Details

sample73.0ms

Algorithm

intervals

Results

50.0ms	182×	body	1280	valid
5.0ms	37×	body	640	valid
5.0ms	240×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify226.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1454	5
9	5001	5
done	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

11.0ms	(- (exp x) 2.0)
57.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
59.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify33.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367
done	5001	367

prune161.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

0.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
12.0ms	(* 1/12 (pow x 4))

series223.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
123.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
41.0ms	(* 1/12 (pow x 4))

simplify96.0ms

Counts

56 → 56

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	143	265
1	544	240
2	2626	237
3	5001	237
done	5001	237

prune139.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
4.8b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`add-exp-log` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `associate-r` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

9.0ms	(+ (exp x) 2.0)
37.0ms	(* (+ (exp x) 2.0) (exp x))
17.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 2.0)
28.0ms	(* (+ (exp x) 2.0) (exp x))
216.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
93.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify38.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	312	834
1	1220	713
2	5002	710
done	5002	710

prune440.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (expm1 (log1p (* (+ (exp x) 2.0) (exp x)))))
0.0b	(expm1 (log1p (* (+ (exp x) 2.0) (exp x))))
4.8b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/r` `associate-/l`
2×	`associate-*l/`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `expm1-udef` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

38.0ms	(* (+ (exp x) 2.0) (exp x))
5.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (expm1 (log1p (* (+ (exp x) 2.0) (exp x)))))
0.0ms	(expm1 (log1p (* (+ (exp x) 2.0) (exp x))))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series572.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ (exp x) 2.0) (exp x))
332.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (expm1 (log1p (* (+ (exp x) 2.0) (exp x)))))
126.0ms	(expm1 (log1p (* (+ (exp x) 2.0) (exp x))))
92.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify41.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	309	1082
1	1225	922
2	5001	913
done	5001	913

prune263.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5
done	11	5

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5700×	body	1280	valid
179.0ms	1220×	body	640	valid
164.0ms	7908×	body	80	valid
52.0ms	612×	body	320	valid
20.0ms	312×	body	160	valid