Details

Time bar (total: 14.2s)

sample87.0ms

Algorithm
intervals
Results
37.0ms62×body1280valid
19.0ms60×body640valid
10.0ms24×body2560valid
4.0ms25×body320valid
3.0ms72×body80valid
2.0ms13×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
079
1108
done108

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ (sqrt (fma x x 1.0)) x)
3.8b
(log (+ (sqrt (fma x x 1.0)) x))
12.8b
(sqrt (fma x x 1.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×fma-def sqrt-prod
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 52
Calls
3 calls:
31.0ms
(+ (sqrt (fma x x 1.0)) x)
7.0ms
(log (+ (sqrt (fma x x 1.0)) x))
3.0ms
(sqrt (fma x x 1.0))

series805.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(+ (sqrt (fma x x 1.0)) x)
640.0ms
(log (+ (sqrt (fma x x 1.0)) x))
83.0ms
(sqrt (fma x x 1.0))

simplify1.6s

Counts
61 → 61
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0125701
1283639
2768573
32364571
done5000556

prune307.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series225.0ms

Counts
1 → 3
Calls
1 calls:
225.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify840.0ms

Counts
13 → 13
Iterations

Useful iterations: done (839.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune89.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b
(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
0.1b
(/ 0.125 (pow x 3))
11.2b
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
888×times-frac
634×add-sqr-sqrt
609×*-un-lft-identity
603×add-cube-cbrt
520×prod-diff
131×unpow-prod-down cube-prod
55×div-inv
45×sqr-pow
43×cube-mult unpow3
13×fma-neg
12×associate-/r*
10×add-exp-log difference-of-squares
6×add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×log-prod div-exp associate-/l*
2×distribute-lft-out--
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log rem-log-exp pow-exp clear-num log-pow frac-sub flip-- fma-udef
Counts
4 → 651
Calls
4 calls:
71.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0ms
(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
8.0ms
(/ 0.125 (pow x 3))
1.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series410.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
52.0ms
(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
52.0ms
(/ 0.125 (pow x 3))
185.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify2.1s

Counts
663 → 663
Iterations

Useful iterations: done (2.1s)

IterNodesCost
075031474
1158325632
2330816708
done500115988

prune704.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.1b
(/ 0.125 (pow x 3))
12.9b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
18.7b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite538.0ms

Algorithm
rewrite-expression-head
Rules
480×*-un-lft-identity
367×times-frac
244×add-sqr-sqrt
218×add-cube-cbrt
200×prod-diff
84×distribute-lft-out
80×unpow-prod-down
68×cube-prod
40×fma-neg
28×sqr-pow
22×cube-mult unpow3
19×associate-/r*
15×add-exp-log
11×log-prod
10×difference-of-squares
9×add-log-exp
8×add-cbrt-cube div-inv
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 408
Calls
4 calls:
15.0ms
(/ 0.0625 (pow x 5))
17.0ms
(/ 0.125 (pow x 3))
241.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
214.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 0.0625 (pow x 5))
58.0ms
(/ 0.125 (pow x 3))
290.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
84.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.6s

Counts
420 → 420
Iterations

Useful iterations: done (1.6s)

IterNodesCost
046617338
1101711893
228049355
done50008895

prune690.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch127.0ms

Steps
ItersRangePoint
10
1.5244367550608482e-07
9556.682540875734
0.8981400227354687
9
-1501.2167507114543
-0.006495210018506858
-1.017049376431383

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13555
done3555

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.6s2224×body1280valid
584.0ms1649×body640valid
356.0ms836×body2560valid
187.0ms2075×body80valid
158.0ms820×body320valid
43.0ms396×body160valid