Details

sample641.0ms

Algorithm

intervals

Results

284.0ms	401×	body	80	nan
147.0ms	206×	body	10240	exit
55.0ms	240×	body	80	valid
4.0ms	19×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	179	12
6	752	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp x) 1.0)

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

36.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
80.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp x) 1.0)

series353.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
99.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
54.0ms	(- (exp (* 2.0 x)) 1.0)
38.0ms	(- (exp x) 1.0)

simplify797.0ms

Counts

135 → 135

Iterations

Useful iterations: done (786.0ms)

Iter	Nodes	Cost
0	189	2376
1	396	2279
2	1220	2169
done	5000	2156

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt`
5×	`sqrt-div`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `difference-of-squares`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*r/` `flip--`
1×	`+-commutative` `pow1/2` `exp-sum` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

67.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)
13.0ms	(- (exp (* 2.0 x)) 1.0)
64.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series217.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)
29.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify881.0ms

Counts

68 → 68

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	144	989
1	350	935
2	1170	860
done	5000	777

prune290.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp (+ x x)) (* 1.0 1.0))
4.1b	(- 1.0 (exp x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `pow-pow` `difference-of-squares`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `exp-prod` `flip3--` `diff-log` `cube-prod` `flip--`
2×	`distribute-lft-out--`
1×	`cube-mult` `pow-to-exp` `unpow3` `exp-sum` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

5.0ms	(pow (exp x) 3)
12.0ms	(- (exp (* 2.0 x)) 1.0)
72.0ms	(- (exp (+ x x)) (* 1.0 1.0))
7.0ms	(- 1.0 (exp x))

series122.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (exp x) 3)
39.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp (+ x x)) (* 1.0 1.0))
17.0ms	(- 1.0 (exp x))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: 2 (300.0ms)

Iter	Nodes	Cost
0	142	727
1	371	662
2	1429	597
done	5001	597

prune367.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 2.0 (* x (+ (* 0.5 x) 1.0)))
0.0b	(* x (+ (* 0.5 x) 1.0))
25.1b	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-r` `associate-l` `sqrt-prod` `flip-+`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

11.0ms	(+ 2.0 (* x (+ (* 0.5 x) 1.0)))
40.0ms	(* x (+ (* 0.5 x) 1.0))
9.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

series217.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ 2.0 (* x (+ (* 0.5 x) 1.0)))
85.0ms	(* x (+ (* 0.5 x) 1.0))
89.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

simplify1.0s

Counts

59 → 59

Iterations

Useful iterations: 2 (284.0ms)

Iter	Nodes	Cost
0	116	826
1	332	766
2	1674	714
done	5002	714

prune169.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes115.0ms

Accuracy

92.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 3.0b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	45
1	33	45
done	33	45

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.6s	6902×	body	10240	exit
1.7s	7372×	body	80	valid
1.0s	12606×	body	80	nan
127.0ms	739×	body	160	valid