Details

sample408.0ms

Algorithm

intervals

Results

248.0ms	101×	body	2560	valid
102.0ms	89×	body	1280	valid
23.0ms	34×	body	640	valid
11.0ms	20×	body	320	valid
9.0ms	256×	pre	80	true
3.0ms	11×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	8
0	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.2b

localize47.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
2.6b	(- (/ 1 x) (/ 1 (tan x)))

rewrite33.0ms

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))
19.0ms	(- (/ 1 x) (/ 1 (tan x)))

series118.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ 1 (tan x))
89.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify2.7s

Counts

268 → 268

Iterations

Iter	Nodes
3	2892
2	1334
1	757
0	342

prune576.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (* x 1/45)) 1/3)
0.1b	(* x (* x 1/45))
0.2b	(* x 1/45)
0.3b	(* x (+ (* x (* x 1/45)) 1/3))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

13.0ms	(+ (* x (* x 1/45)) 1/3)
28.0ms	(* x (* x 1/45))
7.0ms	(* x 1/45)
64.0ms	(* x (+ (* x (* x 1/45)) 1/3))

series247.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* x (* x 1/45)) 1/3)
30.0ms	(* x (* x 1/45))
27.0ms	(* x 1/45)
128.0ms	(* x (+ (* x (* x 1/45)) 1/3))

simplify1.7s

Counts

94 → 94

Iterations

Iter	Nodes
3	3704
2	825
1	261
0	106

prune289.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x 1/45)
0.2b	(* x 1/45)
0.3b	(* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27))
0.4b	(/ (* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27)) (+ (* (* x (* x 1/45)) (* x (* x 1/45))) (- (* 1/3 1/3) (* (* x (* x 1/45)) 1/3))))

rewrite139.0ms

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:

6.0ms	(* x 1/45)
5.0ms	(* x 1/45)
5.0ms	(* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27))
121.0ms	(/ (* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27)) (+ (* (* x (* x 1/45)) (* x (* x 1/45))) (- (* 1/3 1/3) (* (* x (* x 1/45)) 1/3))))

series647.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* x 1/45)
18.0ms	(* x 1/45)
268.0ms	(* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27))
344.0ms	(/ (* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27)) (+ (* (* x (* x 1/45)) (* x (* x 1/45))) (- (* 1/3 1/3) (* (* x (* x 1/45)) 1/3))))

simplify3.5s

Counts

103 → 103

Iterations

Iter	Nodes
3	6068
2	1143
1	314
0	127

prune531.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) 1/91125)
0.2b	(* -1/45 (* x x))
0.2b	(* (* -1/45 (* x x)) 1/3)

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

134×	`pow1`
36×	`pow-prod-up`
35×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
22×	`pow-sqr`
20×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
9×	`add-sqr-sqrt`
8×	`associate-r`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
1×	`swap-sqr`

Counts

4 → 134

Calls

4 calls:

24.0ms	(* (* x x) (* x x))
14.0ms	(* (* x x) 1/91125)
25.0ms	(* -1/45 (* x x))
51.0ms	(* (* -1/45 (* x x)) 1/3)

series174.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* x x) (* x x))
29.0ms	(* (* x x) 1/91125)
42.0ms	(* -1/45 (* x x))
49.0ms	(* (* -1/45 (* x x)) 1/3)

simplify2.5s

Counts

146 → 146

Iterations

Iter	Nodes
3	4135
2	1007
1	333
0	131

prune591.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	25
1	25
0	21

end0.0ms

sample16.6s

Algorithm

intervals

Results

9.6s	3190×	body	2560	valid
4.1s	2568×	body	1280	valid
1.6s	1249×	body	640	valid
473.0ms	628×	body	320	valid
435.0ms	8000×	pre	80	true
123.0ms	322×	body	160	valid
9.0ms	43×	body	80	valid