Details

sample83.0ms

Algorithm

intervals

Results

27.0ms	61×	body	640	valid
17.0ms	18×	body	1280	valid
16.0ms	136×	body	80	valid
9.0ms	25×	body	320	valid
3.0ms	16×	body	160	valid

simplify142.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (+ x 1))
0.0b	(/ 1 (- x 1))
0.9b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite257.0ms

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:

48.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
8.0ms	(/ 1 (+ x 1))
16.0ms	(/ 1 (- x 1))
168.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
22.0ms	(/ 1 (+ x 1))
25.0ms	(/ 1 (- x 1))
145.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify4.5s

Counts

660 → 660

Iterations

Iter	Nodes
2	2786
1	1122
0	495

prune6.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.2b	(/ 2 (pow x 7))
0.3b	(/ 2 (* x (* x x)))
0.3b	(/ 2 (pow x 5))

rewrite52.0ms

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:

25.0ms	(* x (* x x))
5.0ms	(/ 2 (pow x 7))
13.0ms	(/ 2 (* x (* x x)))
5.0ms	(/ 2 (pow x 5))

series320.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* x (* x x))
117.0ms	(/ 2 (pow x 7))
47.0ms	(/ 2 (* x (* x x)))
82.0ms	(/ 2 (pow x 5))

simplify1.8s

Counts

161 → 161

Iterations

Iter	Nodes
3	3569
2	1181
1	403
0	218

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2 (pow x 5)) (/ 2 (pow x 7)))
0.1b	(/ (/ 2 x) (* x x))
0.2b	(/ 2 (pow x 7))
0.3b	(/ 2 (pow x 5))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
74×	`*-un-lft-identity`
66×	`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` `div-inv`
6×	`add-log-exp`
5×	`distribute-lft-out`
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-+` `associate-/l/`

Counts

4 → 190

Calls

4 calls:

21.0ms	(+ (/ 2 (pow x 5)) (/ 2 (pow x 7)))
15.0ms	(/ (/ 2 x) (* x x))
10.0ms	(/ 2 (pow x 7))
9.0ms	(/ 2 (pow x 5))

series588.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(+ (/ 2 (pow x 5)) (/ 2 (pow x 7)))
82.0ms	(/ (/ 2 x) (* x x))
105.0ms	(/ 2 (pow x 7))
102.0ms	(/ 2 (pow x 5))

simplify11.4s

Counts

202 → 202

Iterations

Iter	Nodes
3	6851
2	1801
1	563
0	274

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ 2 x) x) x)
0.1b	(/ (/ 2 x) x)
0.2b	(/ 2 (pow x 7))
0.3b	(/ 2 (pow x 5))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

510×	`times-frac`
262×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
62×	`associate-/l*`
28×	`add-exp-log`
24×	`unpow-prod-down` `div-inv`
22×	`add-cbrt-cube`
20×	`associate-/r*`
15×	`div-exp`
11×	`cbrt-undiv`
8×	`sqr-pow`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `associate-/l/`

Counts

4 → 364

Calls

4 calls:

15.0ms	(/ (/ (/ 2 x) x) x)
10.0ms	(/ (/ 2 x) x)
10.0ms	(/ 2 (pow x 7))
5.0ms	(/ 2 (pow x 5))

series273.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (/ (/ 2 x) x) x)
52.0ms	(/ (/ 2 x) x)
92.0ms	(/ 2 (pow x 7))
68.0ms	(/ 2 (pow x 5))

simplify1.5s

Counts

376 → 376

Iterations

Iter	Nodes
2	2616
1	1101
0	565

prune4.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes103.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.1b

bsearch183.0ms

Steps

Iters	Range		Point
10	1.4996160052323843e-06	45385424.466692075	111.69425311390617
10	-8.26555774309129e+15	-0.755072844465923	-113.57820944408793

simplify4.0ms

Iterations

Iter	Nodes
2	34
1	34
0	29

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	1888×	body	640	valid
515.0ms	4234×	body	80	valid
325.0ms	534×	body	1280	valid
296.0ms	891×	body	320	valid
83.0ms	455×	body	160	valid