Details

Time bar (total: 5.3s)

sample24.0ms

Algorithm
intervals
Results
7.0ms67×body1280valid
5.0ms33×body640valid
3.0ms128×body80valid
1.0ms19×body320valid
0.0ms9×body160valid

simplify22.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.9b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
11.0ms
(/ (+ x 1.0) (- x 1.0))
56.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series200.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
39.0ms
(/ (+ x 1.0) (- x 1.0))
128.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify45.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0392760
11379726
25001716

prune199.0ms

Filtered
113 candidates to 76 candidates (67.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b
(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.1b
(pow (/ x (+ x 1.0)) 3)
2.8b
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
354×*-un-lft-identity
216×times-frac
190×add-sqr-sqrt
104×unpow-prod-down cube-prod
78×add-cube-cbrt
66×distribute-lft-out
61×distribute-lft-out--
44×difference-of-squares
24×swap-sqr
22×add-exp-log add-cbrt-cube
18×associate-*r* associate-*l*
16×associate-/r/
14×sqr-pow
13×pow1
8×div-inv
6×cbrt-undiv pow-unpow flip3-+ div-exp flip-+ add-log-exp
4×cube-div pow-exp prod-exp cbrt-unprod rem-cube-cbrt unswap-sqr
3×flip3-- flip--
2×cube-mult pow-to-exp pow-pow unpow3
1×difference-cubes pow2 frac-times sub-neg pow-plus diff-log associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up frac-sub
Counts
4 → 303
Calls
4 calls:
29.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
12.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
8.0ms
(pow (/ x (+ x 1.0)) 3)
180.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series442.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
60.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
56.0ms
(pow (/ x (+ x 1.0)) 3)
285.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify61.0ms

Algorithm
egg-herbie
Counts
315 → 315
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011642932
150022690

prune526.0ms

Filtered
315 candidates to 141 candidates (44.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.1b
(/ 3.0 (pow x 3))
0.3b
(/ (- 1.0) (pow x 2))
6.0b
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite710.0ms

Algorithm
rewrite-expression-head
Rules
143×times-frac
120×add-sqr-sqrt
105×*-un-lft-identity
78×add-cube-cbrt
48×unpow-prod-down
29×distribute-rgt-neg-in
27×distribute-lft-neg-in
20×associate-/r*
18×sqr-pow
15×difference-of-squares
14×add-exp-log
13×cube-prod associate-/l* unpow2
11×add-log-exp
10×distribute-lft-out--
9×neg-mul-1
8×add-cbrt-cube
6×div-exp
5×frac-sub
4×pow1 cube-mult diff-log unpow3
3×sub-neg flip3-- flip--
2×cbrt-undiv associate--l- neg-sub0 pow-to-exp frac-2neg div-sub pow-exp associate--l+ clear-num div-inv
1×distribute-frac-neg
Counts
4 → 234
Calls
4 calls:
80.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
4.0ms
(/ 3.0 (pow x 3))
8.0ms
(/ (- 1.0) (pow x 2))
608.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series161.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
35.0ms
(/ 3.0 (pow x 3))
24.0ms
(/ (- 1.0) (pow x 2))
36.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify95.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07411813
135251605
250011602

prune408.0ms

Filtered
246 candidates to 133 candidates (54.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (+ (* 12.0 (/ 1 (pow x 2))) (+ (* 9.0 (/ 1 x)) (* 48.0 (/ 1 (pow x 3)))))) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.3b
(* 9.0 (/ 1 x))
0.3b
(/ 1 (pow x 2))
7.5b
(+ (* 12.0 (/ 1 (pow x 2))) (+ (* 9.0 (/ 1 x)) (* 48.0 (/ 1 (pow x 3)))))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
67×frac-add
65×times-frac
59×add-sqr-sqrt
53×*-un-lft-identity
52×add-cube-cbrt
45×associate-*r/
29×un-div-inv
24×add-exp-log
23×associate-/r/
16×frac-times
14×associate-/l/ distribute-neg-frac
13×flip3-+ associate-*r* add-cbrt-cube flip-+ associate-/l*
12×distribute-lft-neg-in unpow-prod-down distribute-rgt-neg-in
11×associate-/r*
10×associate-*l/
9×div-exp add-log-exp
6×pow1
4×neg-mul-1 rec-exp 1-exp prod-exp unpow2 sqr-pow
3×cbrt-undiv pow-to-exp associate-*l* pow-exp sum-log div-inv unswap-sqr
2×frac-2neg clear-num cbrt-unprod
1×+-commutative neg-sub0 associate-+r+ pow-flip div-sub distribute-frac-neg pow-prod-down *-commutative inv-pow
Counts
4 → 212
Calls
4 calls:
183.0ms
(/ (- (+ (* 12.0 (/ 1 (pow x 2))) (+ (* 9.0 (/ 1 x)) (* 48.0 (/ 1 (pow x 3)))))) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
10.0ms
(* 9.0 (/ 1 x))
4.0ms
(/ 1 (pow x 2))
16.0ms
(+ (* 12.0 (/ 1 (pow x 2))) (+ (* 9.0 (/ 1 x)) (* 48.0 (/ 1 (pow x 3)))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(/ (- (+ (* 12.0 (/ 1 (pow x 2))) (+ (* 9.0 (/ 1 x)) (* 48.0 (/ 1 (pow x 3)))))) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
15.0ms
(* 9.0 (/ 1 x))
16.0ms
(/ 1 (pow x 2))
28.0ms
(+ (* 12.0 (/ 1 (pow x 2))) (+ (* 9.0 (/ 1 x)) (* 48.0 (/ 1 (pow x 3)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013044811
150014483

prune711.0ms

Filtered
224 candidates to 149 candidates (66.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch88.0ms

Steps
ItersRangePoint
9
19555.519105776155
5849697155433.691
20005.70299342879
9
-1052513.600169936
-0.041603525395973645
-12471.666509296416

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04638
14638

end0.0ms

sample530.0ms

Algorithm
intervals
Results
174.0ms1700×body1280valid
103.0ms1238×body640valid
97.0ms4097×body80valid
42.0ms648×body320valid
13.0ms317×body160valid