Details

sample163.0ms

Algorithm

intervals

Results

105.0ms	175×	body	1280	valid
16.0ms	46×	body	640	valid
14.0ms	251×	body	80	valid
4.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid

simplify2.4s

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	249	8
9	809	8
10	2899	8
done	5000	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite74.0ms

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×	`neg-sub0` `exp-neg` `expm1-log1p-u` `pow1` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+`

Counts

2 → 65

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
60.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (exp x) 2.0)
68.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify773.0ms

Counts

71 → 71

Iterations

Useful iterations: done (770.0ms)

Iter	Nodes	Cost
0	124	914
1	297	736
2	1176	637
done	5001	609

prune312.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

15.0ms	(* 1/360 (pow x 6))
0.0ms	(fma 1/12 (pow x 4) (* 1/360 (pow x 6)))

series250.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(* 1/360 (pow x 6))
193.0ms	(fma 1/12 (pow x 4) (* 1/360 (pow x 6)))

simplify1.1s

Counts

43 → 43

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	67	403
1	135	371
2	395	345
3	1979	341
done	5001	338

prune190.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (+ x x)) (* 2.0 2.0))
0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
3.9b	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

63.0ms	(- (exp (+ x x)) (* 2.0 2.0))
46.0ms	(* (+ (exp x) 2.0) (exp x))
28.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
1.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

series368.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (exp (+ x x)) (* 2.0 2.0))
33.0ms	(* (+ (exp x) 2.0) (exp x))
208.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
108.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

simplify1.4s

Counts

94 → 94

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	159	1699
1	402	1654
2	1721	1416
done	5000	1402

prune379.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (+ x x)) (* 2.0 2.0))
0.0b	(/ (exp (- x)) (+ (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)))
3.9b	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
25×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
11×	`add-cbrt-cube`
9×	`add-exp-log`
7×	`distribute-lft-out`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `fma-neg` `prod-diff` `associate-/r/` `log1p-expm1-u`
3×	`associate-l` `exp-sum` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`neg-sub0` `exp-neg` `clear-num` `sub-neg` `frac-2neg` `flip3--` `exp-diff` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `flip--`

Counts

4 → 110

Calls

4 calls:

51.0ms	(- (exp (+ x x)) (* 2.0 2.0))
24.0ms	(/ (exp (- x)) (+ (exp x) 2.0))
45.0ms	(* (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (/ (exp (- x)) (+ (exp x) 2.0)))
0.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

series306.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (exp (+ x x)) (* 2.0 2.0))
41.0ms	(/ (exp (- x)) (+ (exp x) 2.0))
158.0ms	(* (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (/ (exp (- x)) (+ (exp x) 2.0)))
76.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

simplify1.1s

Counts

122 → 122

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	193	2358
1	468	2285
2	2040	2019
done	5000	1987

prune745.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes59.0ms

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

sample4.9s

Algorithm

intervals

Results

2.9s	5687×	body	1280	valid
975.0ms	7897×	body	80	valid
444.0ms	1226×	body	640	valid
98.0ms	603×	body	320	valid
33.0ms	309×	body	160	valid