Details

Time bar (total: 6.3s)

sample42.0ms

Algorithm
intervals
Results
10.0ms266×body80nan
9.0ms54×body1280valid
6.0ms49×body640valid
6.0ms129×body80valid
1.0ms11×body320valid
1.0ms13×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite30.0ms

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))
25.0ms
(- (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))

simplify64.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune81.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite46.0ms

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))
16.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
23.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series248.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
148.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0341625
11233566
25001533

prune170.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

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:
21.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
72.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
28.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series834.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
167.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
149.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
344.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify146.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
010338862
141207704
250017682

prune562.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
0.2b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b
(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
0.4b
(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
1804×*-un-lft-identity
1674×times-frac
1600×sqrt-prod
840×cbrt-prod
684×add-sqr-sqrt add-cube-cbrt
640×distribute-lft-out
324×unpow-prod-down cube-prod
64×sqrt-div
60×associate-/r/
36×cube-mult unpow3 associate-/r* associate-/l* sqr-pow
32×flip3-+ flip-+
30×div-inv
12×add-exp-log
10×add-cbrt-cube
6×pow1 cube-div
4×cbrt-undiv cbrt-div div-exp add-log-exp
3×pow-unpow pow-pow
2×frac-2neg clear-num
1×pow-to-exp sqrt-pow1 pow1/2 pow1/3 pow-exp sqrt-pow2 rem-cbrt-cube associate-/l/ rem-cube-cbrt
Counts
4 → 1096
Calls
4 calls:
109.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
27.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
24.0ms
(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
24.0ms
(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

series1.0s

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
341.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
171.0ms
(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
359.0ms
(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

simplify225.0ms

Algorithm
egg-herbie
Counts
1108 → 1108
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0193626487
1500121134

prune874.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes31.0ms

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

sample1.2s

Algorithm
intervals
Results
319.0ms8027×body80nan
285.0ms1695×body1280valid
185.0ms4166×body80valid
172.0ms1241×body640valid
63.0ms588×body320valid
24.0ms310×body160valid