Details

sample138.0ms

Algorithm

intervals

Results

89.0ms	174×	body	1280	valid
13.0ms	43×	body	640	valid
11.0ms	243×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	56	8
5	62	8
6	71	8
7	88	8
8	248	8
9	788	8
10	3132	8
done	5000	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
5.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite89.0ms

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:

14.0ms	(- (exp x) 2.0)
72.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (exp x) 2.0)
78.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify984.0ms

Counts

71 → 71

Iterations

Useful iterations: done (977.0ms)

Iter	Nodes	Cost
0	124	914
1	298	735
2	1173	637
done	5002	609

prune337.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

series293.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
82.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
53.0ms	(* 1/12 (pow x 4))

simplify4.9s

Counts

56 → 56

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	80	619
1	155	581
2	552	529
3	4320	526
done	5000	526

prune263.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
0.0b	(* (exp x) (+ (exp x) 2.0))
4.1b	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

rewrite80.0ms

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-r/` `associate-r*` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `associate-l` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

10.0ms	(+ (exp x) 2.0)
19.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
48.0ms	(* (exp x) (+ (exp x) 2.0))
1.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

series396.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (exp x) 2.0)
256.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
31.0ms	(* (exp x) (+ (exp x) 2.0))
94.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

simplify1.9s

Counts

89 → 89

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	133	1501
1	349	1459
2	1800	1260
done	5000	1257

prune481.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
0.0b	(* (exp x) (+ (exp x) 2.0))
4.1b	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

rewrite108.0ms

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-r/` `associate-r*` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `associate-l` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

9.0ms	(+ (exp x) 2.0)
36.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
60.0ms	(* (exp x) (+ (exp x) 2.0))
0.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

series378.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp x) 2.0)
256.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
33.0ms	(* (exp x) (+ (exp x) 2.0))
81.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

simplify2.5s

Counts

89 → 89

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	133	1501
1	349	1459
2	1800	1260
done	5000	1257

prune473.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	11	13
done	11	13

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.3s	5675×	body	1280	valid
785.0ms	7887×	body	80	valid
424.0ms	1257×	body	640	valid
105.0ms	607×	body	320	valid
83.0ms	308×	body	160	valid