Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	66×	body	640	valid
5.0ms	136×	body	80	valid
3.0ms	31×	body	320	valid
2.0ms	12×	body	1280	valid
1.0ms	12×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
10	4810
9	1188
8	437
7	210
6	162
5	135
4	89
3	41
2	31
1	18
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.8b	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

728×	`*-un-lft-identity`
710×	`times-frac`
526×	`add-sqr-sqrt`
500×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+r+`
94×	`distribute-lft-out`
66×	`div-inv`
60×	`associate-/r/`
29×	`flip3-+` `flip-+`
21×	`fma-def`
18×	`fma-neg`
17×	`distribute-lft-out--`
11×	`add-log-exp` `difference-of-squares`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--`
3×	`frac-add`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`
1×	`+-commutative` `associate-+r-`

Counts

4 → 629

Calls

4 calls:

9.0ms	(/ 1.0 (+ x 1.0))
10.0ms	(/ 1.0 (- x 1.0))
81.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
239.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (+ x 1.0))
47.0ms	(/ 1.0 (- x 1.0))
64.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
321.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

simplify810.0ms

Counts

641 → 641

Iterations

Iter	Nodes
done	5000
1	1564
0	682

prune3.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ 1.0 x))
1.1b	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x))
2.4b	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))

rewrite940.0ms

Algorithm

rewrite-expression-head

Rules

910×	`*-un-lft-identity`
568×	`times-frac`
311×	`distribute-lft-out`
304×	`add-sqr-sqrt`
285×	`add-cube-cbrt`
221×	`prod-diff`
105×	`distribute-lft-out--`
50×	`div-inv`
21×	`fma-def`
17×	`fma-neg`
11×	`add-log-exp`
9×	`associate-/r*` `difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r/` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`flip3-+` `flip3--` `frac-sub` `flip-+` `flip--`
2×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `diff-log` `div-exp` `frac-add`
1×	`+-commutative` `sub-neg` `associate--l+`

Counts

4 → 388

Calls

4 calls:

10.0ms	(/ 1.0 (- x 1.0))
9.0ms	(/ 1.0 (+ 1.0 x))
791.0ms	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x))
85.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (- x 1.0))
41.0ms	(/ 1.0 (+ 1.0 x))
299.0ms	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x))
226.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))

simplify1.7s

Counts

400 → 400

Iterations

Iter	Nodes
done	5000
2	3882
1	966
0	385

prune994.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x 1.0) (- (* 1.0 x) (* 2.0 (+ 1.0 x))))
0.0b	(- (* 1.0 x) (* 2.0 (+ 1.0 x)))
0.0b	(* (* x (+ 1.0 x)) (- x 1.0))
16.5b	(fma 1.0 (* x (+ 1.0 x)) (* (- x 1.0) (- (* 1.0 x) (* 2.0 (+ 1.0 x)))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`prod-diff`
19×	`add-cube-cbrt`
15×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`flip3--` `associate-*r/` `flip--`
8×	`frac-times` `associate-r`
6×	`associate-l` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`*-commutative` `associate--r+` `distribute-lft-out--` `difference-of-squares`
1×	`fma-neg` `diff-log` `fma-udef` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

47.0ms	(* (- x 1.0) (- (* 1.0 x) (* 2.0 (+ 1.0 x))))
7.0ms	(- (* 1.0 x) (* 2.0 (+ 1.0 x)))
44.0ms	(* (* x (+ 1.0 x)) (- x 1.0))
1.0ms	(fma 1.0 (* x (+ 1.0 x)) (* (- x 1.0) (- (* 1.0 x) (* 2.0 (+ 1.0 x)))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- x 1.0) (- (* 1.0 x) (* 2.0 (+ 1.0 x))))
57.0ms	(- (* 1.0 x) (* 2.0 (+ 1.0 x)))
180.0ms	(* (* x (+ 1.0 x)) (- x 1.0))
317.0ms	(fma 1.0 (* x (+ 1.0 x)) (* (- x 1.0) (- (* 1.0 x) (* 2.0 (+ 1.0 x)))))

simplify503.0ms

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
1	708
0	222

prune636.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ 1.0 x))
0.0b	(* (* x (+ 1.0 x)) (- x 1.0))
0.1b	(/ 2.0 (* (* x (+ 1.0 x)) (- x 1.0)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
18×	`prod-diff` `associate-*r/`
12×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1`
9×	`associate-r`
8×	`frac-times` `associate-/r/`
7×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
6×	`flip3--` `flip--`
4×	`associate-l` `pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `cbrt-undiv` `times-frac` `div-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`sub-neg` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 110

Calls

3 calls:

30.0ms	(* x (+ 1.0 x))
58.0ms	(* (* x (+ 1.0 x)) (- x 1.0))
47.0ms	(/ 2.0 (* (* x (+ 1.0 x)) (- x 1.0)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* x (+ 1.0 x))
133.0ms	(* (* x (+ 1.0 x)) (- x 1.0))
145.0ms	(/ 2.0 (* (* x (+ 1.0 x)) (- x 1.0)))

simplify458.0ms

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
1	669
0	210

prune391.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
1	8
0	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

853.0ms	1831×	body	640	valid
394.0ms	4219×	body	80	valid
189.0ms	954×	body	320	valid
178.0ms	546×	body	1280	valid
46.0ms	453×	body	160	valid