Details

Time bar (total: 15.0s)

sample68.0ms

Algorithm
intervals
Results
14.0ms57×body640valid
12.0ms243×body80nan
12.0ms37×body1280valid
8.0ms131×body80valid
4.0ms22×body320valid
1.0ms9×body160valid

simplify26.0ms

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: 20.2b

localize9.0ms

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))
2.3b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
15.0ms
(sqrt (+ x 1.0))
26.0ms
(/ 1.0 (sqrt (+ x 1.0)))
13.0ms
(/ 1.0 (sqrt x))
114.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ x 1.0))
99.0ms
(/ 1.0 (sqrt (+ x 1.0)))
60.0ms
(/ 1.0 (sqrt x))
175.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.1s

Counts
145 → 145
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02151942
14441778
210511698
326471673
done50001657

prune556.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×sqrt-prod
20×*-un-lft-identity
18×add-exp-log add-cbrt-cube
9×pow1 add-cube-cbrt
7×associate-*r*
6×sqrt-div associate-*r/ associate-*l* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp difference-of-squares unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out distribute-lft-out--
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
13.0ms
(sqrt (+ x 1.0))
86.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
34.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
67.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series639.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ x 1.0))
406.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
88.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
102.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts
105 → 105
Iterations

Useful iterations: 2 (477.0ms)

IterNodesCost
01891624
15021459
220281218
done50001218

prune389.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.0b
(- (+ x 1.0) x)

rewrite330.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
46×add-sqr-sqrt
39×sqrt-prod
37×times-frac distribute-lft-out
29×add-exp-log add-cbrt-cube
22×add-cube-cbrt
16×distribute-lft-out--
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod difference-of-squares
7×associate-*r* associate-/r* associate-/l*
6×associate-*l*
5×associate-*r/
4×sqrt-div associate-/r/ unswap-sqr
3×flip3-+ pow-prod-down flip-+ associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 diff-log clear-num flip-- div-inv
1×sub-neg sqrt-unprod div-sub associate--l+ sum-log *-commutative
Counts
4 → 143
Calls
4 calls:
135.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
94.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
33.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
61.0ms
(- (+ x 1.0) x)

series1.1s

Counts
4 → 12
Calls
4 calls:
195.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
762.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
101.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(- (+ x 1.0) x)

simplify1.9s

Counts
155 → 155
Iterations

Useful iterations: 2 (718.0ms)

IterNodesCost
02693162
17262927
230262509
done50002509

prune516.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
31×sqrt-prod
29×add-exp-log add-cbrt-cube
27×add-sqr-sqrt
21×distribute-lft-out
19×add-cube-cbrt times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div associate-/r/ flip-+ associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 116
Calls
4 calls:
42.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
44.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
66.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
51.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.6s

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
226.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.1s
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
101.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.3s

Counts
128 → 128
Iterations

Useful iterations: 2 (535.0ms)

IterNodesCost
02502311
16542082
225411730
done50001730

prune384.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11318
done1318

end0.0ms

sample1.8s

Algorithm
intervals
Results
587.0ms7865×body80nan
427.0ms1833×body640valid
281.0ms1123×body1280valid
197.0ms4161×body80valid
67.0ms602×body320valid
47.0ms281×body160valid