Details

Time bar (total: 5.3s)

sample23.0ms

Algorithm
intervals
Results
6.0ms41×body640valid
5.0ms54×body1280valid
3.0ms125×body80valid
1.0ms19×body320valid
1.0ms17×body160valid

simplify21.0ms

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: 30.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
5.2b
(- (/ 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))
40.0ms
(/ (+ x 1.0) (- x 1.0))
127.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0392760
11379726
25001716

prune220.0ms

Filtered
113 candidates to 76 candidates (67.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.2b
(/ 3.0 (pow x 3))
0.3b
(/ (- 1.0) (pow x 2))
8.2b
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite733.0ms

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:
85.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
4.0ms
(/ 3.0 (pow x 3))
6.0ms
(/ (- 1.0) (pow x 2))
628.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series167.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
36.0ms
(/ 3.0 (pow x 3))
30.0ms
(/ (- 1.0) (pow x 2))
33.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify99.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07381754
134481596
250011578

prune419.0ms

Filtered
246 candidates to 133 candidates (54.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
22.2b
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
43×*-un-lft-identity
42×cbrt-prod
21×times-frac
16×cbrt-div difference-of-squares
14×add-cube-cbrt
11×pow1 distribute-lft-out--
10×swap-sqr
9×flip3-- flip--
8×pow1/3 associate-*r* associate-*l*
6×add-exp-log add-log-exp
4×frac-times add-cbrt-cube unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus diff-log prod-exp *-commutative frac-sub cbrt-unprod distribute-lft-out
Counts
4 → 112
Calls
4 calls:
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
19.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
138.0ms
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(cbrt (- x 1.0))
99.0ms
(cbrt (- x 1.0))
119.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
173.0ms
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify64.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05401361
118011261
250021191

prune306.0ms

Filtered
124 candidates to 91 candidates (73.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(* (cbrt (- x 1.0)) (/ (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (+ x 1.0))))
12.2b
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (/ (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (+ x 1.0))))) (cbrt (- x 1.0))))
14.5b
(cbrt (- (* x x) (* 1.0 1.0)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
85×cbrt-prod
68×times-frac
66×*-un-lft-identity
55×associate-*r*
37×add-cube-cbrt
16×difference-of-squares
10×cbrt-div unswap-sqr
9×add-exp-log
8×associate-*l* distribute-lft-out
6×pow1 add-log-exp
5×flip3-- add-cbrt-cube flip-- distribute-lft-out--
2×frac-times pow1/3 associate-*l/ prod-exp associate-/r/ cbrt-unprod
1×cbrt-undiv sub-neg flip3-+ diff-log associate-*r/ div-exp pow-prod-down *-commutative frac-sub flip-+ div-inv
Counts
4 → 142
Calls
4 calls:
2.0ms
(cbrt (- x 1.0))
42.0ms
(* (cbrt (- x 1.0)) (/ (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (+ x 1.0))))
119.0ms
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (/ (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (+ x 1.0))))) (cbrt (- x 1.0))))
2.0ms
(cbrt (- (* x x) (* 1.0 1.0)))

series826.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(cbrt (- x 1.0))
170.0ms
(* (cbrt (- x 1.0)) (/ (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (+ x 1.0))))
356.0ms
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (/ (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (+ x 1.0))))) (cbrt (- x 1.0))))
199.0ms
(cbrt (- (* x x) (* 1.0 1.0)))

simplify128.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
09792276
143572193
250012143

prune483.0ms

Filtered
154 candidates to 117 candidates (76.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.7b

bsearch80.0ms

Steps
ItersRangePoint
9
6.164824567421913
3268324.1998729478
12427.129501950301
9
-3875183.9477288676
-0.008763241487176904
-12879.754469549705

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03518
13518

end0.0ms

sample530.0ms

Algorithm
intervals
Results
180.0ms1754×body1280valid
112.0ms1255×body640valid
90.0ms4094×body80valid
35.0ms589×body320valid
16.0ms308×body160valid