Details

Time bar (total: 5.4s)

sample25.0ms

Algorithm
intervals
Results
5.0ms276×body80nan
4.0ms51×body1280valid
3.0ms139×body80valid
2.0ms29×body640valid
1.0ms26×body320valid
0.0ms11×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize8.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (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))

series78.0ms

Counts
1 → 3
Calls
1 calls:
78.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify51.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune40.0ms

Filtered
22 candidates to 14 candidates (63.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

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)))

rewrite42.0ms

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

series216.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
147.0ms
(/ 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

prune120.0ms

Filtered
61 candidates to 39 candidates (63.9%)
Pruning

5 alts after pruning (4 fresh and 1 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))))

rewrite180.0ms

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)))
27.0ms
(/ 1.0 (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))))

series844.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
174.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
344.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
151.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify144.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
010338862
141207704
250017681

prune549.0ms

Filtered
457 candidates to 146 candidates (31.9%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(/ (/ 1.0 (* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
123×sqrt-prod
111×times-frac
56×add-sqr-sqrt
52×distribute-lft-out
50×add-cube-cbrt
26×cbrt-div
24×sqrt-div
22×associate-*r/ associate-/r/
19×cbrt-prod
15×add-exp-log add-cbrt-cube
14×flip3-+ flip-+
12×associate-*r*
11×div-inv
9×associate-/r* associate-/l*
6×pow1
5×cbrt-undiv div-exp
4×add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3 prod-exp cbrt-unprod
1×frac-2neg pow-prod-down clear-num *-commutative associate-/l/
Counts
4 → 181
Calls
4 calls:
49.0ms
(* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
46.0ms
(/ (/ 1.0 (* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.5s

Counts
4 → 12
Calls
4 calls:
322.0ms
(* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
500.0ms
(/ (/ 1.0 (* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
321.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
307.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify128.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09514965
140694701
250034581

prune538.0ms

Filtered
193 candidates to 110 candidates (57.0%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes29.0ms

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

sample683.0ms

Algorithm
intervals
Results
161.0ms1797×body1280valid
144.0ms7781×body80nan
87.0ms1283×body640valid
77.0ms3999×body80valid
32.0ms621×body320valid
12.0ms300×body160valid