Details

Time bar (total: 3.2s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms74×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
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×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×flip3-+ flip-+ 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 div-inv
Counts
3 → 61
Calls
3 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series213.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(sqrt (+ x 1.0))
140.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0317483
11159435
25001427

prune135.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ x 1.0)))
0.0b
(sqrt (sqrt (+ x 1.0)))
0.2b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))
0.2b
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))

rewrite48.0ms

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:
4.0ms
(sqrt (sqrt (+ x 1.0)))
5.0ms
(sqrt (sqrt (+ x 1.0)))
28.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))
4.0ms
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (sqrt (+ x 1.0)))
93.0ms
(sqrt (sqrt (+ x 1.0)))
30.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))
143.0ms
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))

simplify68.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05121295
122971129
250011106

prune296.0ms

Pruning

4 alts after pruning (3 fresh and 1 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
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.2b
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
99×*-un-lft-identity
64×add-sqr-sqrt
63×add-cube-cbrt
19×associate-/r*
18×distribute-lft-out
17×add-exp-log
11×add-cbrt-cube
8×div-exp
7×associate-/l*
6×pow1 div-inv add-log-exp
4×cbrt-undiv sqrt-prod
3×flip3-+ flip-+
2×rec-exp frac-2neg sqrt-div 1-exp clear-num associate-/l/
1×+-commutative rem-sqrt-square pow-flip sqrt-pow1 pow1/2 sum-log associate-/r/ inv-pow
Counts
4 → 149
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
25.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
25.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series306.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
47.0ms
(+ 1.0 (sqrt (+ x 1.0)))
85.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
145.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify66.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05931413
126271258
250011171

prune228.0ms

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)
3.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.4b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite110.0ms

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×sum-cubes 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 sqrt-unprod diff-log unpow3 div-exp pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 184
Calls
4 calls:
22.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
6.0ms
(pow (sqrt (+ x 1.0)) 3)
13.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
59.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
70.0ms
(pow (sqrt (+ x 1.0)) 3)
67.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
191.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify129.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
07711703
138771474
250011459

prune411.0ms

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
0109
1109

end0.0ms

sample324.0ms

Algorithm
intervals
Results
154.0ms7999×body80valid
49.0ms2690×body80nan
0.0ms1×body1280valid