Details

Time bar (total: 7.4s)

sample24.0ms

Algorithm
intervals
Results
7.0ms66×body640valid
4.0ms130×body80valid
3.0ms32×body320valid
2.0ms16×body1280valid
1.0ms12×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (- x 1.0))
1.5b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite384.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
14.0ms
(/ 1.0 (+ x 1.0))
64.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
12.0ms
(/ 1.0 (- x 1.0))
290.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ 1.0 (+ x 1.0))
36.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms
(/ 1.0 (- x 1.0))
193.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify48.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0496865
11681827
25001816

prune248.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

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))
17.2b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite374.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
15×cbrt-prod
13×add-sqr-sqrt
9×add-log-exp
7×add-cube-cbrt
6×cbrt-div times-frac distribute-lft-out--
5×distribute-lft-out
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×pow1/3 frac-add difference-of-squares
2×associate-+l+ sum-log
1×+-commutative associate-+l- sub-neg flip3-+ diff-log frac-sub flip-+
Counts
4 → 67
Calls
4 calls:
4.0ms
(cbrt (- x 1.0))
5.0ms
(cbrt (- x 1.0))
4.0ms
(cbrt (- x 1.0))
358.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(cbrt (- x 1.0))
96.0ms
(cbrt (- x 1.0))
90.0ms
(cbrt (- x 1.0))
219.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0420860
11281754
25002708

prune236.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
6.6b
(* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))
11.4b
(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (cbrt (- x 1.0))) (* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))) (* (* (+ x 1.0) x) (cbrt (- x 1.0))))
24.2b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (cbrt (- x 1.0))) (* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
132×associate-*l/
82×frac-times
80×cbrt-div frac-add
70×flip3-- flip--
42×associate-/l/
41×associate-*r/
39×flip3-+ flip-+
34×add-exp-log
28×add-cbrt-cube
16×associate-/r/
15×associate-*r*
14×prod-exp cbrt-unprod
11×add-sqr-sqrt *-un-lft-identity
9×pow1 add-cube-cbrt
7×cbrt-undiv div-exp
6×times-frac add-log-exp
5×cbrt-prod
3×pow-prod-down associate-/l*
2×div-inv
1×+-commutative frac-2neg pow1/3 associate-*l* clear-num associate-/r* sum-log *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 182
Calls
4 calls:
5.0ms
(cbrt (- x 1.0))
82.0ms
(* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))
109.0ms
(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (cbrt (- x 1.0))) (* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))) (* (* (+ x 1.0) x) (cbrt (- x 1.0))))
30.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (cbrt (- x 1.0))) (* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (- x 1.0))
253.0ms
(* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))
822.0ms
(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (cbrt (- x 1.0))) (* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))) (* (* (+ x 1.0) x) (cbrt (- x 1.0))))
414.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (cbrt (- x 1.0))) (* (* (+ x 1.0) x) (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
019435136
150014887

prune968.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
0.0b
(/ 1 (pow x 7))
0.0b
(/ 1 (pow x 5))
0.6b
(/ 1 (pow x 3))

rewrite904.0ms

Algorithm
rewrite-expression-head
Rules
90×*-un-lft-identity
87×times-frac
68×add-sqr-sqrt
66×add-cube-cbrt
36×unpow-prod-down
33×add-exp-log
26×associate-/r*
24×distribute-lft-out
18×div-exp
16×associate-*r* div-inv
12×cube-prod add-cbrt-cube sqr-pow
9×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
6×pow1
5×associate-*r/
4×cube-mult unpow3 frac-add add-log-exp
3×cbrt-undiv pow-flip frac-2neg associate-*l* clear-num inv-pow
2×flip3-+ flip-+
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 217
Calls
4 calls:
864.0ms
(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
9.0ms
(/ 1 (pow x 7))
9.0ms
(/ 1 (pow x 5))
14.0ms
(/ 1 (pow x 3))

series185.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
56.0ms
(/ 1 (pow x 7))
45.0ms
(/ 1 (pow x 5))
30.0ms
(/ 1 (pow x 3))

simplify89.0ms

Algorithm
egg-herbie
Counts
229 → 229
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
06521150
13943931
25001931

prune361.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 25.3b

bsearch112.0ms

Steps
ItersRangePoint
10
8.950540206577903e-05
66689094922.78456
98.64288158088615
10
-1500.694570789724
-6.177030851099824e-09
-93.41206114828162

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04223
14223

end0.0ms

sample618.0ms

Algorithm
intervals
Results
203.0ms1914×body640valid
122.0ms4184×body80valid
79.0ms949×body320valid
69.0ms529×body1280valid
22.0ms428×body160valid