Details

Time bar (total: 6.0s)

sample25.0ms

Algorithm
intervals
Results
5.0ms56×body1280valid
4.0ms245×body80nan
3.0ms49×body640valid
2.0ms111×body80valid
1.0ms28×body320valid
0.0ms12×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: 34.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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:
22.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series72.0ms

Counts
1 → 3
Calls
1 calls:
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

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:
17.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
27.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series202.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295535
11077482
25001453

prune124.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite221.0ms

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:
28.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
128.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series800.0ms

Counts
4 → 12
Calls
4 calls:
346.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
144.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
168.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06472845
131522529
250022489

prune508.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ (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))))
0.3b
(* (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite584.0ms

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-*l*
48×sqrt-div associate-/r/
39×associate-/l*
27×associate-*r*
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:
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
76.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
368.0ms
(* (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series793.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
337.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
172.0ms
(* (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify165.0ms

Algorithm
egg-herbie
Counts
836 → 836
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0146216754
1500115125

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01620
11620

end0.0ms

sample710.0ms

Algorithm
intervals
Results
160.0ms1752×body1280valid
148.0ms8078×body80nan
104.0ms1322×body640valid
76.0ms3992×body80valid
34.0ms628×body320valid
11.0ms306×body160valid