Details

sample410.0ms

Algorithm

intervals

Results

44.0ms	250×	body	10240	exit
22.0ms	26×	body	160	valid
14.0ms	452×	body	80	nan
7.0ms	232×	body	80	valid

simplify75.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7
done	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

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))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp x) 1.0)

rewrite112.0ms

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:

29.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
47.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
15.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series200.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify54.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470
done	5001	1470

prune377.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
5.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.2b	(- (exp (* 2.0 x)) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

19.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
17.0ms	(- (exp (* 2.0 x)) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify42.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	361	673
1	1258	564
2	5002	559
done	5002	559

prune265.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (exp x))
0.3b	(sqrt (exp x))
5.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.2b	(- (exp (* 2.0 x)) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

3.0ms	(sqrt (exp x))
3.0ms	(sqrt (exp x))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
15.0ms	(- (exp (* 2.0 x)) 1.0)

series94.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify92.0ms

Counts

86 → 86

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	219	440
1	605	348
2	2891	335
3	5002	308
done	5002	308

prune297.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 1) (* 1/2 x))
0.3b	(sqrt (exp x))
5.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.2b	(- (exp (* 2.0 x)) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1` `exp-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `pow-pow` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
3×	`unpow-prod-down` `fma-neg` `sqrt-prod`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-unpow` `flip3--` `pow1/2` `diff-log` `pow-exp` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

5.0ms	(pow (exp 1) (* 1/2 x))
3.0ms	(sqrt (exp x))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
14.0ms	(- (exp (* 2.0 x)) 1.0)

series96.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (exp 1) (* 1/2 x))
12.0ms	(sqrt (exp x))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify122.0ms

Counts

88 → 88

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	282	471
1	862	369
2	4166	344
3	5001	329
done	5001	329

prune343.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.6b

bsearch94.0ms

Steps

Iters	Range		Point
8	5.005086428108652e-18	2.791559313082312e-14	5.520088747928308e-17
7	-1.7963352314132997e-16	-1.4237101994674035e-18	-1.1053346182246273e-16

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	40
1	56	40
done	56	40

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6673×	body	10240	exit
379.0ms	12678×	body	80	nan
243.0ms	7440×	body	80	valid
55.0ms	696×	body	160	valid