Details

sample398.0ms

Algorithm

intervals

Results

57.0ms	196×	body	10240	exit
12.0ms	406×	body	80	nan
9.0ms	229×	body	80	valid
3.0ms	35×	body	160	valid

simplify2.0s

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	175	12
6	479	12
7	1665	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
7.2b	(- (exp (* 2.0 x)) 1.0)
7.4b	(- (exp x) 1.0)

rewrite100.0ms

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:

27.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
40.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp x) 1.0)

series205.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	904	2169
3	2293	2156
done	5001	2154

prune325.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
0.3b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
7.2b	(- (exp (* 2.0 x)) 1.0)
7.2b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
230×	`*-un-lft-identity`
188×	`add-sqr-sqrt`
102×	`add-cube-cbrt`
88×	`difference-of-squares`
36×	`distribute-lft-out`
30×	`exp-sum` `associate-/r*`
28×	`distribute-lft-out--`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 253

Calls

4 calls:

92.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
111.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
12.0ms	(- (exp (* 2.0 x)) 1.0)
52.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series189.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
42.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
30.0ms	(- (exp (* 2.0 x)) 1.0)
21.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.3s

Counts

265 → 265

Iterations

Useful iterations: 2 (549.0ms)

Iter	Nodes	Cost
0	362	8009
1	1020	7743
2	3660	7375
done	5001	7375

prune752.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (pow 1.0 3) (pow (exp x) 3)))
7.2b	(- (exp (* 2.0 x)) 1.0)
7.2b	(- (exp (+ x x)) (* 1.0 1.0))
7.6b	(- (* (exp x) (exp x)) (* 1.0 (exp x)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
45×	`times-frac`
33×	`add-sqr-sqrt`
30×	`distribute-lft-out`
24×	`unpow-prod-down` `cube-prod`
23×	`difference-of-squares`
20×	`add-cube-cbrt`
11×	`exp-sum`
10×	`add-log-exp`
9×	`associate-/r*`
6×	`add-exp-log` `sum-cubes` `add-cbrt-cube`
5×	`associate-/l*`
4×	`pow1` `flip3--` `flip--`
3×	`sub-neg` `diff-log`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-out--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 117

Calls

4 calls:

136.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (pow 1.0 3) (pow (exp x) 3)))
13.0ms	(- (exp (* 2.0 x)) 1.0)
49.0ms	(- (exp (+ x x)) (* 1.0 1.0))
19.0ms	(- (* (exp x) (exp x)) (* 1.0 (exp x)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (pow 1.0 3) (pow (exp x) 3)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
21.0ms	(- (exp (+ x x)) (* 1.0 1.0))
49.0ms	(- (* (exp x) (exp x)) (* 1.0 (exp x)))

simplify863.0ms

Counts

129 → 129

Iterations

Useful iterations: done (859.0ms)

Iter	Nodes	Cost
0	208	2740
1	495	2504
2	1495	2331
done	5000	2322

prune443.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
0.3b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
7.2b	(- (exp (+ x x)) (* 1.0 1.0))
7.2b	(- (exp (* 2.0 x)) 1.0)

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

914×	`times-frac`
645×	`*-un-lft-identity`
519×	`add-sqr-sqrt`
432×	`cbrt-prod`
323×	`add-cube-cbrt`
227×	`difference-of-squares`
135×	`unpow-prod-down` `cube-prod`
106×	`distribute-lft-out`
86×	`exp-sum`
55×	`distribute-lft-out--`
43×	`associate-/r/`
30×	`associate-/r*`
27×	`cube-mult` `unpow3` `sqr-pow`
24×	`associate-/l*`
22×	`div-inv`
21×	`flip3-+` `flip-+`
11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
2×	`cube-div` `sub-neg` `cbrt-div` `frac-2neg` `diff-log` `clear-num`
1×	`div-sub`

Counts

4 → 630

Calls

4 calls:

116.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
110.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
51.0ms	(- (exp (+ x x)) (* 1.0 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)

series190.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
49.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)

simplify676.0ms

Counts

642 → 642

Iterations

Useful iterations: done (646.0ms)

Iter	Nodes	Cost
0	696	26791
1	1306	23268
done	5000	22342

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes29.0ms

Accuracy

75.6% (0.7b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 2.9b

bsearch62.0ms

Steps

Iters	Range		Point
8	-2.9262005697949513e-16	-6.905829970388517e-19	-1.3813417721230645e-16

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	66
1	49	66
done	49	66

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6573×	body	10240	exit
387.0ms	12651×	body	80	nan
242.0ms	7430×	body	80	valid
55.0ms	708×	body	160	valid