Details

sample478.0ms

Algorithm

intervals

Results

238.0ms	235×	body	10240	exit
65.0ms	426×	body	80	nan
21.0ms	246×	body	80	valid
4.0ms	21×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	185	12
6	764	12
done	5000	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.9b	(- (exp x) 1.0)

rewrite138.0ms

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:

35.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
21.0ms	(- (exp (* 2.0 x)) 1.0)
17.0ms	(- (exp x) 1.0)

series288.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
107.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
36.0ms	(- (exp (* 2.0 x)) 1.0)
34.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

167 → 167

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	232	2954
1	503	2694
2	1532	2473
done	5000	2423

prune634.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) 1.0))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`times-frac`
21×	`difference-of-squares`
13×	`prod-diff`
9×	`exp-sum`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-prod` `flip--` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `hypot-def` `div-inv` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

17.0ms	(sqrt (+ (exp x) 1.0))
120.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
30.0ms	(- (exp (* 2.0 x)) 1.0)
119.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series306.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (exp x) 1.0))
220.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
27.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.9s

Counts

137 → 137

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	223	2351
1	554	2217
2	2107	1999
done	5001	1955

prune709.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(sqrt (+ (exp x) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def`

Counts

2 → 36

Calls

2 calls:

25.0ms	(+ (exp x) 1.0)
23.0ms	(sqrt (+ (exp x) 1.0))

series60.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ (exp x) 1.0)
51.0ms	(sqrt (+ (exp x) 1.0))

simplify1.3s

Counts

42 → 42

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	65	319
1	149	291
2	465	276
3	1916	270
done	5000	268

prune167.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1.0))
0.0b	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
0.5b	(sqrt (exp x))
0.5b	(sqrt (exp x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `sqrt-prod`
7×	`pow1`
6×	`exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow1/2`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

2.0ms	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1.0))
0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
3.0ms	(sqrt (exp x))
4.0ms	(sqrt (exp x))

series185.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1.0))
57.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
20.0ms	(sqrt (exp x))
22.0ms	(sqrt (exp x))

simplify930.0ms

Counts

73 → 73

Iterations

Useful iterations: done (928.0ms)

Iter	Nodes	Cost
0	73	563
1	124	392
2	313	378
3	1151	372
done	5000	366

prune278.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
done	9	12

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.4s	6754×	body	10240	exit
1.1s	12847×	body	80	nan
727.0ms	7459×	body	80	valid
105.0ms	689×	body	160	valid