Details

sample57.0ms

Algorithm

intervals

Results

29.0ms	68×	body	10240	exit
10.0ms	279×	body	80	valid
3.0ms	5×	body	1280	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.8b	(log (+ 1.0 (exp x)))

rewrite14.0ms

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:

3.0ms	(+ 1.0 (exp x))
6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series135.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
69.0ms	(log (+ 1.0 (exp x)))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	105	724
1	236	686
2	586	635
3	1770	618
done	5001	596

prune182.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(fma y (- x) (log (+ (exp x) 1.0)))
0.8b	(log (+ (exp x) 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

4.0ms	(+ (exp x) 1.0)
0.0ms	(fma y (- x) (log (+ (exp x) 1.0)))
4.0ms	(log (+ (exp x) 1.0))

series129.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ (exp x) 1.0)
55.0ms	(fma y (- x) (log (+ (exp x) 1.0)))
67.0ms	(log (+ (exp x) 1.0))

simplify2.3s

Counts

53 → 53

Iterations

Useful iterations: 4 (822.0ms)

Iter	Nodes	Cost
0	80	466
1	164	451
2	370	407
3	1023	403
4	3348	400
done	5001	400

prune147.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x (- 0.5 y) (log 2.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`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

1 → 10

Calls

1 calls:

0.0ms

(fma x (- 0.5 y) (log 2.0))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

(fma x (- 0.5 y) (log 2.0))

simplify809.0ms

Counts

13 → 13

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	21	131
1	33	131
2	71	108
3	214	108
4	1018	108
done	5000	108

prune33.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (fma y (- x) (log (+ (exp x) 1.0))))
0.6b	(* (sqrt (fma y (- x) (log (+ (exp x) 1.0)))) (sqrt (fma y (- x) (log (+ (exp x) 1.0)))))
0.8b	(log (+ (exp x) 1.0))
0.8b	(log (+ (exp x) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`pow1`
21×	`sqrt-prod`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `log-prod` `swap-sqr`
6×	`associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

1.0ms	(sqrt (fma y (- x) (log (+ (exp x) 1.0))))
7.0ms	(* (sqrt (fma y (- x) (log (+ (exp x) 1.0)))) (sqrt (fma y (- x) (log (+ (exp x) 1.0)))))
3.0ms	(log (+ (exp x) 1.0))
6.0ms	(log (+ (exp x) 1.0))

series313.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (fma y (- x) (log (+ (exp x) 1.0))))
57.0ms	(* (sqrt (fma y (- x) (log (+ (exp x) 1.0)))) (sqrt (fma y (- x) (log (+ (exp x) 1.0)))))
62.0ms	(log (+ (exp x) 1.0))
60.0ms	(log (+ (exp x) 1.0))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	131	1988
1	266	1393
2	667	1253
3	2115	1185
done	5000	1183

prune266.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 11.6b

bsearch32.0ms

Steps

Iters	Range		Point
8	-1.046355961971052	-1.6471395275746527e-05	-1.694724557776266e-05

simplify2.0ms

Iterations

Useful iterations: done (2.0ms)

Iter	Nodes	Cost
0	22	32
1	23	32
done	23	30

end0.0ms

sample1.7s

Algorithm

intervals

Results

962.0ms	2448×	body	10240	exit
301.0ms	8398×	body	80	valid
66.0ms	256×	body	640	valid
62.0ms	122×	body	1280	valid
26.0ms	170×	body	320	valid
10.0ms	114×	body	160	valid