Details

Time bar (total: 7.5s)

sample80.0ms

Algorithm
intervals
Results
55.0ms294×body10240exit
6.0ms210×body80valid
3.0ms29×body320valid
2.0ms10×body640valid
1.0ms11×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
0209
1489
21079
32248
415148
550018

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ wj (+ wj 1))
0.0b
(/ x (+ wj 1))
0.0b
(/ (/ x (+ wj 1)) (exp wj))
3.4b
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
118×*-un-lft-identity
78×add-sqr-sqrt
73×add-cube-cbrt
24×associate-/l*
21×distribute-lft-out
13×add-cbrt-cube
12×associate-/r/
11×add-exp-log associate-/r*
9×add-log-exp
7×flip3-+ flip-+ div-inv
5×cbrt-undiv div-exp
4×pow1
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 → 176
Calls
4 calls:
5.0ms
(/ wj (+ wj 1))
5.0ms
(/ x (+ wj 1))
12.0ms
(/ (/ x (+ wj 1)) (exp wj))
334.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series142.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ wj (+ wj 1))
22.0ms
(/ x (+ wj 1))
44.0ms
(/ (/ x (+ wj 1)) (exp wj))
54.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify78.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07211524
133031471
250011469

prune431.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×pow1 add-exp-log add-cbrt-cube
6×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×diff-log sum-log
1×+-commutative sub-neg flip3-- flip3-+ associate-*r* associate--l+ *-commutative flip-- flip-+ distribute-lft-out
Counts
3 → 44
Calls
3 calls:
4.0ms
(+ x (pow wj 2))
39.0ms
(- (+ x (pow wj 2)) (* 2 (* wj x)))
6.0ms
(* 2 (* wj x))

series82.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ x (pow wj 2))
29.0ms
(- (+ x (pow wj 2)) (* 2 (* wj x)))
23.0ms
(* 2 (* wj x))

simplify124.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0202252
1789232
24182229
35001229

prune99.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ wj (+ wj 1)) (/ wj (+ wj 1)))
0.0b
(+ (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
2.8b
(- (* (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (+ (/ (/ x (+ wj 1)) (exp wj)) wj)) (* (/ wj (+ wj 1)) (/ wj (+ wj 1))))
19.3b
(/ (- (* (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (+ (/ (/ x (+ wj 1)) (exp wj)) wj)) (* (/ wj (+ wj 1)) (/ wj (+ wj 1)))) (+ (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1))))

rewrite846.0ms

Algorithm
rewrite-expression-head
Rules
123×*-un-lft-identity
84×times-frac
63×add-sqr-sqrt
51×add-cube-cbrt
48×frac-sub
44×flip3-+ flip-+
41×frac-times
36×distribute-lft-out
29×associate-*r/ associate-*l/
26×associate-/l/
24×swap-sqr
18×add-exp-log associate-*r* associate-*l* add-cbrt-cube
12×associate-/r/
11×pow1 add-log-exp
7×difference-of-squares
5×cbrt-undiv div-exp associate-/r* div-inv
4×frac-add prod-exp cbrt-unprod associate-/l* unswap-sqr
3×sum-log
2×flip3-- associate--l+ flip--
1×+-commutative pow2 distribute-rgt-in sub-neg associate-+l+ frac-2neg distribute-lft-in pow-plus diff-log div-sub pow-prod-down clear-num pow-sqr *-commutative pow-prod-up
Counts
4 → 216
Calls
4 calls:
29.0ms
(* (/ wj (+ wj 1)) (/ wj (+ wj 1)))
246.0ms
(+ (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
72.0ms
(- (* (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (+ (/ (/ x (+ wj 1)) (exp wj)) wj)) (* (/ wj (+ wj 1)) (/ wj (+ wj 1))))
487.0ms
(/ (- (* (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (+ (/ (/ x (+ wj 1)) (exp wj)) wj)) (* (/ wj (+ wj 1)) (/ wj (+ wj 1)))) (+ (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1))))

series713.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (/ wj (+ wj 1)) (/ wj (+ wj 1)))
56.0ms
(+ (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
186.0ms
(- (* (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (+ (/ (/ x (+ wj 1)) (exp wj)) wj)) (* (/ wj (+ wj 1)) (/ wj (+ wj 1))))
447.0ms
(/ (- (* (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (+ (/ (/ x (+ wj 1)) (exp wj)) wj)) (* (/ wj (+ wj 1)) (/ wj (+ wj 1)))) (+ (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1))))

simplify76.0ms

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012585288
150015040

prune609.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* wj x) (* wj x))
0.2b
(pow (* 2 (* wj x)) 3)
3.5b
(- (pow (+ x (pow wj 2)) 3) (pow (* 2 (* wj x)) 3))
34.3b
(/ (- (pow (+ x (pow wj 2)) 3) (pow (* 2 (* wj x)) 3)) (+ (* (+ x (pow wj 2)) (+ (+ x (pow wj 2)) (* 2 (* wj x)))) (* 4 (* (* wj x) (* wj x)))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
49×pow1
40×difference-of-squares
39×times-frac
33×*-un-lft-identity
31×sqr-pow
24×add-exp-log add-cbrt-cube
23×add-cube-cbrt
20×pow-prod-down
13×associate-/l*
11×unpow-prod-down cube-prod prod-exp cbrt-unprod
6×add-log-exp
5×difference-cubes distribute-lft-out--
4×pow-sqr pow-prod-up
3×pow-unpow pow-pow pow-exp associate-/r* rem-cube-cbrt
2×flip3-- pow-plus associate-/r/ flip-- associate-/l/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg frac-2neg flip3-+ diff-log unpow3 div-sub swap-sqr div-exp associate-*r* associate-*l* clear-num *-commutative flip-+ div-inv
Counts
4 → 153
Calls
4 calls:
9.0ms
(* (* wj x) (* wj x))
5.0ms
(pow (* 2 (* wj x)) 3)
87.0ms
(- (pow (+ x (pow wj 2)) 3) (pow (* 2 (* wj x)) 3))
215.0ms
(/ (- (pow (+ x (pow wj 2)) 3) (pow (* 2 (* wj x)) 3)) (+ (* (+ x (pow wj 2)) (+ (+ x (pow wj 2)) (* 2 (* wj x)))) (* 4 (* (* wj x) (* wj x)))))

series546.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* wj x) (* wj x))
61.0ms
(pow (* 2 (* wj x)) 3)
155.0ms
(- (pow (+ x (pow wj 2)) 3) (pow (* 2 (* wj x)) 3))
298.0ms
(/ (- (pow (+ x (pow wj 2)) 3) (pow (* 2 (* wj x)) 3)) (+ (* (+ x (pow wj 2)) (+ (+ x (pow wj 2)) (* 2 (* wj x)))) (* 4 (* (* wj x) (* wj x)))))

simplify132.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
06153141
131403001
250012996

prune463.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

regimes118.0ms

Accuracy

0% (1.5b remaining)

Error of 2.2b against oracle of 0.7b and baseline of 2.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115
1115

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.5s7938×body10240exit
183.0ms6285×body80valid
78.0ms816×body320valid
67.0ms471×body640valid
34.0ms514×body160valid