))) (/ -1/2 x)))
19.4b	(+ (/ -1/16 (pow x 5)) (/ (/ 1/8 x) (* x x)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
56×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`fma-def`
22×	`add-exp-log`
21×	`unpow-prod-down`
18×	`add-cbrt-cube`
16×	`associate-/l*`
9×	`div-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `sqr-pow`
6×	`add-log-exp`
5×	`pow1` `log-div` `log-prod` `frac-add` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`pow-to-exp` `+-commutative` `sum-log` `rem-log-exp` `pow-exp` `log-pow` `associate-/l/`

Counts

4 → 160

Calls

4 calls:

14.0ms	(/ (/ 1/8 x) (* x x))
8.0ms	(/ -1/16 (pow x 5))
101.0ms	(log (+ (+ (/ -1/16 (pow x 5)) (/ (/ 1/8 x) (* x x))) (/ -1/2 x)))
40.0ms	(+ (/ -1/16 (pow x 5)) (/ (/ 1/8 x) (* x x)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (/ 1/8 x) (* x x))
55.0ms	(/ -1/16 (pow x 5))
122.0ms	(log (+ (+ (/ -1/16 (pow x 5)) (/ (/ 1/8 x) (* x x))) (/ -1/2 x)))
195.0ms	(+ (/ -1/16 (pow x 5)) (/ (/ 1/8 x) (* x x)))

simplify788.0ms

Counts

172 → 172

Iterations

Iter	Nodes
done	2000
2	2000
1	683
0	295

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x)))
0.9b	(- x (hypot 1 x))
3.2b	(log (/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x))))
18.8b	(- (* x x) (* (hypot 1 x) (hypot 1 x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`times-frac`
32×	`add-cube-cbrt`
26×	`log-prod`
22×	`difference-of-squares`
10×	`prod-diff` `distribute-lft-out--`
9×	`add-exp-log`
8×	`add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `associate-/r*` `flip3--` `flip--`
4×	`expm1-log1p-u` `fma-neg` `associate-/r/` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `diff-log` `div-exp` `rem-log-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `div-sub` `log-pow`

Counts

4 → 136

Calls

4 calls:

35.0ms	(/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x)))
5.0ms	(- x (hypot 1 x))
6.0ms	(log (/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x))))
8.0ms	(- (* x x) (* (hypot 1 x) (hypot 1 x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x)))
83.0ms	(- x (hypot 1 x))
618.0ms	(log (/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x))))
221.0ms	(- (* x x) (* (hypot 1 x) (hypot 1 x)))

simplify1.1s

Counts

148 → 148

Iterations

Iter	Nodes
done	2002
3	2002
2	1621
1	590
0	238

prune822.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch90.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.00884177569185373
9	-32298.533864343164	-0.030639508246526274	-1.0612400279589977

simplify4.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	2289×	body	1280	valid
884.0ms	1615×	body	640	valid
486.0ms	793×	body	2560	valid
244.0ms	764×	body	320	valid
188.0ms	2105×	body	80	valid
75.0ms	434×	body	160	valid