Details

Time bar (total: 5.0s)

sample33.0ms

Algorithm
intervals
Results
6.0ms64×body640valid
6.0ms296×body80nan
5.0ms37×body1280valid
3.0ms126×body80valid
1.0ms15×body320valid
1.0ms14×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: 20.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.7b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
47.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (+ x 1.0))
81.0ms
(/ 1.0 (sqrt (+ x 1.0)))
40.0ms
(/ 1.0 (sqrt x))
144.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify53.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04431097
114341038
25001992

prune322.0ms

Filtered
145 candidates to 98 candidates (67.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
3.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×sqrt-prod
20×*-un-lft-identity
18×add-exp-log add-cbrt-cube
9×pow1 add-cube-cbrt
7×associate-*r*
6×sqrt-div associate-*r/ associate-*l* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp difference-of-squares unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out distribute-lft-out--
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
28.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
26.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series444.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
276.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
63.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify73.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0511884
12548762
25002749

prune256.0ms

Filtered
105 candidates to 73 candidates (69.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(+ x (- 1.0 x))

rewrite106.0ms

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)))
7.0ms
(+ x (- 1.0 x))

series716.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
508.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(+ x (- 1.0 x))

simplify97.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07101587
138371359
250011323

prune315.0ms

Filtered
148 candidates to 84 candidates (56.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (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:
17.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series782.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
148.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
507.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
63.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify89.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06711264
135141071
250011043

prune258.0ms

Filtered
128 candidates to 81 candidates (63.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample844.0ms

Algorithm
intervals
Results
181.0ms1832×body640valid
169.0ms7974×body80nan
147.0ms1185×body1280valid
105.0ms4076×body80valid
43.0ms596×body320valid
15.0ms311×body160valid