Details

sample236.0ms

Algorithm

intervals

Results

87.0ms	179×	body	10240	exit
16.0ms	351×	body	80	nan
10.0ms	241×	body	80	valid
2.0ms	19×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	767
5	185
4	76
3	41
2	28
1	19
0	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize36.0ms

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))
4.0b	(- (exp (* 2.0 x)) 1.0)
4.0b	(- (exp x) 1.0)

rewrite109.0ms

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-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 155

Calls

4 calls:

28.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
42.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(- (exp (* 2.0 x)) 1.0)
17.0ms	(- (exp x) 1.0)

series307.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
88.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
44.0ms	(- (exp (* 2.0 x)) 1.0)
37.0ms	(- (exp x) 1.0)

simplify1.4s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	1528
1	502
0	232

prune818.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
4.0b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
4.0b	(- (exp x) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
31×	`times-frac`
30×	`add-cube-cbrt`
21×	`sqrt-prod`
9×	`prod-diff`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--` `associate-/l*`
2×	`rem-sqrt-square` `div-inv`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `fma-udef`

Counts

4 → 112

Calls

4 calls:

13.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
12.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
0.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
15.0ms	(- (exp x) 1.0)

series533.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
175.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
110.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
24.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1059
1	370
0	193

prune741.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (exp x) (+ 1.0 (exp x)))))
0.0b	(* (exp x) (+ 1.0 (exp x)))
3.9b	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))
4.0b	(- (exp (* 2.0 x)) 1.0)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
13×	`prod-diff`
9×	`times-frac`
8×	`add-cbrt-cube` `add-log-exp`
7×	`fma-neg` `add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `associate-l` `flip--` `associate-/l`
2×	`sub-neg` `diff-log` `exp-sum` `associate-*r/` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

34.0ms	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (exp x) (+ 1.0 (exp x)))))
35.0ms	(* (exp x) (+ 1.0 (exp x)))
10.0ms	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (exp x) (+ 1.0 (exp x)))))
35.0ms	(* (exp x) (+ 1.0 (exp x)))
31.0ms	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify2.1s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	2987
1	579
0	216

prune857.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (fma 2 x x)))
0.2b	(sqrt (exp (fma 2 x x)))
4.0b	(- (exp (* 2.0 x)) 1.0)
4.0b	(fma (sqrt (exp (fma 2 x x))) (sqrt (exp (fma 2 x x))) (- (* (* 1.0 1.0) 1.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

3.0ms	(sqrt (exp (fma 2 x x)))
3.0ms	(sqrt (exp (fma 2 x x)))
18.0ms	(- (exp (* 2.0 x)) 1.0)
0.0ms	(fma (sqrt (exp (fma 2 x x))) (sqrt (exp (fma 2 x x))) (- (* (* 1.0 1.0) 1.0)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (exp (fma 2 x x)))
29.0ms	(sqrt (exp (fma 2 x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)
106.0ms	(fma (sqrt (exp (fma 2 x x))) (sqrt (exp (fma 2 x x))) (- (* (* 1.0 1.0) 1.0)))

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	3136
2	650
1	240
0	120

prune613.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes72.0ms

Accuracy

73% (0.9b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.6b

bsearch95.0ms

Steps

Iters	Range		Point
9	-8.433739504313006e-14	-2.0990955826697636e-21	-1.0662941597804906e-14

simplify11.0ms

Iterations

Iter	Nodes
done	30
1	30
0	27

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.9s	6632×	body	10240	exit
1.8s	12660×	body	80	nan
1.1s	7383×	body	80	valid
163.0ms	756×	body	160	valid