Details

sample97.0ms

Algorithm

intervals

Results

40.0ms	69×	body	640	valid
16.0ms	124×	body	80	valid
12.0ms	32×	body	320	valid
11.0ms	17×	body	1280	valid
3.0ms	14×	body	160	valid

simplify169.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	195
10	195
9	187
8	132
7	94
6	83
5	75
4	63
3	43
2	33
1	19
0	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
2.9b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

8.0ms	(/ 1 (- x 1))
8.0ms	(/ 1 (+ x 1))
39.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
185.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (- x 1))
23.0ms	(/ 1 (+ x 1))
43.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
112.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify4.1s

Counts

660 → 660

Iterations

Iter	Nodes
2	2750
1	1122
0	495

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (pow x 7))
0.1b	(/ 2 (pow x 5))
0.1b	(* x (* x x))
0.5b	(/ 2 (* x (* x x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
18×	`pow1`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

10.0ms	(/ 2 (pow x 7))
10.0ms	(/ 2 (pow x 5))
33.0ms	(* x (* x x))
17.0ms	(/ 2 (* x (* x x)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ 2 (pow x 7))
78.0ms	(/ 2 (pow x 5))
63.0ms	(* x (* x x))
74.0ms	(/ 2 (* x (* x x)))

simplify1.8s

Counts

161 → 161

Iterations

Iter	Nodes
3	3723
2	1212
1	404
0	218

prune683.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (pow x 7))
0.1b	(* (/ 1 x) (/ 2 (* x x)))
0.1b	(/ 2 (pow x 5))
0.5b	(/ 2 (* x x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac`
61×	`add-sqr-sqrt`
58×	`add-exp-log`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`unpow-prod-down`
22×	`div-exp`
17×	`prod-exp`
15×	`associate-/r*`
13×	`associate-l`
11×	`cbrt-undiv`
9×	`cbrt-unprod` `associate-/l*`
8×	`sqr-pow`
7×	`associate-r`
6×	`pow1` `unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`pow-to-exp` `pow-exp`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 179

Calls

4 calls:

5.0ms	(/ 2 (pow x 7))
37.0ms	(* (/ 1 x) (/ 2 (* x x)))
9.0ms	(/ 2 (pow x 5))
12.0ms	(/ 2 (* x x))

series286.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ 2 (pow x 7))
72.0ms	(* (/ 1 x) (/ 2 (* x x)))
84.0ms	(/ 2 (pow x 5))
43.0ms	(/ 2 (* x x))

simplify7.6s

Counts

191 → 191

Iterations

Iter	Nodes
3	6716
2	1912
1	583
0	270

prune736.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2 (pow x 5)) (/ (/ 2 x) (* x x)))
0.0b	(/ 2 (pow x 7))
0.1b	(/ (/ 2 x) (* x x))
0.1b	(/ 2 (pow x 5))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac`
66×	`*-un-lft-identity`
64×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`unpow-prod-down`
26×	`add-exp-log`
25×	`fma-def`
20×	`add-cbrt-cube`
19×	`associate-/l*`
15×	`associate-/r*`
12×	`div-exp`
11×	`sqr-pow`
8×	`cbrt-undiv`
6×	`div-inv` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `frac-add` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

4 → 186

Calls

4 calls:

28.0ms	(+ (/ 2 (pow x 5)) (/ (/ 2 x) (* x x)))
5.0ms	(/ 2 (pow x 7))
17.0ms	(/ (/ 2 x) (* x x))
5.0ms	(/ 2 (pow x 5))

series428.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(+ (/ 2 (pow x 5)) (/ (/ 2 x) (* x x)))
108.0ms	(/ 2 (pow x 7))
56.0ms	(/ (/ 2 x) (* x x))
72.0ms	(/ 2 (pow x 5))

simplify11.1s

Counts

198 → 198

Iterations

Iter	Nodes
3	7410
2	1909
1	572
0	272

prune898.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes120.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.9b

bsearch203.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	108.84391371430509
9	-32298.533864343164	-0.030639508246526274	-111.6420365632021

simplify10.0ms

Iterations

Iter	Nodes
2	36
1	36
0	30

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	1927×	body	640	valid
502.0ms	4108×	body	80	valid
363.0ms	564×	body	1280	valid
275.0ms	902×	body	320	valid
140.0ms	500×	body	160	valid