Details

Time bar (total: 6.3s)

sample37.0ms

Algorithm
intervals
Results
11.0ms61×body640valid
6.0ms132×body80valid
4.0ms31×body320valid
4.0ms17×body1280valid
1.0ms15×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.4b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
5.0ms
(/ 1.0 (+ x 1.0))
5.0ms
(/ 1.0 (- x 1.0))
36.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
174.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ 1.0 (+ x 1.0))
27.0ms
(/ 1.0 (- x 1.0))
41.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
215.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify48.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0496865
11681827
25001816

prune247.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
18.5b
(+ (- (/ (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite716.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
32×cbrt-prod
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
12×distribute-lft-out
11×pow1
9×flip3-+ swap-sqr flip-+ add-log-exp
8×pow1/3
7×associate-*r* associate-*l*
6×add-exp-log times-frac
4×frac-times add-cbrt-cube distribute-lft-out-- unswap-sqr
3×frac-add
2×associate-+l+ associate-*r/ pow-prod-down associate-*l/ sum-log pow-sqr pow-prod-up
1×+-commutative pow2 associate-+l- sub-neg flip3-- pow-plus diff-log prod-exp *-commutative frac-sub flip-- cbrt-unprod
Counts
4 → 103
Calls
4 calls:
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
20.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
688.0ms
(+ (- (/ (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (+ x 1.0))
89.0ms
(cbrt (+ x 1.0))
107.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
218.0ms
(+ (- (/ (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05271210
118861089
25002994

prune272.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
10.7b
(/ (+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0)) (* (* (cbrt (+ x 1.0)) x) (- x 1.0)))
23.4b
(+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
186×associate-*l/
100×cbrt-div
56×frac-add
52×flip3-+ flip-+
40×frac-times
35×flip3-- flip--
31×*-un-lft-identity
30×associate-/l/
28×cbrt-prod
24×frac-sub
23×add-sqr-sqrt
15×add-exp-log add-cube-cbrt
12×associate-*r/ add-cbrt-cube
11×pow1
9×swap-sqr
8×associate-/r/
7×pow1/3 associate-*r* associate-*l* distribute-lft-out
6×add-log-exp
4×associate-+l+ prod-exp cbrt-unprod unswap-sqr
3×cbrt-undiv times-frac div-exp associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down pow-sqr pow-prod-up
1×+-commutative pow2 frac-2neg pow-plus clear-num associate-/r* sum-log *-commutative div-inv
Counts
4 → 171
Calls
4 calls:
2.0ms
(cbrt (+ x 1.0))
19.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
111.0ms
(/ (+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0)) (* (* (cbrt (+ x 1.0)) x) (- x 1.0)))
37.0ms
(+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (+ x 1.0))
113.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
720.0ms
(/ (+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0)) (* (* (cbrt (+ x 1.0)) x) (- x 1.0)))
346.0ms
(+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0))

simplify76.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
015394960
150014766

prune840.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
18.5b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*l/
16×flip3-- frac-add flip--
13×flip3-+ flip-+
12×frac-times
11×pow1 add-exp-log add-sqr-sqrt *-un-lft-identity add-cbrt-cube
8×associate-*r* add-log-exp
7×add-cube-cbrt
6×associate-*r/
5×sub-neg associate-*l*
4×distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×+-commutative diff-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 96
Calls
4 calls:
14.0ms
(* (+ x 1.0) x)
2.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
19.0ms
(* (* (+ x 1.0) x) (- x 1.0))
10.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series381.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(* (+ x 1.0) x)
37.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
99.0ms
(* (* (+ x 1.0) x) (- x 1.0))
2.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify121.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07711337
144701257
250011257

prune288.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115
1115

end0.0ms

sample580.0ms

Algorithm
intervals
Results
201.0ms1899×body640valid
121.0ms4184×body80valid
73.0ms527×body1280valid
70.0ms915×body320valid
25.0ms476×body160valid