Details

sample151.0ms

Algorithm

intervals

Results

78.0ms	67×	body	1280	valid
29.0ms	52×	body	640	valid
15.0ms	21×	body	2560	valid
10.0ms	28×	body	320	valid
7.0ms	76×	body	80	valid
2.0ms	12×	body	160	valid

simplify8.0ms

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: 42.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
1.5b	(+ x (hypot 1 x))
2.1b	(log (+ x (hypot 1 x)))

rewrite17.0ms

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)
9.0ms	(+ x (hypot 1 x))
7.0ms	(log (+ x (hypot 1 x)))

series365.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(hypot 1 x)
90.0ms	(+ x (hypot 1 x))
197.0ms	(log (+ x (hypot 1 x)))

simplify977.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
3	2001
2	666
1	244
0	108

prune274.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 3/40 (pow x 5) x)
0.1b	(* (* x x) x)
16.3b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

rewrite25.0ms

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 3/40 (pow x 5) x)
23.0ms	(* (* x x) x)
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

series314.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(fma 3/40 (pow x 5) x)
54.0ms	(* (* x x) x)
84.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

simplify1.3s

Counts

62 → 62

Iterations

Iter	Nodes
done	2003
4	2003
3	1455
2	362
1	133
0	69

prune239.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2 x (/ 1/2 x))
0.1b	(* (* x x) x)
0.2b	(/ -1/8 (* (* x x) x))
11.4b	(log (+ (/ -1/8 (* (* x x) x)) (fma 2 x (/ 1/2 x))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`expm1-log1p-u` `log-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `pow-sqr`
1×	`clear-num` `associate-/r` `frac-2neg` `flip3-+` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma 2 x (/ 1/2 x))
23.0ms	(* (* x x) x)
18.0ms	(/ -1/8 (* (* x x) x))
45.0ms	(log (+ (/ -1/8 (* (* x x) x)) (fma 2 x (/ 1/2 x))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma 2 x (/ 1/2 x))
42.0ms	(* (* x x) x)
56.0ms	(/ -1/8 (* (* x x) x))
116.0ms	(log (+ (/ -1/8 (* (* x x) x)) (fma 2 x (/ 1/2 x))))

simplify965.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	2113
3	2113
2	1162
1	337
0	151

prune328.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1/16 (pow x 5))
0.3b	(/ 1/8 (* x x))
14.1b	(log (- (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ 1/16 (pow x 5))))
19.7b	(- (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ 1/16 (pow x 5)))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

1335×	`times-frac`
1168×	`add-sqr-sqrt`
884×	`*-un-lft-identity`
675×	`prod-diff`
654×	`add-cube-cbrt`
327×	`associate--l+`
164×	`difference-of-squares`
145×	`div-inv`
140×	`unpow-prod-down`
114×	`distribute-lft-out--`
48×	`sqr-pow`
26×	`distribute-rgt-out--`
15×	`add-exp-log`
14×	`fma-neg`
11×	`add-cbrt-cube`
10×	`log-prod` `frac-sub`
9×	`add-log-exp`
8×	`associate-/r*`
6×	`log-div` `associate-/l*`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`cbrt-undiv` `diff-log`
2×	`clear-num` `sub-neg` `frac-2neg` `sub-div`
1×	`associate--l-` `pow-to-exp` `rem-log-exp` `pow-exp` `prod-exp` `log-pow` `cbrt-unprod`

Counts

4 → 819

Calls

4 calls:

6.0ms	(/ 1/16 (pow x 5))
7.0ms	(/ 1/8 (* x x))
152.0ms	(log (- (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ 1/16 (pow x 5))))
302.0ms	(- (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ 1/16 (pow x 5)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1/16 (pow x 5))
46.0ms	(/ 1/8 (* x x))
127.0ms	(log (- (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ 1/16 (pow x 5))))
74.0ms	(- (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ 1/16 (pow x 5)))

simplify1.4s

Counts

831 → 831

Iterations

Iter	Nodes
done	2001
2	2001
1	1843
0	788

prune6.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.5b

bsearch121.0ms

Steps

Iters	Range		Point
10	0.001953933407705698	32640636.358721357	0.9505314742632508
9	-5.107543836967609	-2.6017364714010764e-05	-1.0632494934709653

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	31

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.0s	2353×	body	1280	valid
1.2s	1505×	body	640	valid
510.0ms	782×	body	2560	valid
284.0ms	814×	body	320	valid
193.0ms	2115×	body	80	valid
83.0ms	431×	body	160	valid