Details

Time bar (total: 24.6s)

sample79.0ms

Algorithm
intervals
Results
17.0ms67×body640valid
16.0ms312×body80nan
10.0ms30×body1280valid
8.0ms123×body80valid
5.0ms28×body320valid
1.0ms8×body160valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.4b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-cbrt-cube add-exp-log
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub hypot-def flip--
Counts
4 → 758
Calls
4 calls:
12.0ms
(sqrt (+ x 1.0))
20.0ms
(/ 1.0 (sqrt (+ x 1.0)))
10.0ms
(/ 1.0 (sqrt x))
120.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ x 1.0))
124.0ms
(/ 1.0 (sqrt (+ x 1.0)))
54.0ms
(/ 1.0 (sqrt x))
220.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.7s

Counts
770 → 770
Iterations
IterNodes
done5000
24935
11587
0702

prune3.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 22.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)
15.7b
(- (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ 1.0 (sqrt (+ x 1.0))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
238×times-frac
208×*-un-lft-identity
189×prod-diff
171×add-sqr-sqrt
162×add-cube-cbrt
85×sqrt-prod
36×div-inv
21×distribute-lft-out
14×sqrt-div associate-/r/
13×add-cbrt-cube add-exp-log
7×flip3-+ fma-neg flip-+
6×cbrt-prod add-log-exp
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u
3×associate-/r* difference-of-squares
2×pow1/3 prod-exp cbrt-unprod distribute-lft-out--
1×clear-num sub-neg frac-2neg flip3-- diff-log associate-*r/ frac-sub flip-- associate-/l* associate-/l/
Counts
4 → 268
Calls
4 calls:
18.0ms
(/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
69.0ms
(- (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ 1.0 (sqrt (+ x 1.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
478.0ms
(/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))
267.0ms
(cbrt x)
235.0ms
(cbrt x)
238.0ms
(- (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.7s

Counts
280 → 280
Iterations
IterNodes
done5000
24759
11103
0439

prune2.5s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 22.6b

localize162.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.7b
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ 1.0 (sqrt (+ x 1.0)))))
13.7b
(- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite582.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
22×add-sqr-sqrt
18×frac-sub
17×add-cube-cbrt
12×frac-times associate-*l/ associate-*r/
11×associate-/l/
10×distribute-lft-out
7×difference-of-squares
6×cbrt-prod add-cbrt-cube add-exp-log add-log-exp
5×associate-/r*
4×expm1-log1p-u pow1 log1p-expm1-u associate-/l*
3×associate-/r/
2×flip3-- pow1/3 flip--
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff frac-add flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
472.0ms
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ 1.0 (sqrt (+ x 1.0)))))
102.0ms
(- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
232.0ms
(cbrt x)
227.0ms
(cbrt x)
562.0ms
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ 1.0 (sqrt (+ x 1.0)))))
181.0ms
(- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.9s

Counts
122 → 122
Iterations
IterNodes
done5000
1996
0324

prune1.1s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 22.6b

localize121.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.7b
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) (/ 1.0 (sqrt (+ x 1.0)))))
13.7b
(- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite414.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
22×add-sqr-sqrt
18×frac-sub
17×add-cube-cbrt
12×frac-times associate-*l/ associate-*r/
11×associate-/l/
10×distribute-lft-out
7×difference-of-squares
6×cbrt-prod add-cbrt-cube add-exp-log add-log-exp
5×associate-/r*
4×expm1-log1p-u pow1 log1p-expm1-u associate-/l*
3×associate-/r/
2×flip3-- pow1/3 flip--
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff frac-add flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
324.0ms
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) (/ 1.0 (sqrt (+ x 1.0)))))
85.0ms
(- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series983.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(cbrt x)
202.0ms
(cbrt x)
444.0ms
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) (/ 1.0 (sqrt (+ x 1.0)))))
140.0ms
(- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.6s

Counts
122 → 122
Iterations
IterNodes
done5000
11010
0330

prune932.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 22.6b

regimes502.0ms

Accuracy

93.8% (0.5b remaining)

Error of 19.9b against oracle of 19.4b and baseline of 27.0b

bsearch68.0ms

Steps
ItersRangePoint
8
6.892104867468117e+120
2.157250222111853e+124
8.56379640608457e+122

simplify10.0ms

Iterations
IterNodes
done49
249
145
033

end0.0ms

sample1.6s

Algorithm
intervals
Results
594.0ms7998×body80nan
258.0ms1817×body640valid
243.0ms1102×body1280valid
232.0ms4129×body80valid
76.0ms669×body320valid
18.0ms283×body160valid