Details

sample326.0ms

Algorithm

intervals

Results

40.0ms	213×	body	10240	exit
12.0ms	389×	body	80	nan
7.0ms	233×	body	80	valid
2.0ms	25×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	170	12
6	465	12
7	1663	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

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))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite45.0ms

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:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp x) 1.0)

simplify1.4s

Counts

135 → 135

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	951	2169
3	3523	2156
done	5000	2154

prune324.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

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)
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite63.0ms

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:

27.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
4.0ms	(+ (exp x) 1.0)
4.0ms	(- (exp (* 2.0 x)) 1.0)
27.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series186.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.1s

Counts

68 → 68

Iterations

Useful iterations: 3 (352.0ms)

Iter	Nodes	Cost
0	144	989
1	339	935
2	968	860
3	3343	775
done	5000	775

prune211.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 2.0 (* x (+ 1.0 (* 0.5 x))))
0.0b	(* x (+ 1.0 (* 0.5 x)))
22.5b	(sqrt (+ 2.0 (* x (+ 1.0 (* 0.5 x)))))

rewrite14.0ms

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:

2.0ms	(+ 2.0 (* x (+ 1.0 (* 0.5 x))))
7.0ms	(* x (+ 1.0 (* 0.5 x)))
3.0ms	(sqrt (+ 2.0 (* x (+ 1.0 (* 0.5 x)))))

series171.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ 2.0 (* x (+ 1.0 (* 0.5 x))))
68.0ms	(* x (+ 1.0 (* 0.5 x)))
82.0ms	(sqrt (+ 2.0 (* x (+ 1.0 (* 0.5 x)))))

simplify632.0ms

Counts

59 → 59

Iterations

Useful iterations: done (630.0ms)

Iter	Nodes	Cost
0	116	822
1	305	750
2	1111	698
done	5002	689

prune113.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- 1.0 (exp x))

rewrite37.0ms

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:

2.0ms	(pow (exp x) 3)
27.0ms	(- (exp (+ x x)) (* 1.0 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
3.0ms	(- 1.0 (exp x))

series84.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (exp x) 3)
23.0ms	(- (exp (+ x x)) (* 1.0 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- 1.0 (exp x))

simplify461.0ms

Counts

80 → 80

Iterations

Useful iterations: done (459.0ms)

Iter	Nodes	Cost
0	142	727
1	305	659
2	991	597
done	5000	590

prune296.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

74.1% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.9b

bsearch40.0ms

Steps

Iters	Range		Point
8	-0.0008391074150366579	-8.849834202292668e-07	-1.2887874422510308e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	31	35
done	31	35

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6739×	body	10240	exit
374.0ms	12781×	body	80	nan
232.0ms	7403×	body	80	valid
53.0ms	711×	body	160	valid