Details

Time bar (total: 7.1s)

sample13.0ms

Algorithm
intervals
Results
5.0ms255×body80valid
1.0ms72×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

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

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 expm1-log1p-u frac-2neg flip3-+ div-exp clear-num flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 35
Calls
1 calls:
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series136.0ms

Counts
1 → 3
Calls
1 calls:
136.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify32.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0228304
1898277
25001273

prune73.0ms

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))

rewrite23.0ms

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×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u associate-/l/ add-log-exp
1×pow-flip flip3-+ associate-/r/ flip-+ inv-pow
Counts
2 → 125
Calls
2 calls:
8.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
10.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series228.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
143.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify63.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05121245
124091113
250011021

prune169.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize10.0ms

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))

rewrite235.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 1363
Calls
4 calls:
48.0ms
(/ (/ 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))

series2.0s

Counts
4 → 12
Calls
4 calls:
1.2s
(/ (/ 1 (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))) (cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x)))
274.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
282.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))
275.0ms
(cbrt (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify352.0ms

Algorithm
egg-herbie
Counts
1375 → 1375
Iterations

Useful iterations: 1 (64.0ms)

IterNodesCost
0411337829
1500136985

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)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
87×add-sqr-sqrt
78×prod-diff
62×add-cube-cbrt
38×sqrt-prod
23×distribute-rgt-in distribute-lft-in
21×associate-*l*
16×times-frac
12×difference-of-squares
10×add-log-exp
9×distribute-lft-out
8×add-exp-log add-cbrt-cube
7×fma-neg
6×associate-*r* distribute-lft-out--
5×pow1 sub-neg flip3-- associate--l+ flip--
4×diff-log
3×expm1-log1p-u log1p-expm1-u
2×frac-times associate-*r/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
3 → 175
Calls
3 calls:
20.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
7.0ms
(- 1.0 (sqrt (+ x 1.0)))
8.0ms
(- (- (* 1.0 1.0) x) 1.0)

series141.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
48.0ms
(- 1.0 (sqrt (+ x 1.0)))
16.0ms
(- (- (* 1.0 1.0) x) 1.0)

simplify101.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06842747
131811990
250031901

prune240.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes36.0ms

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

sample314.0ms

Algorithm
intervals
Results
158.0ms7998×body80valid
45.0ms2689×body80nan
0.0ms2×body1280valid