Details

sample83.0ms

Algorithm

intervals

Results

40.0ms	66×	body	10240	exit
20.0ms	267×	body	80	valid
3.0ms	4×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	4×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	19	9
3	23	9
done	23	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.3b	(log (+ 1.0 (exp x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 62

Calls

3 calls:

13.0ms	(- (log (+ 1.0 (exp x))) (* x y))
7.0ms	(+ 1.0 (exp x))
6.0ms	(log (+ 1.0 (exp x)))

series466.0ms

Counts

3 → 9

Calls

3 calls:

390.0ms	(- (log (+ 1.0 (exp x))) (* x y))
11.0ms	(+ 1.0 (exp x))
65.0ms	(log (+ 1.0 (exp x)))

simplify2.9s

Counts

71 → 71

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	105	724
1	237	686
2	579	635
3	1595	618
4	3745	590
done	5000	589

prune235.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
4.9b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
5×	`pow1`
4×	`fma-neg` `prod-diff`
3×	`add-exp-log` `associate--l+` `log-pow` `add-log-exp`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 39

Calls

2 calls:

14.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
2.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series196.0ms

Counts

2 → 6

Calls

2 calls:

119.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
76.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify3.2s

Counts

45 → 45

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	93	722
1	222	681
2	564	626
3	1582	596
4	3752	567
done	5000	566

prune171.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))) (log 2.0))
0.0b	(fma x 0.5 (fma (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))) (log 2.0)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))) (log 2.0))
1.0ms	(fma x 0.5 (fma (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))) (log 2.0)))

series456.0ms

Counts

2 → 6

Calls

2 calls:

406.0ms	(fma (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))) (log 2.0))
50.0ms	(fma x 0.5 (fma (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))) (log 2.0)))

simplify1.5s

Counts

26 → 26

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	39	446
1	60	443
2	139	382
3	471	378
4	2255	363
done	5000	353

prune122.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
0.7b	(pow (- (log (fma (fma 1/2 x 1) x 2.0)) (* x y)) 3)
4.9b	(log (fma (fma 1/2 x 1) x 2.0))
11.8b	(cbrt (pow (- (log (fma (fma 1/2 x 1) x 2.0)) (* x y)) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `log-prod` `cube-prod`
5×	`add-cbrt-cube` `add-log-exp`
4×	`cube-div` `expm1-log1p-u` `fma-neg` `prod-diff` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `associate--l+` `log-pow` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 91

Calls

4 calls:

9.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
10.0ms	(pow (- (log (fma (fma 1/2 x 1) x 2.0)) (* x y)) 3)
1.0ms	(log (fma (fma 1/2 x 1) x 2.0))
14.0ms	(cbrt (pow (- (log (fma (fma 1/2 x 1) x 2.0)) (* x y)) 3))

series572.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
269.0ms	(pow (- (log (fma (fma 1/2 x 1) x 2.0)) (* x y)) 3)
78.0ms	(log (fma (fma 1/2 x 1) x 2.0))
106.0ms	(cbrt (pow (- (log (fma (fma 1/2 x 1) x 2.0)) (* x y)) 3))

simplify953.0ms

Counts

103 → 103

Iterations

Useful iterations: done (947.0ms)

Iter	Nodes	Cost
0	177	2212
1	440	1939
2	1326	1756
done	5000	1700

prune368.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	10	9
done	10	9

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	2465×	body	10240	exit
1.0s	8447×	body	80	valid
87.0ms	134×	body	1280	valid
82.0ms	225×	body	640	valid
79.0ms	186×	body	320	valid
14.0ms	100×	body	160	valid