Details

Time bar (total: 7.5s)

sample77.0ms

Algorithm
intervals
Results
50.0ms238×body10240exit
7.0ms196×body80valid
3.0ms31×body320valid
3.0ms16×body640valid
1.0ms18×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
0219
1529
21139
32408
416258
550018

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ wj (+ wj 1))
0.0b
(/ (/ x (+ wj 1)) (exp wj))
0.0b
(/ x (+ wj 1))
4.7b
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
231×*-un-lft-identity
175×times-frac
129×add-sqr-sqrt
124×add-cube-cbrt
72×prod-diff
52×distribute-lft-out
24×associate-/l*
20×associate-/r/
13×add-cbrt-cube
11×add-exp-log flip3-+ associate-/r* flip-+ div-inv
9×add-log-exp
5×cbrt-undiv div-exp
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u
3×frac-2neg clear-num
2×diff-log frac-sub distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- associate--l+ sum-log flip-- associate-/l/
Counts
4 → 260
Calls
4 calls:
5.0ms
(/ wj (+ wj 1))
13.0ms
(/ (/ x (+ wj 1)) (exp wj))
6.0ms
(/ x (+ wj 1))
441.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series150.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ wj (+ wj 1))
45.0ms
(/ (/ x (+ wj 1)) (exp wj))
23.0ms
(/ x (+ wj 1))
60.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify126.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
010154090
145553249
250013243

prune536.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b
(* 2 (* wj x))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube add-log-exp
5×add-sqr-sqrt add-cube-cbrt
4×fma-neg prod-diff
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u diff-log log1p-expm1-u distribute-lft-out
1×sub-neg flip3-- associate-*r* associate--l+ sum-log *-commutative flip--
Counts
2 → 44
Calls
2 calls:
53.0ms
(- (+ x (pow wj 2)) (* 2 (* wj x)))
6.0ms
(* 2 (* wj x))

series49.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(- (+ x (pow wj 2)) (* 2 (* wj x)))
20.0ms
(* 2 (* wj x))

simplify34.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0195282
1764240
25001222

prune106.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.6b
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.6b
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.6b
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-- pow1/3 flip--
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
153.0ms
(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
19.0ms
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
18.0ms
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
19.0ms
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
320.0ms
(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
281.0ms
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
281.0ms
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
284.0ms
(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

simplify53.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03281663
112611570
250021483

prune334.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.6b
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.6b
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.9b
(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×cbrt-div
9×unpow-prod-down
5×pow1 add-exp-log
4×expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow flip3-- flip--
2×pow-pow
1×pow-to-exp pow-exp sqr-pow
Counts
4 → 80
Calls
4 calls:
19.0ms
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
21.0ms
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
19.0ms
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
38.0ms
(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

series992.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
283.0ms
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
294.0ms
(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
131.0ms
(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

simplify55.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04081346
114111290
250011249

prune377.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

regimes112.0ms

Accuracy

47.5% (0.9b remaining)

Error of 1.2b against oracle of 0.3b and baseline of 2.0b

bsearch40.0ms

Steps
ItersRangePoint
9
4.896495915127463e-10
0.16998237910242062
3.1088434258944978e-06

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03433
13433

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.6s7582×body10240exit
212.0ms6332×body80valid
80.0ms478×body640valid
78.0ms756×body320valid
35.0ms510×body160valid