Details

sample60.0ms

Algorithm

intervals

Results

20.0ms	61×	body	640	valid
10.0ms	40×	body	320	valid
10.0ms	115×	body	80	valid
8.0ms	21×	body	1280	valid
3.0ms	19×	body	160	valid

simplify199.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	214
10	214
9	204
8	139
7	97
6	86
5	78
4	65
3	45
2	35
1	21
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.3b

localize27.0ms

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))
2.0b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite282.0ms

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:

11.0ms	(/ 1 (+ x 1))
11.0ms	(/ 1 (- x 1))
51.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
175.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (+ x 1))
16.0ms	(/ 1 (- x 1))
26.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
119.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.2s

Counts

660 → 660

Iterations

Iter	Nodes
2	2697
1	1123
0	495

prune6.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1 x) (* (+ x 1) 2))
0.0b	(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
0.1b	(* (* (+ x 1) x) (- x 1))
20.5b	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

55×	`prod-diff`
53×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`associate-*l/`
43×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+l+` `flip3--` `flip--`
16×	`frac-times` `frac-add`
14×	`associate-r`
12×	`flip3-+` `flip-+`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-*r/` `add-log-exp`
7×	`sub-neg`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`difference-of-sqr-1` `*-commutative` `distribute-lft-out--`
1×	`+-commutative` `sum-log` `fma-def` `fma-neg` `diff-log` `unswap-sqr`

Counts

4 → 180

Calls

4 calls:

9.0ms	(- (* 1 x) (* (+ x 1) 2))
45.0ms	(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
44.0ms	(* (* (+ x 1) x) (- x 1))
58.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series193.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* 1 x) (* (+ x 1) 2))
29.0ms	(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
119.0ms	(* (* (+ x 1) x) (- x 1))
2.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify1.6s

Counts

192 → 192

Iterations

Iter	Nodes
2	4319
1	1035
0	321

prune2.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* x x) x -1)
0.0b	(* (+ (* x x) x) (fma (* x x) x -1))
20.5b	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
21.5b	(/ (* (+ (* x x) x) (fma (* x x) x -1)) (+ (* x x) (+ (* 1 1) (* x 1))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

40×	`associate-*l/`
22×	`add-sqr-sqrt` `associate-+l+`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`frac-add`
12×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip3--` `flip-+` `flip--`
11×	`add-cbrt-cube` `add-exp-log`
8×	`frac-times`
6×	`pow1` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `times-frac` `associate-r*` `fma-udef`
2×	`cbrt-undiv` `sub-neg` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `distribute-lft1-in` `distribute-rgt-out` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma (* x x) x -1)
23.0ms	(* (+ (* x x) x) (fma (* x x) x -1))
43.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
63.0ms	(/ (* (+ (* x x) x) (fma (* x x) x -1)) (+ (* x x) (+ (* 1 1) (* x 1))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(fma (* x x) x -1)
68.0ms	(* (+ (* x x) x) (fma (* x x) x -1))
3.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
283.0ms	(/ (* (+ (* x x) x) (fma (* x x) x -1)) (+ (* x x) (+ (* 1 1) (* x 1))))

simplify1.7s

Counts

131 → 131

Iterations

Iter	Nodes
2	4397
1	913
0	272

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (pow x 7))
0.1b	(* x (* x x))
0.4b	(/ 2 (pow x 5))
0.4b	(/ 2 (* x (* x x)))

rewrite43.0ms

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:

5.0ms	(/ 2 (pow x 7))
14.0ms	(* x (* x x))
5.0ms	(/ 2 (pow x 5))
17.0ms	(/ 2 (* x (* x x)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ 2 (pow x 7))
58.0ms	(* x (* x x))
73.0ms	(/ 2 (pow x 5))
65.0ms	(/ 2 (* x (* x x)))

simplify1.5s

Counts

161 → 161

Iterations

Iter	Nodes
3	3851
2	1244
1	409
0	218

prune1.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes122.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.6b

bsearch3.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	35
1	35
0	26

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	1866×	body	640	valid
430.0ms	4144×	body	80	valid
299.0ms	570×	body	1280	valid
291.0ms	948×	body	320	valid
102.0ms	474×	body	160	valid