Details

Time bar (total: 24.2s)

sample694.0ms

Algorithm
intervals
Results
502.0ms239×body10240exit
33.0ms435×body80nan
17.0ms237×body80valid
5.0ms26×body160valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5001
6767
5185
476
341
228
119
010

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.6b
(- (exp (* 2.0 x)) 1.0)
5.7b
(- (exp x) 1.0)

rewrite100.0ms

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:
41.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
23.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
11.0ms
(- (exp (* 2.0 x)) 1.0)
12.0ms
(- (exp x) 1.0)

series367.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
168.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
54.0ms
(- (exp (* 2.0 x)) 1.0)
41.0ms
(- (exp x) 1.0)

simplify1.5s

Counts
167 → 167
Iterations
IterNodes
done5000
21525
1502
0232

prune777.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.3b
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
5.7b
(- (exp x) 1.0)
5.7b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
624×*-un-lft-identity
593×sqrt-prod
554×add-sqr-sqrt
528×times-frac
184×difference-of-squares
180×add-cube-cbrt
120×distribute-lft-out--
102×distribute-lft-out
45×prod-diff
13×associate-/r/
9×associate-/r* flip3-- fma-neg flip--
8×add-log-exp
7×div-inv
6×add-cbrt-cube add-exp-log
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×rem-sqrt-square
2×sub-neg diff-log associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp
Counts
4 → 443
Calls
4 calls:
64.0ms
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
97.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
24.0ms
(- (exp x) 1.0)
30.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series695.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
419.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
24.0ms
(- (exp x) 1.0)
62.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify3.2s

Counts
455 → 455
Iterations
IterNodes
done5001
11464
0653

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize113.0ms

Local error

Found 4 expressions with local error:

0.3b
(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.3b
(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
5.8b
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
5.8b
(- (sqrt (exp x)) (sqrt 1.0))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
262×sqrt-prod
133×add-sqr-sqrt
117×prod-diff
107×*-un-lft-identity
89×add-cube-cbrt
15×fma-neg
13×difference-of-squares
8×hypot-def add-log-exp
6×pow1
5×distribute-lft-out--
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u distribute-lft-out
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
4 → 224
Calls
4 calls:
17.0ms
(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
29.0ms
(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
46.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
24.0ms
(- (sqrt (exp x)) (sqrt 1.0))

series498.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
109.0ms
(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
217.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
55.0ms
(- (sqrt (exp x)) (sqrt 1.0))

simplify1.7s

Counts
236 → 236
Iterations
IterNodes
done5001
21686
1598
0280

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x 1.0 (fma (* 0.5 x) x 2.0))
26.5b
(sqrt (fma x 1.0 (fma (* 0.5 x) x 2.0)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt
3×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
2×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
2 → 25
Calls
2 calls:
0.0ms
(fma x 1.0 (fma (* 0.5 x) x 2.0))
2.0ms
(sqrt (fma x 1.0 (fma (* 0.5 x) x 2.0)))

series200.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(fma x 1.0 (fma (* 0.5 x) x 2.0))
139.0ms
(sqrt (fma x 1.0 (fma (* 0.5 x) x 2.0)))

simplify1.7s

Counts
31 → 31
Iterations
IterNodes
done5000
32957
2494
1145
065

prune142.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes79.0ms

Accuracy

76.7% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.2b

bsearch43.0ms

Steps
ItersRangePoint
4
-3.2052418334402957e-07
-2.1180969526925522e-07
-3.162953279719333e-07

simplify7.0ms

Iterations
IterNodes
done25
125
022

end0.0ms

sample7.0s

Algorithm
intervals
Results
4.0s6921×body10240exit
1.5s12816×body80nan
638.0ms7380×body80valid
197.0ms732×body160valid