Details

Time bar (total: 14.5s)

sample90.0ms

Algorithm
intervals
Results
40.0ms77×body1280valid
17.0ms46×body640valid
10.0ms23×body2560valid
6.0ms30×body320valid
4.0ms70×body80valid
1.0ms10×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
079
1108
done108

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.1b

localize7.0ms

Local error

Found 3 expressions with local error:

1.1b
(+ (sqrt (fma x x 1.0)) x)
2.2b
(log (+ (sqrt (fma x x 1.0)) x))
13.3b
(sqrt (fma x x 1.0))

rewrite24.0ms

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:
13.0ms
(+ (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))

series405.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(+ (sqrt (fma x x 1.0)) x)
233.0ms
(log (+ (sqrt (fma x x 1.0)) x))
85.0ms
(sqrt (fma x x 1.0))

simplify1.4s

Counts
61 → 61
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0125701
1283639
2768573
32364571
done5000556

prune272.0ms

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))))

series222.0ms

Counts
1 → 3
Calls
1 calls:
222.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify861.0ms

Counts
13 → 13
Iterations

Useful iterations: done (860.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune69.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
19.5b
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
19.5b
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
19.5b
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
16.0ms
(* (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
1.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
1.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
1.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

series2.8s

Counts
4 → 12
Calls
4 calls:
711.0ms
(* (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
532.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
566.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
942.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

simplify783.0ms

Counts
93 → 93
Iterations

Useful iterations: done (773.0ms)

IterNodesCost
01603869
14013618
214053305
done50002518

prune598.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (pow x 3))
11.4b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
18.5b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite499.0ms

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
(/ 0.0625 (pow x 5))
9.0ms
(/ 0.125 (pow x 3))
184.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
266.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 0.0625 (pow x 5))
44.0ms
(/ 0.125 (pow x 3))
228.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
63.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.5s

Counts
420 → 420
Iterations

Useful iterations: done (1.5s)

IterNodesCost
046617338
1101711893
228049355
done50008895

prune836.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch91.0ms

Steps
ItersRangePoint
10
8.937283511995443e-05
28405617999702.24
0.8904752561288425
9
-7465.585501010854
-0.008005822963963436
-1.0042810433581868

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03356
13756
done3756

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.1s2405×body1280valid
528.0ms1512×body640valid
326.0ms770×body2560valid
174.0ms803×body320valid
155.0ms2109×body80valid
54.0ms401×body160valid