Details

Time bar (total: 3.7s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms110×body80nan

simplify3.0ms

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))))

rewrite31.0ms

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:
6.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series220.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ x 1.0))
45.0ms
(+ 1.0 (sqrt (+ x 1.0)))
144.0ms
(/ 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

prune132.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 106
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
19.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
37.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series323.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (+ x 1.0))
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
103.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
144.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0452821
11973707
25002668

prune186.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l*
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-exp-log add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
3×associate-/r* associate-/l*
2×associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
4.0ms
(sqrt (sqrt (+ x 1.0)))
4.0ms
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
26.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series353.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (sqrt (+ x 1.0)))
89.0ms
(sqrt (sqrt (+ x 1.0)))
140.0ms
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
35.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify72.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05121295
123011129
250011105

prune279.0ms

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

rewrite118.0ms

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:
16.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
17.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
51.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series822.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
130.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
419.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
147.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify105.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
08875646
135015039
250014953

prune422.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes19.0ms

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
0135
1135

end0.0ms

sample322.0ms

Algorithm
intervals
Results
157.0ms7999×body80valid
42.0ms2785×body80nan
0.0ms1×body1280valid