Details

sample161.0ms

Algorithm

intervals

Results

76.0ms	99×	body	10240	exit
47.0ms	272×	body	80	valid
9.0ms	13×	body	640	valid
2.0ms	6×	body	320	valid
2.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.5b	(log (+ 1.0 (exp x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

25.0ms	(- (log (+ 1.0 (exp x))) (* x y))
14.0ms	(+ 1.0 (exp x))
12.0ms	(log (+ 1.0 (exp x)))

series286.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(- (log (+ 1.0 (exp x))) (* x y))
14.0ms	(+ 1.0 (exp x))
121.0ms	(log (+ 1.0 (exp x)))

simplify6.0s

Counts

54 → 54

Iterations

Iter	Nodes
done	5003
4	4794
3	1553
2	529
1	211
0	92

prune444.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
1.2b	(log (sqrt (+ 1.0 (exp x))))
1.2b	(log (sqrt (+ 1.0 (exp x))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

21×	`log-prod`
18×	`*-un-lft-identity`
12×	`sqrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1`
7×	`associate--l+` `add-log-exp`
6×	`add-exp-log` `log-div` `sqrt-div` `log-pow`
4×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-` `sqrt-pow1` `pow1/2` `rem-log-exp`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--`

Counts

4 → 73

Calls

4 calls:

14.0ms	(+ 1.0 (exp x))
39.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
14.0ms	(log (sqrt (+ 1.0 (exp x))))
12.0ms	(log (sqrt (+ 1.0 (exp x))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ 1.0 (exp x))
223.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
184.0ms	(log (sqrt (+ 1.0 (exp x))))
185.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify5.7s

Counts

85 → 85

Iterations

Iter	Nodes
done	5004
4	4631
3	1483
2	539
1	228
0	108

prune717.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (+ 1.0 (exp x)))
0.5b	(log (+ 1.0 (exp x)))
0.6b	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
12.4b	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
19×	`pow1`
16×	`log-prod`
12×	`times-frac`
10×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
6×	`swap-sqr`
4×	`distribute-rgt-in` `log-div` `distribute-lft-in` `associate-r` `associate-l` `distribute-lft-out` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`rem-log-exp` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

11.0ms	(log (+ 1.0 (exp x)))
11.0ms	(log (+ 1.0 (exp x)))
40.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
93.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(log (+ 1.0 (exp x)))
110.0ms	(log (+ 1.0 (exp x)))
148.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
255.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

simplify3.4s

Counts

116 → 116

Iterations

Iter	Nodes
done	5002
2	1537
1	457
0	168

prune927.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize52.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ (* (* 1/2 x) x) (+ 2.0 x))) (* x y))
0.0b	(+ (* (* 1/2 x) x) (+ 2.0 x))
9.3b	(log (+ (* (* 1/2 x) x) (+ 2.0 x)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
6×	`log-prod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `log-div`
3×	`flip3-+` `associate--l+` `sum-log` `add-cbrt-cube` `flip-+`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 44

Calls

3 calls:

67.0ms	(- (log (+ (* (* 1/2 x) x) (+ 2.0 x))) (* x y))
57.0ms	(+ (* (* 1/2 x) x) (+ 2.0 x))
56.0ms	(log (+ (* (* 1/2 x) x) (+ 2.0 x)))

series295.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(- (log (+ (* (* 1/2 x) x) (+ 2.0 x))) (* x y))
32.0ms	(+ (* (* 1/2 x) x) (+ 2.0 x))
115.0ms	(log (+ (* (* 1/2 x) x) (+ 2.0 x)))

simplify2.2s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
2	1066
1	300
0	114

prune410.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes172.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.9s	2450×	body	10240	exit
852.0ms	8429×	body	80	valid
234.0ms	136×	body	1280	valid
127.0ms	244×	body	640	valid
54.0ms	167×	body	320	valid
20.0ms	105×	body	160	valid