Details

sample90.0ms

Algorithm

intervals

Results

38.0ms	120×	body	1280	valid
15.0ms	74×	body	640	valid
9.0ms	286×	body	80	valid
6.0ms	19×	body	160	valid
4.0ms	37×	body	320	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
6	36
5	35
4	33
3	30
2	24
1	14
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.6b

localize14.0ms

Local error

Found 1 expressions with local error:

6.1b	(- (exp x) (exp (- x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

35.0ms

(- (exp x) (exp (- x)))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(- (exp x) (exp (- x)))

simplify3.1s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
4	4704
3	1166
2	418
1	170
0	73

prune102.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (* x x) 2)
0.0b	(fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))
0.0b	(* x (fma 1/3 (* x x) 2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(fma 1/3 (* x x) 2)
0.0ms	(fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))
6.0ms	(* x (fma 1/3 (* x x) 2))

series213.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(fma 1/3 (* x x) 2)
64.0ms	(fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))
90.0ms	(* x (fma 1/3 (* x x) 2))

simplify1.8s

Counts

51 → 51

Iterations

Iter	Nodes
done	5025
3	1864
2	390
1	143
0	66

prune290.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 1/3 (* x x)) x) (* 2 x))
0.0b	(fma (pow x 5) 1/60 (+ (* (* 1/3 (* x x)) x) (* 2 x)))
0.1b	(* (* 1/3 (* x x)) x)
0.2b	(* 1/3 (* x x))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

39.0ms	(+ (* (* 1/3 (* x x)) x) (* 2 x))
0.0ms	(fma (pow x 5) 1/60 (+ (* (* 1/3 (* x x)) x) (* 2 x)))
56.0ms	(* (* 1/3 (* x x)) x)
25.0ms	(* 1/3 (* x x))

series290.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (* (* 1/3 (* x x)) x) (* 2 x))
71.0ms	(fma (pow x 5) 1/60 (+ (* (* 1/3 (* x x)) x) (* 2 x)))
63.0ms	(* (* 1/3 (* x x)) x)
45.0ms	(* 1/3 (* x x))

simplify4.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4972
2	1065
1	295
0	103

prune286.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 3 x))
0.0b	(/ 1 (exp (* 3 x)))
0.0b	(/ (- (exp (* 3 x)) (/ 1 (exp (* 3 x)))) (fma (/ 1 (exp x)) (/ 1 (exp x)) (fma (exp x) (exp x) 1)))
6.0b	(- (exp (* 3 x)) (/ 1 (exp (* 3 x))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
70×	`times-frac`
60×	`add-cube-cbrt`
39×	`prod-diff`
15×	`difference-of-squares`
11×	`associate-/l*`
10×	`div-inv` `distribute-lft-out--`
9×	`add-log-exp`
8×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp` `pow-flip`
2×	`cbrt-undiv` `exp-prod` `clear-num` `frac-2neg` `flip3--` `exp-to-pow` `flip--` `associate-/l/`
1×	`rec-exp` `sub-neg` `diff-log` `1-exp` `div-sub` `inv-pow` `rem-exp-log`

Counts

4 → 160

Calls

4 calls:

3.0ms	(exp (* 3 x))
7.0ms	(/ 1 (exp (* 3 x)))
54.0ms	(/ (- (exp (* 3 x)) (/ 1 (exp (* 3 x)))) (fma (/ 1 (exp x)) (/ 1 (exp x)) (fma (exp x) (exp x) 1)))
21.0ms	(- (exp (* 3 x)) (/ 1 (exp (* 3 x))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp (* 3 x))
17.0ms	(/ 1 (exp (* 3 x)))
224.0ms	(/ (- (exp (* 3 x)) (/ 1 (exp (* 3 x)))) (fma (/ 1 (exp x)) (/ 1 (exp x)) (fma (exp x) (exp x) 1)))
56.0ms	(- (exp (* 3 x)) (/ 1 (exp (* 3 x))))

simplify2.7s

Counts

172 → 172

Iterations

Iter	Nodes
done	5000
3	4155
2	1315
1	618
0	265

prune891.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
1	13
0	12

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.7s	3315×	body	1280	valid
765.0ms	2534×	body	640	valid
430.0ms	8111×	body	80	valid
267.0ms	1268×	body	320	valid
59.0ms	615×	body	160	valid