Details

Time bar (total: 14.6s)

sample114.0ms

Algorithm
intervals
Results
48.0ms72×body1280valid
30.0ms54×body640valid
10.0ms17×body2560valid
6.0ms27×body320valid
4.0ms76×body80valid
2.0ms10×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
1108
done108

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ (sqrt (fma x x 1.0)) x)
2.4b
(log (+ (sqrt (fma x x 1.0)) x))
13.8b
(sqrt (fma x x 1.0))

rewrite21.0ms

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:
10.0ms
(+ (sqrt (fma x x 1.0)) x)
7.0ms
(log (+ (sqrt (fma x x 1.0)) x))
2.0ms
(sqrt (fma x x 1.0))

series407.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(+ (sqrt (fma x x 1.0)) x)
247.0ms
(log (+ (sqrt (fma x x 1.0)) x))
69.0ms
(sqrt (fma x x 1.0))

simplify1.9s

Counts
61 → 61
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0125701
1283639
2768573
32364571
done5000556

prune232.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))))

series211.0ms

Counts
1 → 3
Calls
1 calls:
211.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify928.0ms

Counts
13 → 13
Iterations

Useful iterations: done (927.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune69.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.4b
(/ 0.125 (pow x 3))
8.0b
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
888×times-frac
633×add-sqr-sqrt
608×*-un-lft-identity
602×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×difference-of-squares
9×add-exp-log
5×add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u log-prod div-exp log1p-expm1-u 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--
Counts
3 → 641
Calls
3 calls:
110.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
20.0ms
(/ 0.125 (pow x 3))
2.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series424.0ms

Counts
3 → 9
Calls
3 calls:
138.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
51.0ms
(/ 0.125 (pow x 3))
235.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify2.2s

Counts
650 → 650
Iterations

Useful iterations: done (2.2s)

IterNodesCost
074231264
1157025431
2326916537
done500015817

prune738.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (pow x 3))
9.0b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
19.9b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite505.0ms

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:
12.0ms
(/ 0.0625 (pow x 5))
9.0ms
(/ 0.125 (pow x 3))
225.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
215.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 0.0625 (pow x 5))
49.0ms
(/ 0.125 (pow x 3))
243.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
82.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.7s

Counts
420 → 420
Iterations

Useful iterations: done (1.6s)

IterNodesCost
046617338
1101711893
228049355
done50008895

prune798.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.4b

bsearch116.0ms

Steps
ItersRangePoint
9
0.21963308938311268
137362616.0762091
0.8931378377170596
11
-2445851338.3862987
-4.2674702477225e-16
-1.0064602849522295

simplify17.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13555
done3555

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.9s2366×body1280valid
552.0ms1566×body640valid
470.0ms762×body2560valid
193.0ms2126×body80valid
164.0ms757×body320valid
52.0ms423×body160valid