Details

Time bar (total: 6.8s)

sample17.0ms

Algorithm
intervals
Results
5.0ms255×body80valid
4.0ms72×body80nan
0.0ms1×body1280valid

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

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
12×times-frac
10×add-sqr-sqrt add-cube-cbrt
4×associate-/r* distribute-lft-out
3×add-exp-log add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
1 → 33
Calls
1 calls:
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series139.0ms

Counts
1 → 3
Calls
1 calls:
139.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0223295
1875267
25001266

prune68.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.4b
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
92×*-un-lft-identity
60×add-sqr-sqrt add-cube-cbrt
19×associate-/r*
16×distribute-lft-out
15×add-exp-log
9×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv
4×cbrt-undiv
3×pow1
2×rec-exp frac-2neg 1-exp clear-num associate-/l/ add-log-exp
1×pow-flip flip3-+ associate-/r/ flip-+ inv-pow
Counts
2 → 121
Calls
2 calls:
8.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
10.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series220.0ms

Counts
2 → 6
Calls
2 calls:
81.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
139.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify61.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05011225
123701092
250021005

prune162.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))) (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x)))
0.8b
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
0.8b
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
0.8b
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
3830×times-frac
2291×*-un-lft-identity
2016×cbrt-prod
1535×add-sqr-sqrt add-cube-cbrt
378×distribute-lft-out
147×div-inv
62×associate-/l*
24×cbrt-div
21×associate-/r/
19×associate-/r*
13×add-exp-log
7×pow1
6×div-exp add-cbrt-cube
5×pow1/3
4×add-log-exp
3×cbrt-undiv pow-div
2×pow-flip
1×rec-exp frac-2neg 1-exp clear-num associate-/l/ inv-pow
Counts
4 → 1355
Calls
4 calls:
51.0ms
(/ (/ 1 (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))) (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x)))
7.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
7.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
7.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series1.9s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (/ 1 (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))) (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x)))
273.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
270.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
269.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify351.0ms

Algorithm
egg-herbie
Counts
1367 → 1367
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0408437789
1500236950

prune2.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
1.9b
(- 1.0 (sqrt (+ x 1.0)))
2.1b
(- (- (* 1.0 1.0) x) 1.0)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
25×*-un-lft-identity
21×associate-*l*
16×times-frac
13×add-cube-cbrt
10×add-log-exp
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-*r* distribute-lft-out--
5×pow1 sub-neg flip3-- flip--
4×diff-log
2×distribute-rgt-in frac-times distribute-lft-in associate-*r/ prod-exp associate--l+ sqrt-prod associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
3 → 84
Calls
3 calls:
18.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
6.0ms
(- 1.0 (sqrt (+ x 1.0)))
7.0ms
(- (- (* 1.0 1.0) x) 1.0)

series134.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
51.0ms
(- 1.0 (sqrt (+ x 1.0)))
11.0ms
(- (- (* 1.0 1.0) x) 1.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0388811
11726733
25001725

prune166.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes35.0ms

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

sample321.0ms

Algorithm
intervals
Results
159.0ms7998×body80valid
48.0ms2689×body80nan
0.0ms2×body1280valid