Details

Time bar (total: 22.4s)

sample703.0ms

Algorithm
intervals
Results
468.0ms234×body80valid
90.0ms231×body10240exit
23.0ms392×body80nan
4.0ms25×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5000
6752
5179
474
340
228
119
010

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize26.0ms

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)

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
75×*-un-lft-identity
51×times-frac
31×sqrt-prod
27×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1 associate-/r* flip3-- flip-- associate-/l*
4×associate-/r/
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 → 123
Calls
4 calls:
42.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
35.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms
(- (exp (* 2.0 x)) 1.0)
18.0ms
(- (exp x) 1.0)

series296.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
136.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
35.0ms
(- (exp (* 2.0 x)) 1.0)
38.0ms
(- (exp x) 1.0)

simplify1.2s

Counts
135 → 135
Iterations
IterNodes
done5001
21218
1396
0189

prune710.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×*-un-lft-identity
17×sqrt-prod
10×times-frac
9×add-cbrt-cube add-exp-log
8×add-cube-cbrt add-log-exp difference-of-squares associate-/l/
7×flip3-- flip--
6×distribute-lft-out--
5×pow1 associate-/r*
4×frac-times associate-/r/
3×flip3-+ flip-+
2×cbrt-undiv sub-neg diff-log div-exp associate-*l/ associate-*r/ div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div prod-exp cbrt-unprod associate-/l*
Counts
4 → 89
Calls
4 calls:
65.0ms
(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
58.0ms
(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
14.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
8.0ms
(- (exp x) 1.0)

series763.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
435.0ms
(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
73.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
19.0ms
(- (exp x) 1.0)

simplify3.7s

Counts
101 → 101
Iterations
IterNodes
done5001
23196
1634
0233

prune524.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (+ 1.0 (* x 0.5)))
24.3b
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log
3×associate-*r* associate-*l* sqrt-prod
2×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 37
Calls
2 calls:
18.0ms
(* x (+ 1.0 (* x 0.5)))
12.0ms
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))

series210.0ms

Counts
2 → 6
Calls
2 calls:
98.0ms
(* x (+ 1.0 (* x 0.5)))
112.0ms
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))

simplify1.2s

Counts
43 → 43
Iterations
IterNodes
done5000
21405
1300
0106

prune229.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0)))
0.5b
(* (sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))))
24.3b
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))
24.3b
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*l/ associate-*r/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
12.0ms
(sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0)))
89.0ms
(* (sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))))
18.0ms
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))
17.0ms
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))

series582.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0)))
96.0ms
(* (sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))))
143.0ms
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))
116.0ms
(sqrt (+ (* x (+ 1.0 (* x 0.5))) 2.0))

simplify2.5s

Counts
146 → 146
Iterations
IterNodes
done5000
22338
1466
0193

prune645.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes69.0ms

Accuracy

80.4% (0.7b remaining)

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

bsearch68.0ms

Steps
ItersRangePoint
7
-3.0023583529873386e-08
-9.093059953312438e-10
-2.432272493350688e-08

simplify9.0ms

Iterations
IterNodes
done35
135
029

end0.0ms

sample6.8s

Algorithm
intervals
Results
3.2s6901×body10240exit
2.2s12876×body80nan
642.0ms7402×body80valid
182.0ms727×body160valid