Details

Time bar (total: 18.8s)

sample54.0ms

Algorithm
intervals
Results
17.0ms66×body640valid
9.0ms129×body80valid
6.0ms32×body320valid
6.0ms17×body1280valid
2.0ms12×body160valid

simplify150.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11815
23115
34115
45015
55515
66415
78215
89915
910915
done10915

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.4b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite745.0ms

Algorithm
rewrite-expression-head
Rules
706×*-un-lft-identity
688×times-frac
505×add-sqr-sqrt
481×add-cube-cbrt
468×prod-diff
236×associate-+l+
95×distribute-lft-out
64×div-inv
56×associate-/r/
29×flip3-+ flip-+
18×fma-neg
13×distribute-lft-out--
10×fma-def add-log-exp
8×difference-of-squares
5×add-exp-log add-cbrt-cube
4×associate-/r*
3×pow1 expm1-log1p-u frac-add log1p-expm1-u associate-/l*
2×sub-neg flip3-- diff-log sum-log frac-sub flip--
1×cbrt-undiv +-commutative associate-+l- frac-2neg div-exp clear-num
Counts
3 → 579
Calls
3 calls:
20.0ms
(/ 1.0 (+ x 1.0))
112.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
543.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series389.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(/ 1.0 (+ x 1.0))
55.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
291.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify3.1s

Counts
588 → 588
Iterations

Useful iterations: done (3.0s)

IterNodesCost
045319391
1105116939
2257512510
done50009748

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ 1.0 (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
18.9b
(+ (fma (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0))) (- (* (/ 1 x) 2.0))) (+ 0 (/ 1.0 (- x 1.0))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
52×*-un-lft-identity
36×times-frac
29×add-sqr-sqrt add-cube-cbrt
12×distribute-lft-out
9×add-log-exp
6×associate-/r/
4×pow1 add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×cbrt-div fma-def pow1/3 sum-log div-inv
1×+-commutative associate-+l+ associate-+r+ fma-udef
Counts
4 → 108
Calls
4 calls:
6.0ms
(cbrt (/ 1.0 (+ x 1.0)))
10.0ms
(cbrt (/ 1.0 (+ x 1.0)))
10.0ms
(cbrt (/ 1.0 (+ x 1.0)))
82.0ms
(+ (fma (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0))) (- (* (/ 1 x) 2.0))) (+ 0 (/ 1.0 (- x 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
214.0ms
(cbrt (/ 1.0 (+ x 1.0)))
253.0ms
(cbrt (/ 1.0 (+ x 1.0)))
210.0ms
(cbrt (/ 1.0 (+ x 1.0)))
412.0ms
(+ (fma (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0))) (- (* (/ 1 x) 2.0))) (+ 0 (/ 1.0 (- x 1.0))))

simplify1.3s

Counts
120 → 120
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02012448
14842289
214591804
done50011647

prune619.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3)))
0.1b
(/ 2.0 (pow x 5))
0.4b
(/ 2.0 (pow x 7))
0.4b
(/ 2.0 (pow x 3))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
105×times-frac
85×*-un-lft-identity
77×add-sqr-sqrt add-cube-cbrt
45×unpow-prod-down
26×associate-/r*
25×fma-def
19×add-exp-log
15×sqr-pow
12×cube-prod
10×add-cbrt-cube
9×div-exp associate-/l*
6×div-inv add-log-exp
5×distribute-lft-out
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×+-commutative flip3-+ frac-add sum-log flip-+
Counts
4 → 205
Calls
4 calls:
125.0ms
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3)))
13.0ms
(/ 2.0 (pow x 5))
13.0ms
(/ 2.0 (pow x 7))
15.0ms
(/ 2.0 (pow x 3))

series457.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3)))
77.0ms
(/ 2.0 (pow x 5))
90.0ms
(/ 2.0 (pow x 7))
74.0ms
(/ 2.0 (pow x 3))

simplify1.2s

Counts
217 → 217
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02632139
14981870
213721802
done50001801

prune919.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 2.0 (* x x)) x)
0.1b
(/ 2.0 (pow x 5))
0.4b
(/ 2.0 (pow x 7))
0.7b
(/ 2.0 (* x x))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
28×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube
18×associate-/r*
16×associate-/l*
13×div-exp
9×cbrt-undiv
8×div-inv sqr-pow
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp prod-exp cbrt-unprod
1×associate-/l/
Counts
4 → 167
Calls
4 calls:
38.0ms
(/ (/ 2.0 (* x x)) x)
10.0ms
(/ 2.0 (pow x 5))
8.0ms
(/ 2.0 (pow x 7))
8.0ms
(/ 2.0 (* x x))

series248.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (/ 2.0 (* x x)) x)
72.0ms
(/ 2.0 (pow x 5))
77.0ms
(/ 2.0 (pow x 7))
37.0ms
(/ 2.0 (* x x))

simplify3.7s

Counts
179 → 179
Iterations

Useful iterations: 2 (358.0ms)

IterNodesCost
02561876
14891703
213091597
345521597
done50001597

prune704.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes71.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 26.1b

bsearch207.0ms

Steps
ItersRangePoint
9
0.21963308938311268
137362616.0762091
98.00054950125781
11
-2445851338.3862987
-4.2674702477225e-16
-101.77579100982673

simplify38.0ms

Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03480
14860
25359
done5359

end0.0ms

sample1.8s

Algorithm
intervals
Results
547.0ms570×body1280valid
508.0ms1861×body640valid
253.0ms4132×body80valid
200.0ms961×body320valid
105.0ms480×body160valid