Details

Time bar (total: 8.8s)

sample30.0ms

Algorithm
intervals
Results
6.0ms46×body1280valid
5.0ms54×body640valid
5.0ms226×body80nan
3.0ms123×body80valid
2.0ms23×body320valid
0.0ms10×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0811
11111
21411
done1411

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.0b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×add-sqr-sqrt
69×times-frac
46×sqrt-prod
40×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l*
5×add-log-exp
4×div-inv
3×pow1
2×cbrt-undiv frac-2neg sqrt-div div-exp clear-num associate-/r/
1×sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 117
Calls
3 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
47.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series243.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
130.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
126 → 126
Iterations

Useful iterations: 3 (619.0ms)

IterNodesCost
02011764
14111621
29931549
326581528
done50001528

prune273.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
17×add-exp-log add-cbrt-cube
16×*-un-lft-identity
7×pow1 add-cube-cbrt associate-*r*
6×associate-*r/ associate-*l*
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv sqrt-div div-exp difference-of-squares unswap-sqr
3×pow-prod-down distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/ distribute-lft-out
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 77
Calls
3 calls:
29.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
26.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series384.0ms

Counts
3 → 9
Calls
3 calls:
255.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify797.0ms

Counts
86 → 86
Iterations

Useful iterations: done (795.0ms)

IterNodesCost
01801446
14931304
220391071
done50001064

prune197.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (* 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)))
2.2b
(- (+ x 1.0) x)

rewrite138.0ms

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:
59.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
38.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
21.0ms
(- (+ x 1.0) x)

series689.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
487.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(- (+ x 1.0) x)

simplify1.2s

Counts
155 → 155
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02693162
17452927
231132509
done50002502

prune497.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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:
16.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series708.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
131.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
457.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
57.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify997.0ms

Counts
128 → 128
Iterations

Useful iterations: done (993.0ms)

IterNodesCost
02502311
16712082
225981734
done50001725

prune243.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11318
done1318

end0.0ms

sample863.0ms

Algorithm
intervals
Results
184.0ms1862×body640valid
172.0ms7984×body80nan
151.0ms1165×body1280valid
104.0ms4040×body80valid
45.0ms617×body320valid
18.0ms316×body160valid