Details

sample487.0ms

Algorithm

intervals

Results

307.0ms	109×	body	2560	valid
109.0ms	77×	body	1280	valid
25.0ms	31×	body	640	valid
13.0ms	22×	body	320	valid
13.0ms	256×	pre	80	true
5.0ms	15×	body	160	valid
0.0ms	2×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize58.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.8b	(- (/ 1 x) (/ 1 (tan x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
208×	`add-cube-cbrt`
182×	`prod-diff`
33×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 262

Calls

2 calls:

6.0ms	(/ 1 (tan x))
31.0ms	(- (/ 1 x) (/ 1 (tan x)))

series155.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ 1 (tan x))
113.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.1s

Counts

268 → 268

Iterations

Iter	Nodes
done	2001
3	2001
2	1356
1	762
0	342

prune2.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* x x) (* x 1/45) (fma 1/3 x (* (pow x 5) 2/945)))
0.1b	(* (pow x 5) 2/945)
0.2b	(* x 1/45)
0.3b	(fma 1/3 x (* (pow x 5) 2/945))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`add-exp-log`
10×	`associate-l`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube`
6×	`pow1` `associate-r`
4×	`expm1-log1p-u` `unpow-prod-down` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`*-commutative` `cbrt-unprod` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-prod-down` `pow-exp`

Counts

4 → 71

Calls

4 calls:

0.0ms	(fma (* x x) (* x 1/45) (fma 1/3 x (* (pow x 5) 2/945)))
15.0ms	(* (pow x 5) 2/945)
10.0ms	(* x 1/45)
0.0ms	(fma 1/3 x (* (pow x 5) 2/945))

series299.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma (* x x) (* x 1/45) (fma 1/3 x (* (pow x 5) 2/945)))
62.0ms	(* (pow x 5) 2/945)
16.0ms	(* x 1/45)
157.0ms	(fma 1/3 x (* (pow x 5) 2/945))

simplify1.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	2026
4	2026
3	1823
2	587
1	227
0	111

prune905.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 2/945 (pow x 5))
0.2b	(* (* 1/45 x) x)
0.2b	(* 1/45 x)
0.3b	(fma x (+ 1/3 (* (* 1/45 x) x)) (* 2/945 (pow x 5)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l` `prod-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-exp` `fma-udef`

Counts

4 → 81

Calls

4 calls:

13.0ms	(* 2/945 (pow x 5))
14.0ms	(* (* 1/45 x) x)
5.0ms	(* 1/45 x)
0.0ms	(fma x (+ 1/3 (* (* 1/45 x) x)) (* 2/945 (pow x 5)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 2/945 (pow x 5))
46.0ms	(* (* 1/45 x) x)
29.0ms	(* 1/45 x)
104.0ms	(fma x (+ 1/3 (* (* 1/45 x) x)) (* 2/945 (pow x 5)))

simplify1.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	2029
3	2029
2	712
1	271
0	120

prune965.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* x 1/45) x 1/3)
0.1b	(* 2/945 (pow x 5))
0.2b	(* x 1/45)
0.3b	(* (fma (* x 1/45) x 1/3) x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`associate-r` `add-exp-log`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube`
9×	`associate-l`
8×	`pow1`
5×	`prod-exp` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `cbrt-unprod`
2×	`pow-prod-down` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `fma-udef`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma (* x 1/45) x 1/3)
12.0ms	(* 2/945 (pow x 5))
5.0ms	(* x 1/45)
6.0ms	(* (fma (* x 1/45) x 1/3) x)

series344.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(fma (* x 1/45) x 1/3)
85.0ms	(* 2/945 (pow x 5))
27.0ms	(* x 1/45)
130.0ms	(* (fma (* x 1/45) x 1/3) x)

simplify984.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2001
3	2001
2	676
1	258
0	122

prune841.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes46.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample14.6s

Algorithm

intervals

Results

9.2s	3250×	body	2560	valid
3.6s	2533×	body	1280	valid
950.0ms	1249×	body	640	valid
334.0ms	631×	body	320	valid
278.0ms	8000×	pre	80	true
102.0ms	292×	body	160	valid
8.0ms	45×	body	80	valid