Details

Time bar (total: 15.0s)

sample48.0ms

Algorithm
intervals
Results
9.0ms253×body80nan
9.0ms54×body1280valid
5.0ms143×body80valid
5.0ms34×body640valid
1.0ms14×body320valid
1.0ms11×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06162
19162
210162
done10162

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.5b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ hypot-def flip--
Counts
2 → 89
Calls
2 calls:
11.0ms
(sqrt (+ x 1.0))
86.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series140.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(sqrt (+ x 1.0))
103.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.1s

Counts
95 → 95
Iterations

Useful iterations: done (1.1s)

IterNodesCost
013940498
132232189
2107625383
done500122362

prune359.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
6.0ms
(sqrt (+ x 1.0))
29.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
50.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series313.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(sqrt (+ x 1.0))
91.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
190.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.8s

Counts
103 → 103
Iterations

Useful iterations: done (1.8s)

IterNodesCost
017334529
143925938
2206024770
done500024364

prune492.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
28×sqrt-prod
22×distribute-lft-out
20×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1
3×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
3 → 85
Calls
3 calls:
10.0ms
(sqrt (+ x 1.0))
42.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
69.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series373.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(sqrt (+ x 1.0))
99.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
213.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.4s

Counts
94 → 94
Iterations

Useful iterations: done (1.3s)

IterNodesCost
016229038
139323390
2163222222
done500121858

prune443.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite333.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
708×sqrt-prod
594×times-frac
280×distribute-lft-out
270×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-cbrt-cube add-exp-log
8×hypot-def
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 461
Calls
4 calls:
36.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
37.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
49.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
158.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
199.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
199.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
430.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
202.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify3.9s

Counts
473 → 473
Iterations

Useful iterations: done (3.8s)

IterNodesCost
0448302013
11103251646
24313246755
done5000246705

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07202
19202
done9202

end0.0ms

sample1.6s

Algorithm
intervals
Results
504.0ms7946×body80nan
305.0ms1750×body1280valid
229.0ms4066×body80valid
174.0ms1314×body640valid
55.0ms560×body320valid
21.0ms310×body160valid