Details

Time bar (total: 6.8s)

sample67.0ms

Algorithm
intervals
Results
44.0ms252×body10240exit
6.0ms206×body80valid
2.0ms14×body640valid
2.0ms21×body320valid
1.0ms16×body160valid

simplify47.0ms

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: 11.7b

localize9.0ms

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))
4.2b
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite371.0ms

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))
341.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series140.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ wj (+ wj 1))
24.0ms
(/ x (+ wj 1))
38.0ms
(/ (/ x (+ wj 1)) (exp wj))
57.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify77.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07211524
133031471
250011469

prune426.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

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:
42.0ms
(- (+ x (pow wj 2)) (* 2 (* wj x)))
4.0ms
(+ x (pow wj 2))
6.0ms
(* 2 (* wj x))

series78.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(- (+ x (pow wj 2)) (* 2 (* wj x)))
30.0ms
(+ x (pow wj 2))
19.0ms
(* 2 (* wj x))

simplify126.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0202247
1793231
24232228
35001228

prune95.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (+ (* x x) (- (pow wj 4))) (- x (pow wj 2))) (* 2 (* wj x)))
0.0b
(- x (pow wj 2))
0.0b
(* 2 (* wj x))
21.4b
(/ (+ (* x x) (- (pow wj 4))) (- x (pow wj 2)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
28×*-un-lft-identity
24×times-frac
20×difference-of-squares
18×add-cube-cbrt
11×add-exp-log add-cbrt-cube
9×pow1
8×associate-/r* add-log-exp
6×div-sub
5×unpow-prod-down distribute-lft-out-- unpow2 sqr-pow
3×associate--l- flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×neg-sub0 associate-+r- sub-neg diff-log unsub-neg associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg flip3-+ div-exp associate-*r* clear-num *-commutative flip-+ div-inv
Counts
4 → 104
Calls
4 calls:
134.0ms
(- (/ (+ (* x x) (- (pow wj 4))) (- x (pow wj 2))) (* 2 (* wj x)))
4.0ms
(- x (pow wj 2))
6.0ms
(* 2 (* wj x))
36.0ms
(/ (+ (* x x) (- (pow wj 4))) (- x (pow wj 2)))

series189.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (/ (+ (* x x) (- (pow wj 4))) (- x (pow wj 2))) (* 2 (* wj x)))
32.0ms
(- x (pow wj 2))
18.0ms
(* 2 (* wj x))
84.0ms
(/ (+ (* x x) (- (pow wj 4))) (- x (pow wj 2)))

simplify55.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04101058
11743976
25001951

prune267.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ x (+ wj 1)) (exp wj))
0.0b
(* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj)))
3.0b
(- (* (- (* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj))) (* wj wj)) (+ wj 1)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) wj))
16.5b
(/ (- (* (- (* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj))) (* wj wj)) (+ wj 1)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) wj)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) (+ wj 1)))

rewrite411.0ms

Algorithm
rewrite-expression-head
Rules
555×times-frac
403×*-un-lft-identity
289×add-sqr-sqrt
253×add-cube-cbrt
76×swap-sqr
66×distribute-lft-out
58×associate-*r* associate-*l*
50×add-cbrt-cube
43×associate-*l/
40×associate-/r/
36×add-exp-log
33×flip3-- flip--
32×frac-sub
31×flip3-+ flip-+
23×cbrt-undiv div-exp
22×div-inv
21×frac-times associate-/l*
19×associate-/l/
11×pow1 associate-*r/
10×prod-exp cbrt-unprod
9×unswap-sqr
6×add-log-exp
4×associate-/r*
2×frac-2neg associate--l+ clear-num
1×pow2 distribute-rgt-in sub-neg distribute-lft-in pow-plus diff-log div-sub pow-prod-down pow-sqr *-commutative pow-prod-up
Counts
4 → 403
Calls
4 calls:
14.0ms
(/ (/ x (+ wj 1)) (exp wj))
93.0ms
(* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj)))
87.0ms
(- (* (- (* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj))) (* wj wj)) (+ wj 1)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) wj))
184.0ms
(/ (- (* (- (* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj))) (* wj wj)) (+ wj 1)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) wj)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) (+ wj 1)))

series653.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (/ x (+ wj 1)) (exp wj))
51.0ms
(* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj)))
209.0ms
(- (* (- (* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj))) (* wj wj)) (+ wj 1)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) wj))
350.0ms
(/ (- (* (- (* (/ (/ x (+ wj 1)) (exp wj)) (/ (/ x (+ wj 1)) (exp wj))) (* wj wj)) (+ wj 1)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) wj)) (* (- (/ (/ x (+ wj 1)) (exp wj)) wj) (+ wj 1)))

simplify112.0ms

Algorithm
egg-herbie
Counts
415 → 415
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
025028267
150017858

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

52.8% (0.8b remaining)

Error of 1.2b against oracle of 0.4b and baseline of 2.1b

bsearch36.0ms

Steps
ItersRangePoint
8
1.2456874397123594e-21
5.409776585196184e-17
5.325867851980969e-17

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03845
14245
24245

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.3s7661×body10240exit
179.0ms6278×body80valid
71.0ms807×body320valid
62.0ms440×body640valid
33.0ms540×body160valid