Details

Time bar (total: 15.1s)

sample124.0ms

Algorithm
intervals
Results
56.0ms63×body1280valid
29.0ms64×body640valid
12.0ms23×body2560valid
6.0ms24×body320valid
5.0ms69×body80valid
2.0ms13×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: 52.9b

localize21.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ (sqrt (fma x x 1.0)) x)
3.5b
(log (+ (sqrt (fma x x 1.0)) x))
13.1b
(sqrt (fma x x 1.0))

rewrite20.0ms

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)
8.0ms
(log (+ (sqrt (fma x x 1.0)) x))
2.0ms
(sqrt (fma x x 1.0))

series442.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(+ (sqrt (fma x x 1.0)) x)
271.0ms
(log (+ (sqrt (fma x x 1.0)) x))
81.0ms
(sqrt (fma x x 1.0))

simplify1.6s

Counts
61 → 61
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0125701
1283639
2768573
32364571
done5000556

prune212.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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:
0.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series243.0ms

Counts
1 → 3
Calls
1 calls:
243.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify1.0s

Counts
13 → 13
Iterations

Useful iterations: done (1.0s)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune51.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.2b
(/ 0.125 (pow x 3))
14.1b
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite162.0ms

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:
70.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
8.0ms
(/ 0.125 (pow x 3))
2.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series500.0ms

Counts
3 → 9
Calls
3 calls:
133.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
59.0ms
(/ 0.125 (pow x 3))
307.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify2.2s

Counts
650 → 650
Iterations

Useful iterations: done (2.1s)

IterNodesCost
074231264
1157025431
2326916537
done500015817

prune872.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.125 (pow x 3))
0.5b
(/ 0.0625 (pow x 5))
15.1b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
19.6b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite439.0ms

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:
8.0ms
(/ 0.125 (pow x 3))
7.0ms
(/ 0.0625 (pow x 5))
169.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
208.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series812.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ 0.125 (pow x 3))
68.0ms
(/ 0.0625 (pow x 5))
597.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
77.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.8s

Counts
420 → 420
Iterations

Useful iterations: done (1.8s)

IterNodesCost
046617338
1101711893
228029355
done50009035

prune690.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch113.0ms

Steps
ItersRangePoint
10
1.0194597579740466e-06
20796729.49276672
0.9017023301953626
8
-11.923248480236845
-0.0008047768791668974
-1.002814715336328

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13555
done3555

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.7s2305×body1280valid
623.0ms1572×body640valid
429.0ms828×body2560valid
412.0ms394×body160valid
206.0ms771×body320valid
120.0ms2130×body80valid