Details

sample329.0ms

Algorithm

intervals

Results

39.0ms	213×	body	10240	exit
12.0ms	389×	body	80	nan
7.0ms	233×	body	80	valid
2.0ms	25×	body	160	valid

simplify1.3s

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	175	12
6	476	12
7	1519	12
done	5001	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)

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)))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series197.0ms

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))
24.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

167 → 167

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	232	2954
1	475	2688
2	1077	2471
3	3777	2398
done	5000	2396

prune381.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (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))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`prod-diff`
10×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `flip3-+` `sqrt-div` `diff-log` `flip--` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

6.0ms	(sqrt (+ (exp x) 1.0))
4.0ms	(+ (exp x) 1.0)
5.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series85.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
28.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.4s

Counts

100 → 100

Iterations

Useful iterations: 3 (512.0ms)

Iter	Nodes	Cost
0	166	1120
1	360	992
2	925	858
3	3377	795
done	5000	795

prune322.0ms

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	(hypot (sqrt (exp x)) (sqrt 1.0))
0.2b	(sqrt (exp x))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

0.0ms	(hypot (sqrt (exp x)) (sqrt 1.0))
1.0ms	(sqrt (exp x))
5.0ms	(- (exp (* 2.0 x)) 1.0)
32.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series197.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(hypot (sqrt (exp x)) (sqrt 1.0))
11.0ms	(sqrt (exp x))
24.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: 3 (442.0ms)

Iter	Nodes	Cost
0	172	1073
1	346	931
2	841	798
3	2888	735
done	5000	735

prune334.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (+ (exp x) 1.0)))
0.1b	(log1p (+ (exp x) 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `prod-diff`
8×	`add-log-exp`
7×	`fma-neg`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `distribute-lft-out--` `expm1-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(expm1 (log1p (+ (exp x) 1.0)))
0.0ms	(log1p (+ (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
34.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series230.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(expm1 (log1p (+ (exp x) 1.0)))
70.0ms	(log1p (+ (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.2s

Counts

86 → 86

Iterations

Useful iterations: 3 (442.0ms)

Iter	Nodes	Cost
0	157	1030
1	329	900
2	856	763
3	3008	705
done	5000	705

prune324.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

73.9% (0.7b remaining)

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

bsearch46.0ms

Steps

Iters	Range		Point
8	-0.0008391074150366579	-8.849834202292668e-07	-1.3181801234810229e-05

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	38
1	30	38
done	30	38

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	6739×	body	10240	exit
368.0ms	12781×	body	80	nan
233.0ms	7403×	body	80	valid
56.0ms	711×	body	160	valid