Details

Time bar (total: 6.7s)

sample36.0ms

Algorithm
intervals
Results
7.0ms41×body1280valid
7.0ms71×body640valid
5.0ms278×body80nan
3.0ms114×body80valid
1.0ms21×body320valid
0.0ms9×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146
done146

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.5b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite188.0ms

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:
13.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
87.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series266.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(/ 1.0 (sqrt (+ x 1.0)))
44.0ms
(/ 1.0 (sqrt x))
154.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify229.0ms

Counts
748 → 748
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
0151724924
1419718301
2500118266
done500118266

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.8b

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)))
2.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite180.0ms

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:
91.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
55.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series381.0ms

Counts
3 → 9
Calls
3 calls:
257.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
54.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify89.0ms

Counts
141 → 141
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06141715
128831280
250021185
done50021185

prune302.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.1b

localize12.0ms

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)))
1.7b
(+ x (- 1.0 x))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
112×*-un-lft-identity
41×distribute-lft-out
36×add-sqr-sqrt
35×sqrt-prod
31×times-frac
29×add-exp-log add-cbrt-cube
28×add-cube-cbrt
11×associate-+r+
9×cbrt-undiv div-exp prod-diff add-log-exp
8×pow1 prod-exp cbrt-unprod distribute-lft-out--
7×associate-*r* associate-/r*
6×associate-*l* associate-/l*
5×flip3-+ associate-*r/ flip-+
4×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u unswap-sqr
3×fma-def pow-prod-down associate-/l/
2×associate-+r- frac-2neg sqrt-pow1 pow1/2 clear-num sum-log div-inv
1×+-commutative sub-neg sqrt-unprod diff-log div-sub *-commutative
Counts
4 → 156
Calls
4 calls:
89.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
61.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
17.0ms
(+ x (- 1.0 x))

series887.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
687.0ms
(/ (* 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))

simplify107.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
07991711
142361448
250011435
done50011435

prune404.0ms

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)))

rewrite161.0ms

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:
35.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
45.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
467.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
55.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify90.0ms

Counts
143 → 143
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07041320
136361120
250021050
done50021050

prune321.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0119
1119
done119

end0.0ms

sample874.0ms

Algorithm
intervals
Results
181.0ms1962×body640valid
160.0ms8018×body80nan
135.0ms1075×body1280valid
101.0ms4041×body80valid
41.0ms610×body320valid
15.0ms312×body160valid