Details

sample343.0ms

Algorithm

intervals

Results

232.0ms	114×	body	2560	valid
58.0ms	63×	body	1280	valid
20.0ms	42×	body	640	valid
8.0ms	22×	body	320	valid
8.0ms	256×	pre	80	true
3.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize44.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.3b	(- (/ 1 x) (/ 1 (tan x)))

rewrite52.0ms

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:

12.0ms	(/ 1 (tan x))
27.0ms	(- (/ 1 x) (/ 1 (tan x)))

series135.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ 1 (tan x))
107.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify2.1s

Counts

268 → 268

Iterations

Iter	Nodes
done	5024
3	3081
2	1356
1	762
0	342

prune523.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l` `fma-udef`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 34

Calls

2 calls:

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

series224.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))
140.0ms	(* x (fma 1/45 (* x x) 1/3))

simplify1.4s

Counts

40 → 40

Iterations

Iter	Nodes
done	5046
3	1517
2	343
1	129
0	62

prune210.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/945 (* (* x (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))))
0.4b	(* (* x (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3)))
0.4b	(* x (sqrt (fma 1/45 (* x x) 1/3)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

0.0ms	(fma (pow x 5) 2/945 (* (* x (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))))
20.0ms	(* (* x (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3)))
9.0ms	(* x (sqrt (fma 1/45 (* x x) 1/3)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma (pow x 5) 2/945 (* (* x (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))))
105.0ms	(* (* x (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3)))
151.0ms	(* x (sqrt (fma 1/45 (* x x) 1/3)))

simplify2.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5007
3	3008
2	822
1	266
0	111

prune307.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 5) 2/945 (* (* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (fma 1/45 (* x x) 1/3))))
0.0b	(* x (sqrt (sqrt (fma 1/45 (* x x) 1/3))))
0.3b	(* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3))))
0.4b	(* (* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (fma 1/45 (* x x) 1/3)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (pow x 5) 2/945 (* (* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (fma 1/45 (* x x) 1/3))))
9.0ms	(* x (sqrt (sqrt (fma 1/45 (* x x) 1/3))))
41.0ms	(* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3))))
117.0ms	(* (* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (fma 1/45 (* x x) 1/3)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma (pow x 5) 2/945 (* (* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (fma 1/45 (* x x) 1/3))))
193.0ms	(* x (sqrt (sqrt (fma 1/45 (* x x) 1/3))))
127.0ms	(* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3))))
103.0ms	(* (* (* x (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (fma 1/45 (* x x) 1/3)))

simplify1.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	1527
1	463
0	188

prune452.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample12.0s

Algorithm

intervals

Results

7.0s	3282×	body	2560	valid
3.6s	2465×	body	1280	valid
668.0ms	1254×	body	640	valid
380.0ms	8000×	pre	80	true
190.0ms	636×	body	320	valid
65.0ms	309×	body	160	valid
6.0ms	54×	body	80	valid