Details

Time bar (total: 6.6s)

sample26.0ms

Algorithm
intervals
Results
7.0ms130×body80valid
5.0ms53×body640valid
3.0ms40×body320valid
2.0ms19×body1280valid
1.0ms14×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: 11.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (- x 1.0))
2.6b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
707×*-un-lft-identity
691×times-frac
514×add-sqr-sqrt
482×add-cube-cbrt
468×prod-diff
236×associate-+l+
91×distribute-lft-out
64×div-inv
56×associate-/r/
28×flip3-+ flip-+
18×fma-neg
17×distribute-lft-out--
12×difference-of-squares
10×fma-def add-log-exp
5×add-exp-log associate-/r* add-cbrt-cube
3×pow1 expm1-log1p-u flip3-- frac-add flip-- log1p-expm1-u associate-/l*
2×sub-neg diff-log sum-log frac-sub
1×cbrt-undiv +-commutative associate-+l- frac-2neg div-exp clear-num
Counts
3 → 583
Calls
3 calls:
79.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
11.0ms
(/ 1.0 (- x 1.0))
339.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series261.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms
(/ 1.0 (- x 1.0))
195.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify151.0ms

Algorithm
egg-herbie
Counts
592 → 592
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
0110810776
134078118
250017502

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
0.1b
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
10.7b
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
18.8b
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
61×*-un-lft-identity
27×times-frac
21×distribute-lft-out
19×add-sqr-sqrt add-cube-cbrt
16×unpow-prod-down cube-prod
11×add-log-exp
9×associate-/r*
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u associate-+r+ fma-def sum-cubes log1p-expm1-u
3×flip3-+ sum-log flip-+ fma-udef associate-/l*
2×+-commutative associate-/r/
1×cbrt-undiv associate-+r- sub-neg associate-+l+ frac-2neg diff-log div-exp prod-diff clear-num div-inv
Counts
4 → 103
Calls
4 calls:
18.0ms
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
38.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
6.0ms
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
0.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
65.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
263.0ms
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
56.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0)))

simplify62.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05131187
122061075
250011037

prune404.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

18.8b
(fma (* (/ (sqrt 1.0) (* (cbrt (+ (pow x 3) (pow 1.0 3))) (cbrt (+ (pow x 3) (pow 1.0 3))))) (/ (sqrt 1.0) (cbrt (+ (pow x 3) (pow 1.0 3))))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0)))
19.0b
(cbrt (+ (pow x 3) (pow 1.0 3)))
19.0b
(cbrt (+ (pow x 3) (pow 1.0 3)))
19.0b
(cbrt (+ (pow x 3) (pow 1.0 3)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
27×cbrt-prod
15×distribute-lft-out
12×unpow-prod-down cube-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 sum-cubes flip-+
1×fma-udef
Counts
4 → 73
Calls
4 calls:
0.0ms
(fma (* (/ (sqrt 1.0) (* (cbrt (+ (pow x 3) (pow 1.0 3))) (cbrt (+ (pow x 3) (pow 1.0 3))))) (/ (sqrt 1.0) (cbrt (+ (pow x 3) (pow 1.0 3))))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0)))
20.0ms
(cbrt (+ (pow x 3) (pow 1.0 3)))
16.0ms
(cbrt (+ (pow x 3) (pow 1.0 3)))
17.0ms
(cbrt (+ (pow x 3) (pow 1.0 3)))

series1.2s

Counts
4 → 12
Calls
4 calls:
113.0ms
(fma (* (/ (sqrt 1.0) (* (cbrt (+ (pow x 3) (pow 1.0 3))) (cbrt (+ (pow x 3) (pow 1.0 3))))) (/ (sqrt 1.0) (cbrt (+ (pow x 3) (pow 1.0 3))))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 1 x) 2.0)))
360.0ms
(cbrt (+ (pow x 3) (pow 1.0 3)))
362.0ms
(cbrt (+ (pow x 3) (pow 1.0 3)))
353.0ms
(cbrt (+ (pow x 3) (pow 1.0 3)))

simplify43.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03081012
11221902
25002877

prune439.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3))))
0.1b
(/ 1 (pow x 5))
0.2b
(/ 1 (pow x 3))
0.2b
(/ 1 (pow x 7))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
61×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
31×add-exp-log
26×associate-/r*
18×div-exp
12×cube-prod sqr-pow
10×add-cbrt-cube
9×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
1×fma-udef
Counts
4 → 195
Calls
4 calls:
0.0ms
(fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3))))
8.0ms
(/ 1 (pow x 5))
9.0ms
(/ 1 (pow x 3))
12.0ms
(/ 1 (pow x 7))

series238.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3))))
43.0ms
(/ 1 (pow x 5))
29.0ms
(/ 1 (pow x 3))
54.0ms
(/ 1 (pow x 7))

simplify47.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0430931
12266731
25001726

prune334.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.9b

bsearch141.0ms

Steps
ItersRangePoint
10
26.826342714152005
1.350953981158519e+19
109.74138080467836
8
-4116.604674393256
-5.56536991933885
-86.60693860825424

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06443
16743
26743

end0.0ms

sample632.0ms

Algorithm
intervals
Results
208.0ms1887×body640valid
122.0ms4130×body80valid
78.0ms574×body1280valid
77.0ms930×body320valid
26.0ms480×body160valid