Details

Time bar (total: 14.8s)

sample59.0ms

Algorithm
intervals
Results
11.0ms56×body640valid
11.0ms250×body80nan
8.0ms142×body80valid
7.0ms29×body1280valid
3.0ms17×body320valid
1.0ms12×body160valid

simplify21.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize11.0ms

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))
3.2b
(- (/ 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-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- hypot-def
Counts
4 → 758
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
14.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
104.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
111.0ms
(/ 1.0 (sqrt (+ x 1.0)))
50.0ms
(/ 1.0 (sqrt x))
163.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.8s

Counts
770 → 770
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
070140764
1158535304
2497827512
done500027512

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 17.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.3b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
11×add-exp-log add-cube-cbrt add-cbrt-cube
9×pow1
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ times-frac pow1/2 pow-prod-down flip-+ associate-/l*
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ flip-- cbrt-unprod associate-/l/ distribute-lft-out
1×sub-neg rem-sqrt-square frac-2neg fma-neg sqrt-unprod diff-log div-sub prod-diff clear-num associate-/r* *-commutative hypot-def div-inv
Counts
4 → 98
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
56.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
26.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series537.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (+ x 1.0))
321.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
72.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
112.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.6s

Counts
110 → 110
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02041790
15871665
228051364
done50011356

prune450.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.7b
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
22×add-sqr-sqrt times-frac
16×*-un-lft-identity
14×add-cube-cbrt associate-/l*
12×cbrt-undiv div-exp
11×sqrt-prod
10×associate-*r/
8×pow1 associate-/r/
7×associate-*r* prod-exp cbrt-unprod
6×associate-*l* add-log-exp
5×flip3-+ flip-+ distribute-lft-out--
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv unswap-sqr
3×div-sub pow-prod-down associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 associate--l+ clear-num associate-/r* flip--
1×distribute-rgt-in sub-neg distribute-lft-in fma-neg sqrt-unprod diff-log prod-diff *-commutative distribute-lft-out
Counts
4 → 133
Calls
4 calls:
87.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
86.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
25.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
36.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

series707.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
499.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
3.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

simplify386.0ms

Counts
145 → 145
Iterations

Useful iterations: done (379.0ms)

IterNodesCost
02954063
19103406
done50012860

prune451.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
26×add-sqr-sqrt
19×*-un-lft-identity
18×times-frac
15×add-cube-cbrt sqrt-prod
12×cbrt-undiv div-exp associate-/l*
10×associate-*r/
9×pow1
8×associate-/r/
7×associate-*r* prod-exp cbrt-unprod
6×flip3-+ sqrt-div associate-*l* flip-+
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp unswap-sqr
3×sqrt-pow1 pow1/2 pow-prod-down
2×frac-2neg clear-num associate-/r* distribute-lft-out
1×rem-sqrt-square sqrt-unprod *-commutative hypot-def associate-/l/
Counts
4 → 125
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
26.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
43.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
30.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series743.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
139.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
506.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.8s

Counts
137 → 137
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02672512
17602188
243721848
done50001815

prune393.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01229
11729
done1729

end0.0ms

sample2.0s

Algorithm
intervals
Results
647.0ms7835×body80nan
388.0ms1809×body640valid
342.0ms1184×body1280valid
214.0ms4100×body80valid
78.0ms627×body320valid
24.0ms280×body160valid