Details

Time bar (total: 34.3s)

sample52.0ms

Algorithm
intervals
Results
11.0ms309×body80nan
10.0ms59×body1280valid
7.0ms51×body640valid
4.0ms117×body80valid
2.0ms23×body320valid
0.0ms6×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize6.0ms

Local error

Found 1 expressions with local error:

2.4b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
65.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series443.0ms

Counts
1 → 3
Calls
1 calls:
442.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.1s

Counts
22 → 22
Iterations

Useful iterations: done (2.1s)

IterNodesCost
059310
1133285
2336263
3802257
42104250
done5001246

prune76.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
61.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
89.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series313.0ms

Counts
2 → 6
Calls
2 calls:
114.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
198.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.1s

Counts
61 → 61
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0128947
1297865
2790788
32333774
done5001766

prune217.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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))))

rewrite405.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×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-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
59.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
41.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
54.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
172.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
227.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
257.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
463.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
231.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.8s

Counts
457 → 457
Iterations

Useful iterations: done (1.8s)

IterNodesCost
044015237
1103112250
2220811576
done500010949

prune869.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
21584×sqrt-prod
15024×*-un-lft-identity
14958×times-frac
5512×distribute-lft-out
5380×add-sqr-sqrt
5378×add-cube-cbrt
586×sqrt-div
555×associate-/l*
292×associate-/r/
147×flip3-+ flip-+
146×div-inv
33×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×pow1
4×sqrt-pow1 add-log-exp
3×frac-2neg clear-num
2×rem-sqrt-square pow1/2 associate-/l/
Counts
4 → 5792
Calls
4 calls:
62.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
90.0ms
(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
552.0ms
(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
204.0ms
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
460.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
568.0ms
(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
207.0ms
(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
486.0ms
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify3.9s

Counts
5804 → 5804
Iterations

Useful iterations: done (3.2s)

IterNodesCost
02648333199
done5000301081

prune14.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample1.5s

Algorithm
intervals
Results
358.0ms8101×body80nan
355.0ms1721×body1280valid
180.0ms4137×body80valid
157.0ms1224×body640valid
93.0ms610×body320valid
19.0ms308×body160valid