Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	68×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	26×	body	320	valid
2.0ms	14×	body	1280	valid
1.0ms	15×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	50	15
5	55	15
6	64	15
7	82	15
8	99	15
9	109	15
done	109	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (- x 1.0))
2.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

707×	`*-un-lft-identity`
691×	`times-frac`
514×	`add-sqr-sqrt`
482×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
91×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
10×	`fma-def` `add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 583

Calls

3 calls:

85.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
12.0ms	(/ 1.0 (- x 1.0))
360.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series282.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
27.0ms	(/ 1.0 (- x 1.0))
211.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.9s

Counts

592 → 592

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	485	19448
1	1101	16993
2	2677	12566
done	5000	9801

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
2.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

1395×	`*-un-lft-identity`
1134×	`times-frac`
749×	`add-sqr-sqrt`
708×	`associate-+l+`
705×	`add-cube-cbrt`
702×	`prod-diff`
220×	`distribute-lft-out`
98×	`distribute-lft-out--`
93×	`div-inv`
78×	`associate-/r/`
76×	`cbrt-prod`
60×	`cbrt-div`
54×	`flip3-+` `flip-+`
45×	`frac-add`
30×	`fma-def` `swap-sqr`
25×	`frac-times`
19×	`add-log-exp`
15×	`flip3--` `frac-sub` `flip--`
12×	`associate-r` `associate-l` `difference-of-squares`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `sum-log`
5×	`associate-r/` `associate-l/`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`+-commutative` `associate-+l-` `sub-neg` `diff-log`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 923

Calls

4 calls:

1.5s	(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
358.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
357.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
362.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

479.0ms	(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
216.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
212.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
223.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.5s

Counts

935 → 935

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	328	28392
1	730	25938
2	2173	20448
done	5000	18083

prune3.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cbrt 1.0) (cbrt (+ x 1.0)))
0.3b	(cbrt (+ x 1.0))
0.4b	(pow (/ (cbrt 1.0) (cbrt (+ x 1.0))) 3)
20.9b	(+ (+ (- (pow (/ (cbrt 1.0) (cbrt (+ x 1.0))) 3) (/ 2.0 x)) 0) (/ 1.0 (- x 1.0)))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

146×	`cbrt-prod`
145×	`*-un-lft-identity`
126×	`times-frac`
91×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `cube-prod`
27×	`distribute-lft-out`
13×	`add-log-exp`
9×	`add-exp-log`
8×	`cbrt-div`
7×	`associate-/r*`
6×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*`
5×	`pow1` `fma-def` `sum-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `div-inv`
2×	`cbrt-undiv` `associate-+l-` `div-exp` `frac-add` `pow-exp` `distribute-lft-out--` `rem-cube-cbrt`
1×	`+-commutative` `cube-div` `cube-mult` `pow-to-exp` `associate-+l+` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `unpow3` `clear-num` `sqr-pow`

Counts

4 → 232

Calls

4 calls:

14.0ms	(/ (cbrt 1.0) (cbrt (+ x 1.0)))
4.0ms	(cbrt (+ x 1.0))
21.0ms	(pow (/ (cbrt 1.0) (cbrt (+ x 1.0))) 3)
5.2s	(+ (+ (- (pow (/ (cbrt 1.0) (cbrt (+ x 1.0))) 3) (/ 2.0 x)) 0) (/ 1.0 (- x 1.0)))

series771.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (cbrt 1.0) (cbrt (+ x 1.0)))
90.0ms	(cbrt (+ x 1.0))
258.0ms	(pow (/ (cbrt 1.0) (cbrt (+ x 1.0))) 3)
264.0ms	(+ (+ (- (pow (/ (cbrt 1.0) (cbrt (+ x 1.0))) 3) (/ 2.0 x)) 0) (/ 1.0 (- x 1.0)))

simplify1.5s

Counts

244 → 244

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	367	4626
1	1110	3843
2	3466	3253
done	5001	3241

prune460.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
31.0b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

39.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
9.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
54.0ms	(* (* (+ x 1.0) x) (- x 1.0))
0.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series636.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
38.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
100.0ms	(* (* (+ x 1.0) x) (- x 1.0))
185.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify1.7s

Counts

123 → 123

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	227	3140
1	618	2926
2	2311	2478
done	5000	2453

prune252.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
done	11	11

end0.0ms

sample632.0ms

Algorithm

intervals

Results

194.0ms	1878×	body	640	valid
128.0ms	4173×	body	80	valid
80.0ms	579×	body	1280	valid
74.0ms	912×	body	320	valid
24.0ms	459×	body	160	valid