Details

sample347.0ms

Algorithm

intervals

Results

45.0ms	214×	body	10240	exit
15.0ms	457×	body	80	nan
8.0ms	231×	body	80	valid
2.0ms	30×	body	160	valid

simplify856.0ms

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	464	12
7	1492	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.9b	(- (exp x) 1.0)

rewrite50.0ms

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:

20.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series195.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify911.0ms

Counts

135 → 135

Iterations

Useful iterations: done (906.0ms)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	896	2169
3	2389	2156
done	5000	2154

prune321.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.3b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
25×	`times-frac`
21×	`difference-of-squares`
16×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`pow1` `exp-sum` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`sqrt-div` `associate-/r` `associate-/l`
4×	`flip3--` `flip--`
2×	`frac-times` `sub-neg` `sqrt-pow1` `flip3-+` `diff-log` `associate-*r/` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 96

Calls

4 calls:

40.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
24.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series335.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
129.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify863.0ms

Counts

108 → 108

Iterations

Useful iterations: done (859.0ms)

Iter	Nodes	Cost
0	196	2198
1	479	2130
2	1380	1971
done	5000	1866

prune335.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)))
0.3b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3))) (+ (exp x) 1.0)))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
96×	`cbrt-prod`
95×	`times-frac`
90×	`*-un-lft-identity`
48×	`add-cube-cbrt`
47×	`difference-of-squares`
30×	`unpow-prod-down` `cube-prod`
21×	`distribute-lft-out--`
19×	`associate-/r*`
13×	`exp-sum`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `cube-mult` `unpow3` `sqr-pow`
5×	`sqrt-div` `add-cbrt-cube` `associate-/l*`
4×	`flip3--` `flip--`
2×	`cube-div` `frac-times` `sub-neg` `cbrt-div` `sqrt-pow1` `flip3-+` `diff-log` `associate-*r/` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 180

Calls

4 calls:

77.0ms	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)))
46.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3))) (+ (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
27.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series342.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)))
129.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3))) (+ (exp x) 1.0)))
29.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify679.0ms

Counts

192 → 192

Iterations

Useful iterations: done (672.0ms)

Iter	Nodes	Cost
0	290	5468
1	676	4683
2	2054	4320
done	5001	4318

prune458.0ms

Pruning

4 alts after pruning (2 fresh and 2 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)))
0.3b	(sqrt (* (/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
95×	`add-sqr-sqrt` `times-frac`
74×	`*-un-lft-identity`
55×	`difference-of-squares`
48×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
21×	`exp-sum`
19×	`associate-/l*`
13×	`distribute-lft-out--`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `cube-mult` `unpow3` `sqr-pow`
5×	`sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`flip3--` `flip--`
2×	`cube-div` `frac-times` `sub-neg` `cbrt-div` `sqrt-pow1` `flip3-+` `diff-log` `associate-*r/` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 179

Calls

4 calls:

52.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0)))
32.0ms	(sqrt (* (/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series339.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0)))
132.0ms	(sqrt (* (/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify633.0ms

Counts

191 → 191

Iterations

Useful iterations: 2 (216.0ms)

Iter	Nodes	Cost
0	301	5335
1	598	4575
2	1959	4256
done	5000	4256

prune448.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes27.0ms

Accuracy

77.5% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.7b

bsearch39.0ms

Steps

Iters	Range		Point
5	-4.022447873684564e-15	-1.6668736937815573e-15	-2.5679454952614643e-15

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	57
1	45	57
done	45	57

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	6643×	body	10240	exit
406.0ms	12688×	body	80	nan
261.0ms	7478×	body	80	valid
59.0ms	664×	body	160	valid