Details

Time bar (total: 5.9s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms78×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
7.0ms
(sqrt (+ x 1.0))
18.0ms
(+ 1.0 (sqrt (+ x 1.0)))
31.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series194.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(sqrt (+ x 1.0))
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
126.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0317483
11159435
25001427

prune135.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.3b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
232×sqrt-prod
192×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
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 → 317
Calls
4 calls:
28.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
27.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
89.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
33.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series762.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
117.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
134.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
396.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify106.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
08875646
135015039
250014956

prune438.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
15.0ms
(+ 1.0 (sqrt (+ x 1.0)))
33.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
82.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(sqrt (+ x 1.0))
43.0ms
(+ 1.0 (sqrt (+ x 1.0)))
275.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
123.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05291281
122431134
250011107

prune260.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
0.0b
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
0.0b
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
8.4b
(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

rewrite503.0ms

Algorithm
rewrite-expression-head
Rules
70×add-exp-log
31×prod-exp
24×div-exp
22×associate-*r/
20×frac-add
18×add-cbrt-cube add-log-exp
16×times-frac
14×add-sqr-sqrt pow-to-exp *-un-lft-identity pow-exp
12×add-cube-cbrt associate-*r* frac-sub
9×unpow-prod-down
8×associate-/l*
6×pow1 flip3-+ sum-log flip-+
5×cbrt-unprod
4×cbrt-undiv frac-times flip3-- associate-*l/ flip--
3×diff-log associate-*l* unpow2 sqr-pow
2×sub-neg associate-+r+ div-inv
1×+-commutative associate-+r- associate-+l+ frac-2neg pow-prod-down clear-num associate-/r* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 132
Calls
4 calls:
26.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
71.0ms
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
357.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
43.0ms
(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
173.0ms
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
656.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
461.0ms
(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08783731
150023581

prune545.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.2b 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
084
184

end0.0ms

sample343.0ms

Algorithm
intervals
Results
155.0ms7997×body80valid
38.0ms2613×body80nan
0.0ms3×body1280valid