Details

Time bar (total: 3.9s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms110×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))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×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×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u 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 hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series216.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
45.0ms
(+ 1.0 (sqrt (+ x 1.0)))
141.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0334508
11222457
25002445

prune161.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize7.0ms

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)))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
34×add-sqr-sqrt
26×times-frac
24×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×expm1-log1p-u flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+ log1p-expm1-u
3×fma-def 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 hypot-def inv-pow
Counts
4 → 118
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
17.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
41.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (+ x 1.0))
49.0ms
(+ 1.0 (sqrt (+ x 1.0)))
105.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
147.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0472857
12046741
25002696

prune235.0ms

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))))

rewrite47.0ms

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×expm1-log1p-u frac-times rem-sqrt-square log1p-expm1-u 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 → 169
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))))))
27.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(sqrt (sqrt (+ x 1.0)))
99.0ms
(sqrt (sqrt (+ x 1.0)))
144.0ms
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
36.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify76.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05301344
123961172
250011118

prune338.0ms

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)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
234×sqrt-prod
200×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 expm1-log1p-u div-exp hypot-def log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 329
Calls
4 calls:
17.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
17.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
18.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
53.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series868.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
132.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
453.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
145.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify103.0ms

Algorithm
egg-herbie
Counts
341 → 341
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
09065696
135685078
250015052

prune464.0ms

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

sample333.0ms

Algorithm
intervals
Results
165.0ms7999×body80valid
46.0ms2785×body80nan
0.0ms1×body1280valid