Details

Time bar (total: 4.9s)

sample21.0ms

Algorithm
intervals
Results
7.0ms66×body1280valid
3.0ms37×body640valid
3.0ms132×body80valid
1.0ms11×body320valid
0.0ms10×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite124.0ms

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:
10.0ms
(/ x (+ x 1.0))
23.0ms
(/ (+ x 1.0) (- x 1.0))
86.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series185.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
34.0ms
(/ (+ x 1.0) (- x 1.0))
118.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0392760
11379726
25001716

prune197.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
2.2b
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
46×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
15×cbrt-div
9×distribute-lft-out
7×frac-sub
6×associate-/r/ add-log-exp
5×frac-times associate-*l/
4×pow1 add-exp-log add-cbrt-cube
3×flip3-+ pow1/3 associate-*r/ flip-+ div-inv
1×sub-neg flip3-- diff-log flip--
Counts
4 → 100
Calls
4 calls:
5.0ms
(cbrt (/ x (+ x 1.0)))
7.0ms
(cbrt (/ x (+ x 1.0)))
5.0ms
(cbrt (/ x (+ x 1.0)))
89.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(cbrt (/ x (+ x 1.0)))
143.0ms
(cbrt (/ x (+ x 1.0)))
142.0ms
(cbrt (/ x (+ x 1.0)))
131.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04171239
112411113
250011072

prune302.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
2.1b
(+ (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) 3))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
48×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
15×cbrt-div
10×distribute-lft-out
9×cube-div frac-add distribute-neg-frac
8×add-log-exp
6×frac-times associate-*r/ associate-*l/ associate-/r/
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 div-inv
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-log
Counts
4 → 104
Calls
4 calls:
5.0ms
(cbrt (/ x (+ x 1.0)))
5.0ms
(cbrt (/ x (+ x 1.0)))
5.0ms
(cbrt (/ x (+ x 1.0)))
13.0ms
(+ (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) 3))

series646.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (/ x (+ x 1.0)))
140.0ms
(cbrt (/ x (+ x 1.0)))
148.0ms
(cbrt (/ x (+ x 1.0)))
210.0ms
(+ (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) 3))

simplify70.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04851352
120291185
250031147

prune392.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
2.1b
(log (exp (+ (- 0 (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (cbrt (/ x (+ x 1.0))) 6))))
2.1b
(+ (- 0 (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (cbrt (/ x (+ x 1.0))) 6))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
36×cbrt-prod
24×times-frac
22×add-sqr-sqrt add-cube-cbrt
9×add-log-exp
8×distribute-lft-out
5×pow1 log-pow
4×add-exp-log log-prod exp-prod associate-/r/ add-cbrt-cube
3×flip3-+ flip-+
2×associate-+l- associate-+l+ cbrt-div pow1/3 sum-log div-inv
1×+-commutative sub-neg log-div exp-diff diff-log rem-log-exp exp-sum
Counts
4 → 88
Calls
4 calls:
5.0ms
(cbrt (/ x (+ x 1.0)))
5.0ms
(cbrt (/ x (+ x 1.0)))
209.0ms
(log (exp (+ (- 0 (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (cbrt (/ x (+ x 1.0))) 6))))
62.0ms
(+ (- 0 (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (cbrt (/ x (+ x 1.0))) 6))

series715.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (/ x (+ x 1.0)))
140.0ms
(cbrt (/ x (+ x 1.0)))
214.0ms
(log (exp (+ (- 0 (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (cbrt (/ x (+ x 1.0))) 6))))
211.0ms
(+ (- 0 (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (pow (cbrt (/ x (+ x 1.0))) 6))

simplify44.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03851183
112821065
250011040

prune379.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch96.0ms

Steps
ItersRangePoint
8
3974.013529084827
227507829.52260175
7255.026949556487
9
-28256763.0897718
-0.23317146499959118
-11437.80933531395

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05341
15641
25841
36141
46141

end0.0ms

sample544.0ms

Algorithm
intervals
Results
183.0ms1687×body1280valid
106.0ms1262×body640valid
89.0ms4127×body80valid
36.0ms601×body320valid
13.0ms323×body160valid