Details

sample537.0ms

Algorithm

intervals

Results

322.0ms	98×	body	2560	valid
123.0ms	79×	body	1280	valid
40.0ms	41×	body	640	valid
16.0ms	23×	body	320	valid
13.0ms	256×	pre	80	true
6.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	14
2	14
1	10
0	6

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.6b	(- (/ 1 x) (/ 1 (tan x)))

rewrite45.0ms

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))
32.0ms	(- (/ 1 x) (/ 1 (tan x)))

series157.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ 1 (tan x))
109.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.4s

Counts

268 → 268

Iterations

Iter	Nodes
3	2873
2	1360
1	758
0	342

prune2.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 5) 2/945 (* x (+ (* 1/45 (* x x)) 1/3)))
0.0b	(+ (* 1/45 (* x x)) 1/3)
0.2b	(* 1/45 (* x x))
0.4b	(* x (+ (* 1/45 (* x x)) 1/3))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `fma-def` `distribute-lft-in` `fma-udef`

Counts

4 → 73

Calls

4 calls:

0.0ms	(fma (pow x 5) 2/945 (* x (+ (* 1/45 (* x x)) 1/3)))
15.0ms	(+ (* 1/45 (* x x)) 1/3)
24.0ms	(* 1/45 (* x x))
43.0ms	(* x (+ (* 1/45 (* x x)) 1/3))

series376.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(fma (pow x 5) 2/945 (* x (+ (* 1/45 (* x x)) 1/3)))
107.0ms	(+ (* 1/45 (* x x)) 1/3)
51.0ms	(* 1/45 (* x x))
112.0ms	(* x (+ (* 1/45 (* x x)) 1/3))

simplify1.5s

Counts

85 → 85

Iterations

Iter	Nodes
3	3375
2	811
1	270
0	111

prune897.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x 1/45)
0.3b	(* x 1/45)
0.3b	(* x (fma (* (* x (* x 1/45)) (* x (* x 1/45))) (* x (* x 1/45)) 1/27))
0.3b	(/ (* x (fma (* (* x (* x 1/45)) (* x (* x 1/45))) (* x (* x 1/45)) 1/27)) (+ (* (* 1/45 (* x x)) (* 1/45 (* x x))) (- (* 1/3 1/3) (* (* 1/45 (* x x)) 1/3))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `fma-udef`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

10.0ms	(* x 1/45)
10.0ms	(* x 1/45)
11.0ms	(* x (fma (* (* x (* x 1/45)) (* x (* x 1/45))) (* x (* x 1/45)) 1/27))
157.0ms	(/ (* x (fma (* (* x (* x 1/45)) (* x (* x 1/45))) (* x (* x 1/45)) 1/27)) (+ (* (* 1/45 (* x x)) (* 1/45 (* x x))) (- (* 1/3 1/3) (* (* 1/45 (* x x)) 1/3))))

series873.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* x 1/45)
23.0ms	(* x 1/45)
405.0ms	(* x (fma (* (* x (* x 1/45)) (* x (* x 1/45))) (* x (* x 1/45)) 1/27))
428.0ms	(/ (* x (fma (* (* x (* x 1/45)) (* x (* x 1/45))) (* x (* x 1/45)) 1/27)) (+ (* (* 1/45 (* x x)) (* 1/45 (* x x))) (- (* 1/3 1/3) (* (* 1/45 (* x x)) 1/3))))

simplify2.9s

Counts

103 → 103

Iterations

Iter	Nodes
3	6007
2	1142
1	314
0	127

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x 1/45)
0.3b	(* x 1/45)
0.3b	(* x 1/45)
0.3b	(* x 1/45)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
12×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

6.0ms	(* x 1/45)
9.0ms	(* x 1/45)
10.0ms	(* x 1/45)
11.0ms	(* x 1/45)

series109.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* x 1/45)
28.0ms	(* x 1/45)
27.0ms	(* x 1/45)
17.0ms	(* x 1/45)

simplify2.6s

Counts

96 → 96

Iterations

Iter	Nodes
8	4878
7	1574
6	640
5	352
4	235
3	171
2	105
1	63
0	34

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample16.5s

Algorithm

intervals

Results

10.8s	3293×	body	2560	valid
3.5s	2450×	body	1280	valid
1.1s	1255×	body	640	valid
403.0ms	632×	body	320	valid
318.0ms	8000×	pre	80	true
186.0ms	329×	body	160	valid
8.0ms	41×	body	80	valid