Details

Time bar (total: 24.0s)

sample296.0ms

Algorithm
intervals
Results
117.0ms231×body10240exit
20.0ms392×body80nan
15.0ms234×body80valid
3.0ms25×body160valid

simplify4.2s

Counts
1 → 1
Iterations
IterNodes
done5043
84148
71069
6332
5133
465
337
227
119
010

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize36.0ms

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)

rewrite143.0ms

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:
51.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
42.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
18.0ms
(- (exp (* 2.0 x)) 1.0)
19.0ms
(- (exp x) 1.0)

series273.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
131.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
38.0ms
(- (exp (* 2.0 x)) 1.0)
25.0ms
(- (exp x) 1.0)

simplify2.3s

Counts
135 → 135
Iterations
IterNodes
done5000
33198
21003
1396
0189

prune667.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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)

rewrite148.0ms

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:
75.0ms
(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
34.0ms
(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
22.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
11.0ms
(- (exp x) 1.0)

series737.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
434.0ms
(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
67.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
20.0ms
(- (exp x) 1.0)

simplify2.9s

Counts
101 → 101
Iterations
IterNodes
done5002
22397
1630
0233

prune580.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

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:
16.0ms
(* x (+ 1.0 (* 0.5 x)))
15.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series236.0ms

Counts
2 → 6
Calls
2 calls:
98.0ms
(* x (+ 1.0 (* 0.5 x)))
138.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify1.3s

Counts
43 → 43
Iterations
IterNodes
done5005
21102
1298
0106

prune179.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

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 (* 0.5 x))) 2.0)))
76.0ms
(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
11.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
11.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series533.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
94.0ms
(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
103.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
117.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify1.7s

Counts
146 → 146
Iterations
IterNodes
done5001
21295
1457
0193

prune594.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes61.0ms

Accuracy

80.3% (0.7b remaining)

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

bsearch73.0ms

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

simplify7.0ms

Iterations
IterNodes
done36
136
030

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.8s6901×body10240exit
1.1s7402×body80valid
1.0s12876×body80nan
222.0ms727×body160valid