Details

Time bar (total: 4.1s)

sample20.0ms

Algorithm
intervals
Results
7.0ms66×body1280valid
3.0ms128×body80valid
3.0ms31×body640valid
1.0ms19×body320valid
1.0ms12×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
3.2b
(- (/ 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)))

series213.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(/ x (+ x 1.0))
38.0ms
(/ (+ x 1.0) (- x 1.0))
135.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0392760
11379726
25001716

prune212.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
10.5b
(- (* (/ (* (cbrt x) (cbrt x)) (sqrt (+ x 1.0))) (/ (cbrt x) (sqrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3 frac-sub
1×frac-times sub-neg flip3-- diff-log associate-*r/ associate-*l/ flip--
Counts
4 → 48
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
1.0ms
(cbrt x)
32.0ms
(- (* (/ (* (cbrt x) (cbrt x)) (sqrt (+ x 1.0))) (/ (cbrt x) (sqrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series707.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt x)
183.0ms
(cbrt x)
191.0ms
(cbrt x)
149.0ms
(- (* (/ (* (cbrt x) (cbrt x)) (sqrt (+ x 1.0))) (/ (cbrt x) (sqrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify115.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0222489
1788433
24027402
35002402

prune173.0ms

Pruning

4 alts after pruning (3 fresh and 1 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))
0.1b
(/ 3.0 (pow x 3))
0.3b
(/ (- 1.0) (pow x 2))
7.6b
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite899.0ms

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:
79.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
4.0ms
(/ 3.0 (pow x 3))
6.0ms
(/ (- 1.0) (pow x 2))
797.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series166.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
39.0ms
(/ 3.0 (pow x 3))
25.0ms
(/ (- 1.0) (pow x 2))
32.0ms
(- (- (/ (- 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 (75.0ms)

IterNodesCost
07411813
135251605
250011602

prune399.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x (+ 3.0 (* x 1.0))) 1.0)
0.0b
(* x (+ 3.0 (* x 1.0)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×distribute-rgt-in associate-+l+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
4.0ms
(+ (* x (+ 3.0 (* x 1.0))) 1.0)
7.0ms
(* x (+ 3.0 (* x 1.0)))

series87.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(+ (* x (+ 3.0 (* x 1.0))) 1.0)
65.0ms
(* x (+ 3.0 (* x 1.0)))

simplify37.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0209215
1933199
25002199

prune65.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.0b

bsearch83.0ms

Steps
ItersRangePoint
9
251.47950061764826
104248118811.33417
11941.154113525668
10
-578421416.8415484
-0.03925098124715615
-0.9978230783997364

simplify7.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03623
13623

end0.0ms

sample530.0ms

Algorithm
intervals
Results
191.0ms1767×body1280valid
100.0ms1219×body640valid
93.0ms4085×body80valid
38.0ms610×body320valid
13.0ms319×body160valid