Details

Time bar (total: 4.8s)

sample30.0ms

Algorithm
intervals
Results
6.0ms276×body80nan
5.0ms40×body1280valid
4.0ms40×body640valid
4.0ms141×body80valid
2.0ms25×body320valid
0.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.0b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×add-sqr-sqrt
69×times-frac
46×sqrt-prod
40×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l*
5×add-log-exp
4×div-inv
3×pow1
2×cbrt-undiv frac-2neg sqrt-div div-exp clear-num associate-/r/
1×sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 117
Calls
3 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
48.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series258.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(/ 1.0 (sqrt (+ x 1.0)))
38.0ms
(/ 1.0 (sqrt x))
142.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify44.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04101006
11310954
25001912

prune277.0ms

Filtered
126 candidates to 84 candidates (66.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
17×add-exp-log add-cbrt-cube
16×*-un-lft-identity
7×pow1 add-cube-cbrt associate-*r*
6×associate-*r/ associate-*l*
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv sqrt-div div-exp difference-of-squares unswap-sqr
3×pow-prod-down distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/ distribute-lft-out
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 77
Calls
3 calls:
29.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
26.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series408.0ms

Counts
3 → 9
Calls
3 calls:
271.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
63.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
75.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify65.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0492793
12495678
25002667

prune217.0ms

Filtered
86 candidates to 59 candidates (68.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(+ x (- 1.0 x))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
105×*-un-lft-identity
41×distribute-lft-out
35×sqrt-prod
31×times-frac
29×add-exp-log add-sqr-sqrt add-cbrt-cube
21×add-cube-cbrt
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod distribute-lft-out--
7×associate-*r* associate-/r*
6×associate-*l* associate-/l*
5×flip3-+ associate-*r/ flip-+
4×sqrt-div associate-/r/ unswap-sqr
3×pow-prod-down associate-/l/
2×associate-+r- associate-+r+ frac-2neg sqrt-pow1 pow1/2 clear-num sum-log div-inv
1×+-commutative sub-neg sqrt-unprod diff-log div-sub *-commutative
Counts
4 → 136
Calls
4 calls:
45.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
33.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
8.0ms
(+ x (- 1.0 x))

series714.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
507.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(+ x (- 1.0 x))

simplify94.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07101587
138371359
250011323

prune312.0ms

Filtered
148 candidates to 84 candidates (56.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
0.2b
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
31×sqrt-prod
29×add-exp-log add-cbrt-cube
27×add-sqr-sqrt
21×distribute-lft-out
19×add-cube-cbrt times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div associate-/r/ flip-+ associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 116
Calls
4 calls:
20.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
22.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series768.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
62.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
496.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify85.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06711264
135251071
250021043

prune267.0ms

Filtered
128 candidates to 81 candidates (63.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01820
11820

end0.0ms

sample830.0ms

Algorithm
intervals
Results
177.0ms1882×body640valid
165.0ms7781×body80nan
152.0ms1201×body1280valid
101.0ms3999×body80valid
44.0ms618×body320valid
14.0ms300×body160valid