Details

Time bar (total: 6.2s)

sample29.0ms

Algorithm
intervals
Results
6.0ms293×body80nan
4.0ms43×body1280valid
3.0ms141×body80valid
3.0ms37×body640valid
1.0ms19×body320valid
1.0ms16×body160valid

simplify5.0ms

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: 27.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
4.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite51.0ms

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:
7.0ms
(sqrt (+ x 1.0))
43.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify62.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune84.0ms

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)))

rewrite83.0ms

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:
7.0ms
(sqrt (+ x 1.0))
33.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
41.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series234.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
61.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
138.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify40.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0341624
11239566
25001533

prune159.0ms

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

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
44.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
42.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
198.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series792.0ms

Counts
4 → 12
Calls
4 calls:
339.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
148.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
165.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify101.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06472845
131522529
250022489

prune514.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite798.0ms

Algorithm
rewrite-expression-head
Rules
1687×sqrt-prod
1429×*-un-lft-identity
1208×times-frac
570×add-sqr-sqrt
540×distribute-lft-out
484×add-cube-cbrt
306×associate-*r*
48×sqrt-div associate-/r/
39×associate-/l*
27×associate-*l*
24×flip3-+ associate-/r* flip-+ div-inv unswap-sqr
15×add-exp-log add-cbrt-cube
8×pow1
5×cbrt-undiv div-exp
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
2×sqrt-pow1 pow1/2
1×frac-times sqrt-unprod associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod associate-/l/
Counts
4 → 824
Calls
4 calls:
42.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
41.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
502.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
120.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series753.0ms

Counts
4 → 12
Calls
4 calls:
314.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
161.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
136.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify157.0ms

Algorithm
egg-herbie
Counts
836 → 836
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0167916907
1500114624

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 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

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195

end0.0ms

sample722.0ms

Algorithm
intervals
Results
151.0ms1719×body1280valid
140.0ms7890×body80nan
84.0ms1221×body640valid
76.0ms4122×body80valid
31.0ms624×body320valid
11.0ms314×body160valid