Details

sample74.0ms

Algorithm

intervals

Results

25.0ms	45×	body	1280	valid
16.0ms	40×	body	640	valid
12.0ms	140×	body	80	valid
6.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify12.0s

Counts

1 → 1

Iterations

Iter	Nodes
9	9494
8	1963
7	550
6	229
5	103
4	51
3	30
2	22
1	18
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
3.4b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
63×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-cbrt-cube` `div-inv`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`expm1-def` `difference-of-sqr-1` `div-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 150

Calls

3 calls:

11.0ms	(+ 1 (exp (* -2 x)))
11.0ms	(/ 2 (+ 1 (exp (* -2 x))))
88.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series113.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1 (exp (* -2 x)))
23.0ms	(/ 2 (+ 1 (exp (* -2 x))))
74.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.1s

Counts

159 → 159

Iterations

Iter	Nodes
3	2004
2	866
1	407
0	183

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* -2 x))))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
0.0b	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
3.4b	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
88×	`times-frac`
70×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
26×	`distribute-lft-out`
24×	`swap-sqr`
20×	`add-cbrt-cube` `add-exp-log`
18×	`associate-r` `associate-l`
12×	`associate-/r/`
11×	`pow1`
8×	`associate-/r*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef`

Counts

4 → 174

Calls

4 calls:

25.0ms	(/ 2 (+ 1 (exp (* -2 x))))
21.0ms	(/ 2 (+ 1 (exp (* -2 x))))
85.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
0.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

series211.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 2 (+ 1 (exp (* -2 x))))
32.0ms	(/ 2 (+ 1 (exp (* -2 x))))
35.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
121.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

simplify4.0s

Counts

186 → 186

Iterations

Iter	Nodes
3	5357
2	1637
1	556
0	181

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* x x))
0.2b	(fma (pow x 5) 2/15 x)
22.0b	(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

rewrite21.0ms

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:

16.0ms	(* x (* x x))
4.0ms	(fma (pow x 5) 2/15 x)
0.0ms	(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

series262.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* x (* x x))
156.0ms	(fma (pow x 5) 2/15 x)
64.0ms	(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

simplify2.9s

Counts

58 → 58

Iterations

Iter	Nodes
4	7009
3	1200
2	310
1	123
0	71

prune532.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes235.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.8b

bsearch138.0ms

Steps

Iters	Range		Point
8	4.2592438902487584e-05	0.10106394179147121	0.007644269470426118
9	-3.0421098639022524	-5.8481452536585384e-08	-0.005900779815178019

simplify30.0ms

Iterations

Iter	Nodes
2	37
1	37
0	28

end0.0ms

sample2.5s

Algorithm

intervals

Results

980.0ms	1773×	body	1280	valid
674.0ms	4033×	body	80	valid
447.0ms	1248×	body	640	valid
216.0ms	603×	body	320	valid
54.0ms	343×	body	160	valid