Details

sample322.0ms

Algorithm

intervals

Results

38.0ms	192×	body	10240	exit
13.0ms	393×	body	80	nan
8.0ms	245×	body	80	valid
1.0ms	13×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	176	12
6	496	12
7	1977	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

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))
3.5b	(- (exp (* 2.0 x)) 1.0)
3.5b	(- (exp x) 1.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 155

Calls

4 calls:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
22.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(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)
24.0ms	(- (exp x) 1.0)

simplify668.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (158.0ms)

Iter	Nodes	Cost
0	232	2954
1	492	2688
2	1518	2453
done	5000	2453

prune387.0ms

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	(+ (exp x) 1.0)
0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
3.5b	(- (exp (* 2.0 x)) 1.0)
3.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
13×	`prod-diff`
10×	`add-log-exp`
7×	`pow1` `fma-neg`
5×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `exp-sum` `flip-+` `difference-of-squares`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*r/` `flip--`
1×	`+-commutative` `pow1/2` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
25.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series185.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
128.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
29.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify617.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (147.0ms)

Iter	Nodes	Cost
0	183	1444
1	437	1302
2	1524	1139
done	5001	1139

prune306.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
3.5b	(- (exp (* 2.0 x)) 1.0)
3.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`prod-diff`
8×	`sqrt-pow1` `add-log-exp`
7×	`fma-neg`
6×	`pow1` `exp-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `pow1/2` `diff-log` `flip--`
1×	`distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

1.0ms	(sqrt (exp x))
1.0ms	(sqrt (exp x))
7.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series67.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
24.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.9s

Counts

100 → 100

Iterations

Useful iterations: 3 (506.0ms)

Iter	Nodes	Cost
0	141	1009
1	297	881
2	898	747
3	4615	669
done	5000	669

prune343.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (exp (* 2.0 x)) 1.0)
3.5b	(- (exp (+ x x)) (* 1.0 1.0))
3.5b	(- (exp (+ x x)) (* 1.0 1.0))
3.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`prod-diff`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`fma-neg`
12×	`add-log-exp`
9×	`exp-sum`
7×	`difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`distribute-lft-out--`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series85.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.7s

Counts

112 → 112

Iterations

Useful iterations: 3 (455.0ms)

Iter	Nodes	Cost
0	114	1475
1	260	1351
2	807	1115
3	4306	979
done	5000	979

prune413.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

75.8% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.8b

bsearch44.0ms

Steps

Iters	Range		Point
7	-7.520341406059738e-16	-2.574374193275519e-17	-7.268542916058787e-16

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	39
1	27	39
done	27	39

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6629×	body	10240	exit
381.0ms	12553×	body	80	nan
238.0ms	7427×	body	80	valid
58.0ms	715×	body	160	valid