Details

Time bar (total: 38.4s)

sample28.0ms

Algorithm
intervals
Results
7.0ms54×body1280valid
5.0ms268×body80nan
3.0ms41×body640valid
3.0ms134×body80valid
1.0ms17×body320valid
0.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
22.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series104.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(sqrt (+ x 1.0))
73.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify57.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune90.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

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)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 71
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
20.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series238.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
68.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify44.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0341624
11239566
25001533

prune170.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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)))
0.1b
(/ 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))))

rewrite191.0ms

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:
23.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
77.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series804.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
333.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
140.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify138.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
010338864
141207704
250017681

prune587.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
56169×sqrt-prod
42381×times-frac
38028×*-un-lft-identity
14256×add-sqr-sqrt add-cube-cbrt
13584×distribute-lft-out
1391×sqrt-div
1389×associate-/r/
714×div-inv
676×flip3-+ flip-+
383×associate-/r*
51×associate-/l*
15×add-exp-log add-cbrt-cube
6×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num add-log-exp
3×sqrt-undiv associate-/l/
Counts
4 → 12717
Calls
4 calls:
25.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
28.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
77.0ms
(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
411.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
682.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
339.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
487.0ms
(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
174.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

simplify4.2s

Algorithm
egg-herbie
Counts
12729 → 12729
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
06268572364

prune26.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195

end0.0ms

sample629.0ms

Algorithm
intervals
Results
135.0ms1712×body1280valid
133.0ms7994×body80nan
79.0ms1209×body640valid
73.0ms4129×body80valid
32.0ms651×body320valid
9.0ms299×body160valid