Details

sample97.0ms

Algorithm

intervals

Results

52.0ms	82×	body	10240	exit
15.0ms	263×	body	80	valid
8.0ms	11×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	320	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* y x))
0.2b	(log (+ 1.0 (exp x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

18.0ms	(- (log (+ 1.0 (exp x))) (* y x))
9.0ms	(log (+ 1.0 (exp x)))

series187.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (log (+ 1.0 (exp x))) (* y x))
110.0ms	(log (+ 1.0 (exp x)))

simplify1.2s

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
3	2579
2	540
1	183
0	84

prune179.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.2b	(log (+ 1.0 (exp x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

21.0ms	(- (log (+ 1.0 (exp x))) (* x y))
5.0ms	(log (+ 1.0 (exp x)))

series151.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (log (+ 1.0 (exp x))) (* x y))
80.0ms	(log (+ 1.0 (exp x)))

simplify1.2s

Counts

39 → 39

Iterations

Iter	Nodes
done	5001
3	2458
2	524
1	181
0	83

prune198.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 0.5 (* 0.25 x)))
0.0b	(- (+ (+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0))) (* x (+ 0.5 (* 0.25 x)))) (* x y))
0.0b	(+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0)))
6.6b	(+ (+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0))) (* x (+ 0.5 (* 0.25 x))))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-log-exp`
9×	`add-sqr-sqrt`
7×	`sum-log` `*-un-lft-identity` `flip3-+` `add-cube-cbrt` `flip-+`
6×	`pow1` `add-cbrt-cube` `associate-*r/` `add-exp-log`
4×	`associate-+l+` `frac-add`
3×	`log-prod` `diff-log` `associate-r` `associate-l`
2×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in`
1×	`sub-neg` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

21.0ms	(* x (+ 0.5 (* 0.25 x)))
166.0ms	(- (+ (+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0))) (* x (+ 0.5 (* 0.25 x)))) (* x y))
13.0ms	(+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0)))
29.0ms	(+ (+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0))) (* x (+ 0.5 (* 0.25 x))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* x (+ 0.5 (* 0.25 x)))
59.0ms	(- (+ (+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0))) (* x (+ 0.5 (* 0.25 x)))) (* x y))
339.0ms	(+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0)))
38.0ms	(+ (+ (log 2.0) (* (* -1/2 (/ x 2.0)) (/ x 2.0))) (* x (+ 0.5 (* 0.25 x))))

simplify1.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5002
2	2457
1	494
0	155

prune490.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (+ 1.0 (exp x)))
0.6b	(* (+ (log (+ 1.0 (exp x))) (* x y)) (log (+ 1.0 (exp x))))
0.7b	(pow (log (+ 1.0 (exp x))) 3)
15.8b	(/ (- (pow (log (+ 1.0 (exp x))) 3) (pow (* x y) 3)) (+ (* (* y x) (* y x)) (* (+ (log (+ 1.0 (exp x))) (* x y)) (log (+ 1.0 (exp x))))))

rewrite537.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
39×	`times-frac`
32×	`difference-of-squares`
30×	`add-cube-cbrt`
25×	`sqr-pow`
13×	`associate-/l*`
12×	`log-prod` `unpow-prod-down` `cube-prod`
11×	`pow1`
10×	`add-exp-log`
9×	`add-cbrt-cube`
4×	`distribute-rgt-in` `difference-cubes` `distribute-lft-in` `associate-r` `log-pow` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `associate-/r` `flip3-+` `associate-l*` `flip-+` `distribute-lft-out`
2×	`log-div` `associate-*l/` `associate-/r/` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `cbrt-undiv` `clear-num` `pow-pow` `frac-2neg` `flip3--` `unpow3` `div-sub` `div-exp` `rem-log-exp` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

5.0ms	(log (+ 1.0 (exp x)))
406.0ms	(* (+ (log (+ 1.0 (exp x))) (* x y)) (log (+ 1.0 (exp x))))
3.0ms	(pow (log (+ 1.0 (exp x))) 3)
119.0ms	(/ (- (pow (log (+ 1.0 (exp x))) 3) (pow (* x y) 3)) (+ (* (* y x) (* y x)) (* (+ (log (+ 1.0 (exp x))) (* x y)) (log (+ 1.0 (exp x))))))

series826.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(log (+ 1.0 (exp x)))
199.0ms	(* (+ (log (+ 1.0 (exp x))) (* x y)) (log (+ 1.0 (exp x))))
172.0ms	(pow (log (+ 1.0 (exp x))) 3)
388.0ms	(/ (- (pow (log (+ 1.0 (exp x))) 3) (pow (* x y) 3)) (+ (* (* y x) (* y x)) (* (+ (log (+ 1.0 (exp x))) (* x y)) (log (+ 1.0 (exp x))))))

simplify2.6s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
2	4530
1	791
0	278

prune825.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes175.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.2s	2439×	body	10240	exit
690.0ms	8334×	body	80	valid
128.0ms	299×	body	640	valid
124.0ms	124×	body	1280	valid
49.0ms	199×	body	320	valid
16.0ms	111×	body	160	valid