Details

sample539.0ms

Algorithm

intervals

Results

297.0ms	101×	body	2560	valid
131.0ms	87×	body	1280	valid
63.0ms	33×	body	640	valid
13.0ms	19×	body	320	valid
12.0ms	256×	pre	80	true
5.0ms	12×	body	160	valid
1.0ms	4×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	32
3	32
2	30
1	22
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.2b

localize52.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.1b	(- (/ 1 x) (/ 1 (tan x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
12×	`add-cube-cbrt`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
5×	`div-inv`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`div-exp` `insert-posit16`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 63

Calls

2 calls:

12.0ms	(/ 1 (tan x))
32.0ms	(- (/ 1 x) (/ 1 (tan x)))

series170.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ 1 (tan x))
118.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.1s

Counts

69 → 69

Iterations

Iter	Nodes
4	2261
3	1328
2	779
1	444
0	120

prune523.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`associate-r`
13×	`pow1`
12×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`prod-exp`
6×	`cbrt-unprod`
5×	`pow-prod-down` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp`
2×	`associate-*l/` `sqr-pow`
1×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 85

Calls

4 calls:

10.0ms	(* 2/945 (pow x 5))
12.0ms	(* x (* 1/45 x))
6.0ms	(* 1/45 x)
56.0ms	(* (+ (* x (* 1/45 x)) 1/3) x)

series237.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* 2/945 (pow x 5))
40.0ms	(* x (* 1/45 x))
15.0ms	(* 1/45 x)
105.0ms	(* (+ (* x (* 1/45 x)) 1/3) x)

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
3	3416
2	1238
1	524
0	130

prune983.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/45 x)
0.2b	(* 1/45 x)
0.3b	(* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x)
0.4b	(/ (* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x) (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))

rewrite168.0ms

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×	`associate-*l/` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `flip3-+` `times-frac` `pow-prod-down` `-commutative` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* 1/45 x)
5.0ms	(* 1/45 x)
11.0ms	(* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x)
146.0ms	(/ (* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x) (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/45 x)
17.0ms	(* 1/45 x)
309.0ms	(* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x)
405.0ms	(/ (* (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) x) (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))

simplify4.9s

Counts

97 → 97

Iterations

Iter	Nodes
3	10447
2	1959
1	610
0	131

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/45 x)
0.2b	(* 1/45 x)
0.3b	(* (/ (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))) (/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))))
0.3b	(/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3)))))

rewrite928.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
66×	`times-frac`
49×	`*-un-lft-identity` `add-cube-cbrt`
36×	`sqrt-prod`
30×	`associate-r` `associate-l`
22×	`add-cbrt-cube` `add-exp-log`
11×	`unswap-sqr`
10×	`pow1`
6×	`associate-/r*` `sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`insert-posit16` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 158

Calls

4 calls:

10.0ms	(* 1/45 x)
10.0ms	(* 1/45 x)
701.0ms	(* (/ (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))) (/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))))
202.0ms	(/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3)))))

series615.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/45 x)
15.0ms	(* 1/45 x)
403.0ms	(* (/ (+ 1/27 (* (* (* x x) (* (* x x) 1/91125)) (* x x))) (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))) (/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3))))))
167.0ms	(/ x (sqrt (+ (* (* x (* 1/45 x)) (* x (* 1/45 x))) (- (* 1/3 1/3) (* (* x (* 1/45 x)) 1/3)))))

simplify1.3s

Counts

170 → 170

Iterations

Iter	Nodes
2	2658
1	1037
0	227

prune2.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	38
1	38
0	26

end0.0ms

sample16.5s

Algorithm

intervals

Results

9.9s	3294×	body	2560	valid
4.3s	2480×	body	1280	valid
1.0s	1283×	body	640	valid
367.0ms	614×	body	320	valid
355.0ms	8000×	pre	80	true
207.0ms	295×	body	160	valid
33.0ms	34×	body	80	valid