Details

sample109.0ms

Algorithm

intervals

Results

71.0ms	179×	body	1280	valid
10.0ms	274×	body	80	valid
7.0ms	36×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	12×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	49	8
5	54	8
6	63	8
7	80	8
8	95	8
9	103	8
10	111	8
done	111	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite83.0ms

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:

17.0ms	(- (exp x) 2.0)
63.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series105.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (exp x) 2.0)
79.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify2.7s

Counts

71 → 71

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	124	914
1	274	729
2	709	628
3	3051	557
done	5000	554

prune252.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-r`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`associate-l` `prod-exp` `unswap-sqr`
2×	`pow1` `expm1-log1p-u` `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:

1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
24.0ms	(* 1/12 (pow x 4))

series265.0ms

Counts

2 → 6

Calls

2 calls:

186.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
79.0ms	(* 1/12 (pow x 4))

simplify1.9s

Counts

43 → 43

Iterations

Useful iterations: 3 (295.0ms)

Iter	Nodes	Cost
0	67	403
1	125	371
2	284	345
3	930	342
done	5000	342

prune188.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(- (exp x) 2.0)
0.0b	(* (- (exp x) 2.0) (- (exp x) 2.0))
5.4b	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (exp (* x -2)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
57×	`prod-diff`
47×	`add-cube-cbrt`
22×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
11×	`pow1`
10×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`distribute-lft-out--`
7×	`sub-neg` `fma-neg` `swap-sqr` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

28.0ms	(- (exp x) 2.0)
19.0ms	(- (exp x) 2.0)
86.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
73.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (exp (* x -2)))

series188.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (exp x) 2.0)
15.0ms	(- (exp x) 2.0)
40.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
109.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (exp (* x -2)))

simplify1.1s

Counts

174 → 174

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	204	3047
1	445	2309
2	1351	1937
done	5000	1786

prune663.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(pow (exp x) 2)
0.0b	(pow (exp x) -2)
3.5b	(- (+ (pow (exp x) 2) 4.0) (fma 4.0 (exp x) (pow (exp x) -2)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
21×	`prod-diff`
11×	`add-log-exp`
8×	`pow-pow`
7×	`fma-neg`
6×	`pow1` `unpow-prod-down` `pow-unpow` `exp-prod`
5×	`distribute-lft-out`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`diff-log` `distribute-lft-out--`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `flip--` `difference-of-squares` `sqr-pow`
1×	`associate--l+` `sum-log` `fma-udef` `associate--r+` `unpow2`

Counts

4 → 109

Calls

4 calls:

25.0ms	(- (exp x) 2.0)
9.0ms	(pow (exp x) 2)
9.0ms	(pow (exp x) -2)
223.0ms	(- (+ (pow (exp x) 2) 4.0) (fma 4.0 (exp x) (pow (exp x) -2)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (exp x) 2.0)
23.0ms	(pow (exp x) 2)
37.0ms	(pow (exp x) -2)
129.0ms	(- (+ (pow (exp x) 2) 4.0) (fma 4.0 (exp x) (pow (exp x) -2)))

simplify4.3s

Counts

121 → 121

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	200	2111
1	431	1592
2	1074	1296
3	4707	1065
done	5000	1065

prune476.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes41.0ms

Accuracy

52.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.6b

bsearch60.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.038555408130684456

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	41
1	30	41
done	30	41

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.6s	5661×	body	1280	valid
472.0ms	7952×	body	80	valid
397.0ms	1239×	body	640	valid
170.0ms	634×	body	320	valid
36.0ms	318×	body	160	valid