Details

Time bar (total: 4.5s)

sample21.0ms

Algorithm
intervals
Results
7.0ms59×body1280valid
3.0ms38×body640valid
3.0ms131×body80valid
1.0ms19×body320valid
0.0ms9×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.1b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
2.1b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
40×times-frac
35×add-sqr-sqrt
18×distribute-lft-out--
14×distribute-lft-out
13×add-cube-cbrt
9×difference-of-squares
5×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-+ div-inv
Counts
2 → 71
Calls
2 calls:
8.0ms
(/ (+ x 1.0) (- x 1.0))
33.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series167.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (+ x 1.0) (- x 1.0))
127.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify151.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0317591
11003565
24508559
35003559

prune140.0ms

Filtered
77 candidates to 50 candidates (64.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New73477
Fresh000
Picked101
Done000
Total74478

Merged error: 0.1b

Counts
78 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 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)))))
0.0b
(pow (/ x (+ x 1.0)) 3)
0.1b
(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.0b
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
1102×*-un-lft-identity
735×times-frac
560×add-sqr-sqrt
344×unpow-prod-down cube-prod
273×distribute-lft-out--
188×difference-of-squares
176×distribute-lft-out
124×add-cube-cbrt
77×associate-/l*
62×sqr-pow
31×associate-/r/
27×frac-add
16×frac-times associate-*r/
12×add-exp-log add-cbrt-cube
10×associate-*l/
9×flip3-+ flip-+
6×pow1 cube-div pow-unpow add-log-exp
5×difference-cubes div-inv
4×flip3-- pow-exp flip-- rem-cube-cbrt
3×cbrt-undiv div-exp associate-/r* associate-/l/
2×cube-mult pow-to-exp pow-pow unpow3 frac-sub
1×sub-neg frac-2neg diff-log div-sub clear-num
Counts
4 → 565
Calls
4 calls:
154.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 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)))))
7.0ms
(pow (/ x (+ x 1.0)) 3)
10.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
101.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series979.0ms

Counts
4 → 12
Calls
4 calls:
566.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 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)))))
57.0ms
(pow (/ x (+ x 1.0)) 3)
59.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
297.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify193.0ms

Algorithm
egg-herbie
Counts
577 → 577
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0167717362
1500117123

prune740.0ms

Filtered
577 candidates to 203 candidates (35.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New5761577
Fresh033
Picked011
Done000
Total5765581

Merged error: 0.1b

Counts
581 → 5

localize10.0ms

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)))
18.3b
(- (/ x (+ x 1.0)) (/ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (- x 1.0) (cbrt (+ x 1.0)))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
34×cbrt-prod *-un-lft-identity
16×cbrt-div
14×add-cube-cbrt times-frac
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out difference-of-squares
7×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 flip3-- pow-plus diff-log prod-exp *-commutative frac-sub flip-- cbrt-unprod distribute-lft-out--
Counts
4 → 103
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
48.0ms
(- (/ x (+ x 1.0)) (/ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (- x 1.0) (cbrt (+ x 1.0)))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))
102.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
132.0ms
(- (/ x (+ x 1.0)) (/ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (- x 1.0) (cbrt (+ x 1.0)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04781211
116061142
250021081

prune231.0ms

Filtered
115 candidates to 80 candidates (69.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1150115
Fresh033
Picked011
Done011
Total1155120

Merged error: 0.1b

Counts
120 → 5

localize5.0ms

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)))

rewrite11.0ms

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:
5.0ms
(+ (* x (+ 3.0 (* x 1.0))) 1.0)
5.0ms
(* x (+ 3.0 (* x 1.0)))

series87.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(+ (* x (+ 3.0 (* x 1.0))) 1.0)
66.0ms
(* x (+ 3.0 (* x 1.0)))

simplify35.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0209215
1933199
25002199

prune51.0ms

Filtered
41 candidates to 28 candidates (68.3%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New41041
Fresh022
Picked011
Done022
Total41546

Merged error: 0.1b

Counts
46 → 5

regimes35.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.0b

bsearch89.0ms

Steps
ItersRangePoint
9
0.0002199982819353488
137964.03928948785
9800.367801442988
9
-30563.43924112807
-0.41295360884021565
-15302.050174017617

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04634
14634

end0.0ms

sample552.0ms

Algorithm
intervals
Results
193.0ms1705×body1280valid
106.0ms1231×body640valid
99.0ms4133×body80valid
41.0ms625×body320valid
16.0ms306×body160valid