Details

sample100.0ms

Algorithm

intervals

Results

44.0ms	62×	body	10240	exit
20.0ms	271×	body	80	valid
5.0ms	5×	body	1280	valid
3.0ms	8×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.5b	(log (+ 1.0 (exp x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

7.0ms	(+ 1.0 (exp x))
9.0ms	(log (+ 1.0 (exp x)))

series82.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ 1.0 (exp x))
73.0ms	(log (+ 1.0 (exp x)))

simplify2.3s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
4	2295
3	869
2	335
1	142
0	65

prune193.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (+ 1.0 (exp x)))
0.5b	(log (+ 1.0 (exp x)))
0.7b	(cbrt (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))))
0.7b	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
19×	`pow1`
16×	`log-prod`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
8×	`add-exp-log` `log-pow`
6×	`add-cbrt-cube` `swap-sqr`
4×	`distribute-rgt-in` `expm1-log1p-u` `log-div` `distribute-lft-in` `associate-r` `associate-l` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`flip3-+` `rem-log-exp` `flip-+`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

5.0ms	(log (+ 1.0 (exp x)))
5.0ms	(log (+ 1.0 (exp x)))
12.0ms	(cbrt (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))))
15.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(log (+ 1.0 (exp x)))
98.0ms	(log (+ 1.0 (exp x)))
77.0ms	(cbrt (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))))
115.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))

simplify2.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
4	3476
3	1275
2	561
1	248
0	104

prune544.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
8.3b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`fma-neg` `prod-diff`
3×	`associate--l+` `add-exp-log` `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:

13.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
2.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series247.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
106.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify2.5s

Counts

45 → 45

Iterations

Iter	Nodes
done	5003
3	1936
2	617
1	227
0	94

prune279.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b	(cbrt (log (fma (fma 1/2 x 1) x 2.0)))
8.3b	(log (fma (fma 1/2 x 1) x 2.0))
8.3b	(log (fma (fma 1/2 x 1) x 2.0))
8.3b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
8×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
7×	`add-exp-log`
4×	`cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`pow1/3`

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (log (fma (fma 1/2 x 1) x 2.0)))
2.0ms	(log (fma (fma 1/2 x 1) x 2.0))
2.0ms	(log (fma (fma 1/2 x 1) x 2.0))
2.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series520.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt (log (fma (fma 1/2 x 1) x 2.0)))
88.0ms	(log (fma (fma 1/2 x 1) x 2.0))
83.0ms	(log (fma (fma 1/2 x 1) x 2.0))
73.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify2.3s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	3727
2	924
1	308
0	124

prune530.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes161.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.1s	2391×	body	10240	exit
664.0ms	8401×	body	80	valid
131.0ms	264×	body	640	valid
90.0ms	117×	body	1280	valid
49.0ms	201×	body	320	valid
19.0ms	128×	body	160	valid