Details

Time bar (total: 4.5s)

sample24.0ms

Algorithm
intervals
Results
4.0ms50×body1280valid
4.0ms227×body80nan
3.0ms52×body640valid
2.0ms123×body80valid
1.0ms25×body320valid
0.0ms6×body160valid

simplify7.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.0b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series104.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(sqrt (+ x 1.0))
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify49.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
02991161
1921822
25001744

prune142.0ms

Filtered
95 candidates to 44 candidates (46.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New91495
Fresh000
Picked101
Done000
Total92496

Merged error: 0.1b

Counts
96 → 4

localize8.0ms

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 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
16.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series241.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(sqrt (+ x 1.0))
63.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify63.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0409789
11675716
25001675

prune228.0ms

Filtered
103 candidates to 68 candidates (66.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New967103
Fresh213
Picked101
Done000
Total998107

Merged error: 0.0b

Counts
107 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
27×add-sqr-sqrt
21×add-cube-cbrt
20×times-frac
19×distribute-lft-out
13×cbrt-prod
10×associate-*r*
9×sqrt-prod
8×add-exp-log associate-*l* add-cbrt-cube
6×pow1 cbrt-div
5×flip3-+ associate-/r* flip-+
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 110
Calls
4 calls:
23.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
8.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series458.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
97.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
88.0ms
(cbrt (+ x 1.0))
90.0ms
(cbrt (+ x 1.0))

simplify137.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
09381753
145401628
250011624

prune433.0ms

Filtered
122 candidates to 95 candidates (77.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1220122
Fresh077
Picked011
Done000
Total1228130

Merged error: 0.0b

Counts
130 → 8

localize10.0ms

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 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
1134×*-un-lft-identity
918×sqrt-prod
774×times-frac
465×distribute-lft-out
313×add-sqr-sqrt
295×add-cube-cbrt
50×associate-/l*
28×sqrt-div
27×associate-/r*
24×associate-/r/
22×associate-/l/
16×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
8×hypot-def
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 580
Calls
4 calls:
9.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
19.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
35.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series821.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
345.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
143.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify189.0ms

Algorithm
egg-herbie
Counts
592 → 592
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0112211393
145889895
250019895

prune681.0ms

Filtered
592 candidates to 172 candidates (29.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New5884592
Fresh426
Picked101
Done011
Total5937600

Merged error: 0b

Counts
600 → 7

regimes31.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01915
12315
22315

end0.0ms

sample676.0ms

Algorithm
intervals
Results
147.0ms1630×body1280valid
136.0ms8087×body80nan
86.0ms1262×body640valid
78.0ms4166×body80valid
34.0ms634×body320valid
11.0ms308×body160valid