Details

Time bar (total: 13.6s)

sample59.0ms

Algorithm
intervals
Results
12.0ms334×body80nan
10.0ms46×body1280valid
8.0ms50×body640valid
5.0ms130×body80valid
2.0ms16×body320valid
1.0ms14×body160valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite280.0ms

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:
9.0ms
(sqrt (+ x 1.0))
21.0ms
(/ 1.0 (sqrt (+ x 1.0)))
12.0ms
(/ 1.0 (sqrt x))
155.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ x 1.0))
105.0ms
(/ 1.0 (sqrt (+ x 1.0)))
53.0ms
(/ 1.0 (sqrt x))
164.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.6s

Counts
770 → 770
Iterations

Useful iterations: done (2.5s)

IterNodesCost
070140764
1153135216
2301226244
done500120672

prune986.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
3.6b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite125.0ms

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))
58.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
35.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
21.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series535.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ x 1.0))
325.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
65.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
105.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.6s

Counts
110 → 110
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02041790
15571653
218681321
done50001277

prune721.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
22×add-sqr-sqrt
18×times-frac
16×*-un-lft-identity
14×add-cube-cbrt
12×cbrt-undiv div-exp associate-/l*
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-+
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 → 128
Calls
4 calls:
98.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
99.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
29.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
59.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

series689.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
487.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
3.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

simplify1.5s

Counts
140 → 140
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02893978
18403760
238292747
done50002704

prune413.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
27×*-un-lft-identity
24×add-sqr-sqrt
19×sqrt-prod
18×times-frac
16×add-cube-cbrt
12×cbrt-undiv div-exp associate-/l*
10×associate-*r/
8×pow1 associate-/r/
7×fma-def associate-*r* prod-exp cbrt-unprod
6×flip3-+ associate-*l* flip-+ distribute-lft-out add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r*
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 129
Calls
4 calls:
36.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
30.0ms
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
53.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
30.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
138.0ms
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
476.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
54.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.2s

Counts
141 → 141
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02682572
17162230
228051845
done50001806

prune314.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01019
11419
done1419

end0.0ms

sample940.0ms

Algorithm
intervals
Results
178.0ms1894×body640valid
177.0ms8104×body80nan
138.0ms1147×body1280valid
112.0ms4054×body80valid
42.0ms600×body320valid
15.0ms305×body160valid