Details

sample105.0ms

Algorithm

intervals

Results

53.0ms	64×	body	10240	exit
17.0ms	268×	body	80	valid
5.0ms	10×	body	640	valid
4.0ms	5×	body	1280	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

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:

10.0ms	(+ 1.0 (exp x))
18.0ms	(- (log (+ 1.0 (exp x))) (* y x))
9.0ms	(log (+ 1.0 (exp x)))

series214.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ 1.0 (exp x))
103.0ms	(- (log (+ 1.0 (exp x))) (* y x))
101.0ms	(log (+ 1.0 (exp x)))

simplify1.8s

Counts

54 → 54

Iterations

Iter	Nodes
done	5002
3	4061
2	756
1	216
0	93

prune291.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

10.0ms	(+ 1.0 (exp x))
101.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* y x))
6.0ms	(log (sqrt (+ 1.0 (exp x))))
5.0ms	(log (sqrt (+ 1.0 (exp x))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp x))
229.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* y x))
174.0ms	(log (sqrt (+ 1.0 (exp x))))
171.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify635.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	984
1	279
0	123

prune463.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* y x))) (cbrt (- (log (+ 1.0 (exp x))) (* y x)))) (cbrt (- (log (+ 1.0 (exp x))) (* y x))))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
23×	`pow1`
14×	`associate-*l/`
13×	`cbrt-prod`
12×	`pow1/3`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-exp-log` `pow-prod-up` `add-cube-cbrt`
8×	`associate-*r/`
6×	`pow-plus` `associate-r`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2` `unswap-sqr`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 100

Calls

4 calls:

68.0ms	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* y x))) (cbrt (- (log (+ 1.0 (exp x))) (* y x)))) (cbrt (- (log (+ 1.0 (exp x))) (* y x))))
5.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))
7.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))
6.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))

series1.5s

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* y x))) (cbrt (- (log (+ 1.0 (exp x))) (* y x)))) (cbrt (- (log (+ 1.0 (exp x))) (* y x))))
431.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))
470.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))
466.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* y x)))

simplify842.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	2090
1	481
0	188

prune655.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* 1/2 (* x x)))
0.0b	(- (log (+ (+ x (* 1/2 (* x x))) 2.0)) (* y x))
6.8b	(log (+ (+ x (* 1/2 (* x x))) 2.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-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-+`
2×	`associate--l-` `distribute-lft-out`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 44

Calls

3 calls:

5.0ms	(+ x (* 1/2 (* x x)))
18.0ms	(- (log (+ (+ x (* 1/2 (* x x))) 2.0)) (* y x))
18.0ms	(log (+ (+ x (* 1/2 (* x x))) 2.0))

series278.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(+ x (* 1/2 (* x x)))
107.0ms	(- (log (+ (+ x (* 1/2 (* x x))) 2.0)) (* y x))
92.0ms	(log (+ (+ x (* 1/2 (* x x))) 2.0))

simplify847.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5001
2	1580
1	335
0	122

prune272.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes114.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	2402×	body	10240	exit
1.0s	8365×	body	80	valid
114.0ms	261×	body	640	valid
102.0ms	137×	body	1280	valid
78.0ms	184×	body	320	valid
16.0ms	108×	body	160	valid