Details

Time bar (total: 3.9s)

sample13.0ms

Algorithm
intervals
Results
5.0ms255×body80valid
1.0ms84×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

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))))

rewrite30.0ms

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))))

series221.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ x 1.0))
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
145.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0334508
11222457
25002445

prune159.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize6.0ms

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 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-exp-log add-sqr-sqrt
8×add-cbrt-cube
7×add-cube-cbrt
5×add-log-exp
4×pow1 sqrt-prod
3×expm1-log1p-u fma-def flip3-+ times-frac div-exp flip-+ log1p-expm1-u associate-/l*
2×cbrt-undiv sqrt-div associate-*r/ prod-exp associate-/r/ distribute-lft-out
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/r* sum-log cbrt-unprod hypot-def div-inv
Counts
3 → 62
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
11.0ms
(/ x (* 1 (+ 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 (+ 1.0 (sqrt (+ x 1.0)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0383430
11688363
25002358

prune144.0ms

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))))
0.4b
(/ (/ 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)))))

rewrite122.0ms

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:
19.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
50.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
17.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series857.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
139.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
151.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
434.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
341 → 341
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
09065694
135745078
250015045

prune479.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b
(pow (sqrt (+ x 1.0)) 3)
3.1b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.5b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u sum-cubes log1p-expm1-u sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 194
Calls
4 calls:
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms
(pow (sqrt (+ x 1.0)) 3)
13.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
56.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
71.0ms
(pow (sqrt (+ x 1.0)) 3)
64.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
206.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify148.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
08251791
141261518
250011510

prune440.0ms

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
1155
2155

end0.0ms

sample308.0ms

Algorithm
intervals
Results
156.0ms7998×body80valid
40.0ms2714×body80nan
0.0ms2×body1280valid