Details

Time bar (total: 4.2s)

sample25.0ms

Algorithm
intervals
Results
4.0ms51×body1280valid
4.0ms237×body80nan
2.0ms130×body80valid
2.0ms35×body640valid
1.0ms25×body320valid
1.0ms15×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.8b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
7.0ms
(sqrt (+ x 1.0))
45.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series89.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
59.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify56.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0182266
1538243
22004233
35002230

prune87.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
20×sqrt-prod
18×times-frac
17×distribute-lft-out
15×add-sqr-sqrt
14×add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube
3×pow1 associate-/l*
2×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 57
Calls
2 calls:
7.0ms
(sqrt (+ x 1.0))
47.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series154.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(sqrt (+ x 1.0))
128.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify38.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0309501
11128459
25002430

prune139.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite125.0ms

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:
10.0ms
(sqrt (sqrt (+ x 1.0)))
8.0ms
(sqrt (sqrt (+ x 1.0)))
47.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
52.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(sqrt (sqrt (+ x 1.0)))
85.0ms
(sqrt (sqrt (+ x 1.0)))
137.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
30.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify76.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05251350
123291176
250011152

prune364.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
46.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
45.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
213.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series767.0ms

Counts
4 → 12
Calls
4 calls:
342.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
128.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
158.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify107.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06472845
131522529
250022489

prune552.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.1b 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
095
195

end0.0ms

sample720.0ms

Algorithm
intervals
Results
149.0ms1727×body1280valid
142.0ms8191×body80nan
83.0ms1282×body640valid
75.0ms4038×body80valid
32.0ms649×body320valid
10.0ms304×body160valid