Details

sample123.0ms

Algorithm

intervals

Results

81.0ms	180×	body	1280	valid
10.0ms	41×	body	640	valid
9.0ms	245×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
10	2899
9	809
8	249
7	88
6	71
5	62
4	56
3	40
2	26
1	14
0	7

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.3b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite115.0ms

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

Counts

2 → 61

Calls

2 calls:

20.0ms	(- (exp (- x)) 2.0)
94.0ms	(+ (- (exp (- x)) 2.0) (exp x))

series86.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (exp (- x)) 2.0)
65.0ms	(+ (- (exp (- x)) 2.0) (exp x))

simplify800.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	1104
1	278
0	111

prune331.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

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

series230.0ms

Counts

2 → 6

Calls

2 calls:

101.0ms	(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (* x x)))
129.0ms	(fma (pow x 4) 1/12 (* x x))

simplify1.0s

Counts

26 → 26

Iterations

Iter	Nodes
done	5002
3	1140
2	217
1	57
0	37

prune150.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (- x)) 2.0)
0.0b	(fma (- 2.0) 2.0 (exp (* x -2)))
0.0b	(/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (exp (- x)) 2.0))
4.0b	(+ (/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (exp (- x)) 2.0)) (exp x))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`fma-def`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `div-inv`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef`

Counts

4 → 94

Calls

4 calls:

16.0ms	(+ (exp (- x)) 2.0)
0.0ms	(fma (- 2.0) 2.0 (exp (* x -2)))
24.0ms	(/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (exp (- x)) 2.0))
151.0ms	(+ (/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (exp (- x)) 2.0)) (exp x))

series319.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (exp (- x)) 2.0)
51.0ms	(fma (- 2.0) 2.0 (exp (* x -2)))
90.0ms	(/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (exp (- x)) 2.0))
166.0ms	(+ (/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (exp (- x)) 2.0)) (exp x))

simplify726.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1218
1	355
0	152

prune701.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 2.0 2.0) (* (exp (- x)) 2.0))
0.0b	(* (exp (- x)) (exp (- x)))
0.0b	(pow (exp (- x)) 3)
60.5b	(fma (/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (pow (exp (- x)) 3) (pow 2.0 3))) (+ (* (exp (- x)) (exp (- x))) (- (* 2.0 2.0) (* (exp (- x)) 2.0))) (exp x))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

86×	`exp-prod`
46×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
27×	`distribute-rgt-neg-in`
23×	`distribute-lft-neg-in`
15×	`pow-prod-down`
13×	`pow-sqr` `pow-prod-up`
12×	`pow1`
11×	`pow-pow`
9×	`neg-mul-1`
8×	`exp-neg`
7×	`neg-sub0` `add-cbrt-cube` `exp-diff`
6×	`add-log-exp`
4×	`expm1-log1p-u` `frac-times` `add-exp-log` `log1p-expm1-u`
3×	`pow-unpow` `unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
2×	`cube-div` `associate-l/` `associate-r/`
1×	`pow2` `cube-mult` `pow-to-exp` `sub-neg` `pow-plus` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `unpow3` `prod-diff` `pow-exp` `prod-exp` `un-div-inv` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

7.0ms	(- (* 2.0 2.0) (* (exp (- x)) 2.0))
67.0ms	(* (exp (- x)) (exp (- x)))
12.0ms	(pow (exp (- x)) 3)
0.0ms	(fma (/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (pow (exp (- x)) 3) (pow 2.0 3))) (+ (* (exp (- x)) (exp (- x))) (- (* 2.0 2.0) (* (exp (- x)) 2.0))) (exp x))

series424.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* 2.0 2.0) (* (exp (- x)) 2.0))
17.0ms	(* (exp (- x)) (exp (- x)))
42.0ms	(pow (exp (- x)) 3)
328.0ms	(fma (/ (fma (- 2.0) 2.0 (exp (* x -2))) (+ (pow (exp (- x)) 3) (pow 2.0 3))) (+ (* (exp (- x)) (exp (- x))) (- (* 2.0 2.0) (* (exp (- x)) 2.0))) (exp x))

simplify2.9s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	4053
1	711
0	251

prune797.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
0	10

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.3s	5605×	body	1280	valid
795.0ms	1277×	body	640	valid
551.0ms	8051×	body	80	valid
106.0ms	661×	body	320	valid
31.0ms	303×	body	160	valid