Details

sample103.0ms

Algorithm

intervals

Results

64.0ms	93×	body	10240	exit
17.0ms	275×	body	80	valid
2.0ms	6×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

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` `log-div` `associate--l+` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

5.0ms	(+ 1.0 (exp x))
9.0ms	(- (log (+ 1.0 (exp x))) (* x y))
5.0ms	(log (+ 1.0 (exp x)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ 1.0 (exp x))
101.0ms	(- (log (+ 1.0 (exp x))) (* x y))
93.0ms	(log (+ 1.0 (exp x)))

simplify1.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	3089
2	648
1	211
0	92

prune241.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (- (exp x) 1.0))
0.4b	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
0.5b	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
3.9b	(- (exp x) 1.0)

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`log-prod`
10×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-r`
4×	`associate-/r/`
3×	`associate-/r` `sub-neg` `flip3-+` `associate-l` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `div-exp` `rem-log-exp` `associate-*r/` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

46.0ms	(* (exp x) (- (exp x) 1.0))
124.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
36.0ms	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
8.0ms	(- (exp x) 1.0)

series397.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (exp x) (- (exp x) 1.0))
105.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
229.0ms	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
17.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1968
1	484
0	195

prune743.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ 1.0 (exp x)))
0.2b	(sqrt (+ 1.0 (exp x)))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 (exp x)))
8.0ms	(sqrt (+ 1.0 (exp x)))
6.0ms	(log (sqrt (+ 1.0 (exp x))))
10.0ms	(log (sqrt (+ 1.0 (exp x))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ 1.0 (exp x)))
60.0ms	(sqrt (+ 1.0 (exp x)))
136.0ms	(log (sqrt (+ 1.0 (exp x))))
154.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
3	2813
2	517
1	166
0	86

prune407.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

56.0ms	(- (log (+ (+ (* (* x x) 1/2) 2.0) x)) (* x y))
112.0ms	(+ (+ (* (* x x) 1/2) 2.0) x)
74.0ms	(log (+ (+ (* (* x x) 1/2) 2.0) x))

series180.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(- (log (+ (+ (* (* x x) 1/2) 2.0) x)) (* x y))
19.0ms	(+ (+ (* (* x x) 1/2) 2.0) x)
60.0ms	(log (+ (+ (* (* x x) 1/2) 2.0) x))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	5002
2	1198
1	287
0	114

prune334.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes146.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.0s	2554×	body	10240	exit
683.0ms	8468×	body	80	valid
105.0ms	120×	body	1280	valid
101.0ms	254×	body	640	valid
43.0ms	183×	body	320	valid
13.0ms	93×	body	160	valid