Details

Time bar (total: 10.2s)

sample30.0ms

Algorithm
intervals
Results
6.0ms46×body1280valid
5.0ms54×body640valid
4.0ms226×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

localize11.0ms

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))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
875×*-un-lft-identity
742×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
562×sqrt-prod
73×distribute-lft-out
54×div-inv
46×sqrt-div associate-/r/
23×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube
6×associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 739
Calls
3 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
70.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series261.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(/ 1.0 (sqrt (+ x 1.0)))
38.0ms
(/ 1.0 (sqrt x))
145.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
748 → 748
Iterations

Useful iterations: done (1.2s)

IterNodesCost
069140576
1145835050
2317326088
done500025770

prune892.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.9b

localize8.0ms

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))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
68×sqrt-prod
58×*-un-lft-identity
51×add-sqr-sqrt
42×prod-diff
35×add-cube-cbrt
17×add-exp-log add-cbrt-cube
9×distribute-lft-out
7×pow1 fma-neg 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×expm1-log1p-u pow-prod-down log1p-expm1-u distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 132
Calls
3 calls:
55.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
31.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series399.0ms

Counts
3 → 9
Calls
3 calls:
267.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
56.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
75.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify953.0ms

Counts
141 → 141
Iterations

Useful iterations: done (949.0ms)

IterNodesCost
02312993
16102339
223601821
done50001813

prune278.0ms

Pruning

13 alts after pruning (13 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)

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
129×*-un-lft-identity
54×add-sqr-sqrt
41×distribute-lft-out
39×sqrt-prod
37×times-frac
30×add-cube-cbrt
29×add-exp-log add-cbrt-cube
16×distribute-lft-out--
12×prod-diff
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×expm1-log1p-u fma-neg sqrt-div associate-/r/ log1p-expm1-u 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 → 167
Calls
4 calls:
65.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
41.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
22.0ms
(- (+ x 1.0) x)

series703.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
496.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(- (+ x 1.0) x)

simplify1.3s

Counts
179 → 179
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02973589
18153225
233092751
done50002731

prune375.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

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)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
60×*-un-lft-identity
35×sqrt-prod
29×add-exp-log add-sqr-sqrt add-cbrt-cube
22×distribute-lft-out
21×add-cube-cbrt
19×times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×fma-def associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×expm1-log1p-u flip3-+ sqrt-div associate-/r/ flip-+ log1p-expm1-u 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 → 131
Calls
4 calls:
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
27.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series945.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
329.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
495.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.1s

Counts
143 → 143
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02582403
17042171
227081814
done50011804

prune284.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11318
done1318

end0.0ms

sample820.0ms

Algorithm
intervals
Results
176.0ms1862×body640valid
156.0ms7984×body80nan
145.0ms1165×body1280valid
105.0ms4040×body80valid
43.0ms617×body320valid
15.0ms316×body160valid