Details

Time bar (total: 18.6s)

sample118.0ms

Algorithm
intervals
Results
53.0ms63×body1280valid
26.0ms64×body640valid
12.0ms23×body2560valid
6.0ms24×body320valid
4.0ms69×body80valid
2.0ms13×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
079
1108
done108

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize16.0ms

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))

rewrite62.0ms

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:
41.0ms
(+ (sqrt (fma x x 1.0)) x)
14.0ms
(log (+ (sqrt (fma x x 1.0)) x))
3.0ms
(sqrt (fma x x 1.0))

series459.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(+ (sqrt (fma x x 1.0)) x)
285.0ms
(log (+ (sqrt (fma x x 1.0)) x))
96.0ms
(sqrt (fma x x 1.0))

simplify1.7s

Counts
61 → 61
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0125701
1283639
2768573
32364571
done5000556

prune258.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))))

series223.0ms

Counts
1 → 3
Calls
1 calls:
223.0ms
(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

prune96.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
888×times-frac
635×add-sqr-sqrt
633×*-un-lft-identity
604×add-cube-cbrt
520×prod-diff
131×unpow-prod-down cube-prod
55×div-inv
45×sqr-pow
43×cube-mult unpow3
15×add-log-exp
13×fma-neg
12×associate-/r* distribute-lft-out
10×add-exp-log difference-of-squares
6×log-prod add-cbrt-cube
5×pow1 fma-def sum-log distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×div-exp associate-/l*
2×associate-+l- log-div flip3-+ diff-log flip-+
1×cbrt-undiv +-commutative pow-to-exp sub-neg associate-+l+ flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow frac-sub flip--
Counts
4 → 671
Calls
4 calls:
1.9s
(+ (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x) x)
98.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
9.0ms
(/ 0.125 (pow x 3))
913.0ms
(log (+ (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x) x))

series523.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x) x)
151.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
49.0ms
(/ 0.125 (pow x 3))
229.0ms
(log (+ (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x) x))

simplify2.7s

Counts
683 → 683
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
077331849
1165725992
2362117014
done500017014

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

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)))

rewrite658.0ms

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:
16.0ms
(/ 0.125 (pow x 3))
14.0ms
(/ 0.0625 (pow x 5))
274.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
311.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ 0.125 (pow x 3))
85.0ms
(/ 0.0625 (pow x 5))
307.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
59.0ms
(- (/ 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
228029355
done50009035

prune817.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch95.0ms

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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03356
13756
done3756

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.6s2305×body1280valid
597.0ms1572×body640valid
444.0ms828×body2560valid
186.0ms771×body320valid
145.0ms2130×body80valid
46.0ms394×body160valid