Details

Time bar (total: 4.4s)

sample19.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
2.0ms77×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))))

rewrite28.0ms

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:
7.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
15.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series222.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
37.0ms
(sqrt (+ x 1.0))
145.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0317483
11159435
25001427

prune136.0ms

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
232×sqrt-prod
192×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 div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 317
Calls
4 calls:
14.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
14.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
17.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
49.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series830.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
126.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
432.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
140.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
08875646
135015039
250014953

prune450.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

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)
4.0b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite98.0ms

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:
19.0ms
(* (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))))
53.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
71.0ms
(pow (sqrt (+ x 1.0)) 3)
61.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
199.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify141.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
07711703
138731474
250021459

prune409.0ms

Pruning

4 alts after pruning (1 fresh and 3 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)))
0.0b
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(+ 1.0 (sqrt (+ x 1.0)))
20.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
42.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series521.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(sqrt (+ x 1.0))
47.0ms
(+ 1.0 (sqrt (+ x 1.0)))
306.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
138.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05291282
122321134
250011107

prune257.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes34.0ms

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

sample510.0ms

Algorithm
intervals
Results
314.0ms7997×body80valid
75.0ms2707×body80nan
1.0ms3×body1280valid