Details

Time bar (total: 5.3s)

sample41.0ms

Algorithm
intervals
Results
10.0ms268×body80nan
10.0ms63×body1280valid
4.0ms34×body640valid
4.0ms118×body80valid
3.0ms31×body320valid
1.0ms10×body160valid

simplify6.0ms

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: 32.8b

localize5.0ms

Local error

Found 1 expressions with local error:

3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite22.0ms

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:
21.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series70.0ms

Counts
1 → 3
Calls
1 calls:
70.0ms
(- (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

prune42.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

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)))

rewrite44.0ms

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:
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
23.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series203.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
134.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295535
11077482
25001453

prune312.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite212.0ms

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:
25.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
23.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
121.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series801.0ms

Counts
4 → 12
Calls
4 calls:
341.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
155.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
138.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06472845
131522529
250022489

prune522.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize8.0ms

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))))

rewrite182.0ms

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)))
22.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
28.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
74.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series836.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
163.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
337.0ms
(/ 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))))

simplify136.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
010338864
141207704
250017681

prune517.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes81.0ms

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
01113
11113

end0.0ms

sample1.0s

Algorithm
intervals
Results
262.0ms1694×body1280valid
227.0ms7862×body80nan
146.0ms1191×body640valid
139.0ms4146×body80valid
58.0ms656×body320valid
18.0ms313×body160valid