Details

Time bar (total: 20.2s)

sample605.0ms

Algorithm
intervals
Results
299.0ms25×body160valid
92.0ms231×body10240exit
25.0ms392×body80nan
17.0ms234×body80valid

simplify1.4s

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.3b
(- (exp (* 2.0 x)) 1.0)
5.4b
(- (exp x) 1.0)

rewrite133.0ms

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:
64.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
35.0ms
(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)

series242.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
104.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
29.0ms
(- (exp (* 2.0 x)) 1.0)
31.0ms
(- (exp x) 1.0)

simplify1.4s

Counts
167 → 167
Iterations
IterNodes
done5000
21525
1502
0232

prune880.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
0.2b
(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
5.4b
(- (exp x) 1.0)
5.4b
(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite38.0ms

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:
12.0ms
(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
13.0ms
(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
9.0ms
(- (exp x) 1.0)
0.0ms
(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series554.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
234.0ms
(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
16.0ms
(- (exp x) 1.0)
121.0ms
(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify985.0ms

Counts
124 → 124
Iterations
IterNodes
done5001
21122
1370
0193

prune728.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x 1.0 (fma (* x x) 0.4999999999999998 2.0))
0.1b
(fma (* x x) 0.4999999999999998 2.0)
24.3b
(sqrt (fma x 1.0 (fma (* x x) 0.4999999999999998 2.0)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×pow1 *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u add-cbrt-cube add-exp-log sqrt-prod log1p-expm1-u add-log-exp
2×fma-udef
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
3 → 35
Calls
3 calls:
0.0ms
(fma x 1.0 (fma (* x x) 0.4999999999999998 2.0))
0.0ms
(fma (* x x) 0.4999999999999998 2.0)
1.0ms
(sqrt (fma x 1.0 (fma (* x x) 0.4999999999999998 2.0)))

series222.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(fma x 1.0 (fma (* x x) 0.4999999999999998 2.0))
60.0ms
(fma (* x x) 0.4999999999999998 2.0)
127.0ms
(sqrt (fma x 1.0 (fma (* x x) 0.4999999999999998 2.0)))

simplify2.2s

Counts
44 → 44
Iterations
IterNodes
done5000
34207
2594
1157
076

prune223.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (fma x 0.4999999999999998 1.0))
2.6b
(expm1 (log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0)))))
24.3b
(sqrt (expm1 (log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0))))))
25.4b
(log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* sqrt-prod
2×fma-udef
1×distribute-rgt-in rem-sqrt-square log1p-udef expm1-log1p distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod expm1-udef unswap-sqr
Counts
4 → 59
Calls
4 calls:
5.0ms
(* x (fma x 0.4999999999999998 1.0))
0.0ms
(expm1 (log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0)))))
1.0ms
(sqrt (expm1 (log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0))))))
0.0ms
(log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0))))

series753.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* x (fma x 0.4999999999999998 1.0))
194.0ms
(expm1 (log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0)))))
342.0ms
(sqrt (expm1 (log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0))))))
123.0ms
(log1p (+ 2.0 (* x (fma x 0.4999999999999998 1.0))))

simplify1.6s

Counts
71 → 71
Iterations
IterNodes
done5001
22153
1529
0211

prune419.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes51.0ms

Accuracy

80.4% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 3.5b

bsearch60.0ms

Steps
ItersRangePoint
7
-3.0023583529873386e-08
-9.093059953312438e-10
-2.9618730431138167e-08

simplify11.0ms

Iterations
IterNodes
done30
130
027

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.5s6901×body10240exit
1.2s12876×body80nan
1.1s7402×body80valid
113.0ms727×body160valid