Details

Time bar (total: 3.4s)

sample12.0ms

Algorithm
intervals
Results
5.0ms255×body80valid
1.0ms81×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: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 45
Calls
2 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series181.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(+ 1.0 (sqrt (+ x 1.0)))
138.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify32.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278393
11058351
25002347

prune97.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
5.0ms
(* (cbrt x) (cbrt x))
0.0ms
(cbrt x)
0.0ms
(cbrt x)
1.0ms
(cbrt x)

series695.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(* (cbrt x) (cbrt x))
168.0ms
(cbrt x)
172.0ms
(cbrt x)
168.0ms
(cbrt x)

simplify86.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0115288
1472261
22959238
35003235

prune172.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.1b
(pow (sqrt (+ x 1.0)) 3)
4.9b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.6b
(/ 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×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:
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))))
55.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
62.0ms
(pow (sqrt (+ x 1.0)) 3)
63.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
188.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify127.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
07711703
138731474
250021459

prune382.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
53×add-sqr-sqrt
52×times-frac
37×add-cube-cbrt
35×sqrt-prod
30×associate-*r*
14×distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-*l* associate-/l* unswap-sqr
5×pow1 add-log-exp
4×associate-/r* associate-/r/
3×flip3-+ flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 116
Calls
3 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
17.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
46.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series450.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ 1.0 (sqrt (+ x 1.0)))
276.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
129.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04911191
121421050
250021025

prune202.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes45.0ms

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

sample295.0ms

Algorithm
intervals
Results
148.0ms7996×body80valid
40.0ms2823×body80nan
0.0ms4×body1280valid