Details

Time bar (total: 13.3s)

sample61.0ms

Algorithm
intervals
Results
25.0ms61×body1280valid
15.0ms65×body640valid
7.0ms28×body2560valid
3.0ms22×body320valid
2.0ms69×body80valid
1.0ms11×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
079
1108
done108

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.4b
(+ (sqrt (fma x x 1.0)) x)
2.7b
(log (+ (sqrt (fma x x 1.0)) x))
15.2b
(sqrt (fma x x 1.0))

rewrite11.0ms

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:
5.0ms
(+ (sqrt (fma x x 1.0)) x)
4.0ms
(log (+ (sqrt (fma x x 1.0)) x))
1.0ms
(sqrt (fma x x 1.0))

series318.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(+ (sqrt (fma x x 1.0)) x)
191.0ms
(log (+ (sqrt (fma x x 1.0)) x))
57.0ms
(sqrt (fma x x 1.0))

simplify1.1s

Counts
61 → 61
Iterations

Useful iterations: 3 (410.0ms)

IterNodesCost
0125701
1283639
2761573
32506571
done5000571

prune181.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

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))))

series155.0ms

Counts
1 → 3
Calls
1 calls:
155.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify634.0ms

Counts
13 → 13
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
025295
151295
2168259
3864256
done5001256

prune39.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.5b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.3b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite846.0ms

Algorithm
rewrite-expression-head
Rules
1674×add-sqr-sqrt
1602×times-frac
1026×*-un-lft-identity
895×prod-diff
848×add-cube-cbrt
522×associate--l+
330×unpow-prod-down
268×difference-of-squares
181×cube-prod
146×sqr-pow
70×div-inv
62×distribute-lft-out--
43×cube-mult unpow3
19×associate-/r*
15×add-exp-log fma-neg
10×log-prod
9×add-log-exp
8×frac-sub add-cbrt-cube
6×div-exp associate-/l*
5×pow1 log-div
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp clear-num
1×associate--l- rem-log-exp log-pow
Counts
4 → 1078
Calls
4 calls:
4.0ms
(/ 0.0625 (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
259.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
463.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 0.0625 (pow x 5))
44.0ms
(/ 0.125 (pow x 3))
189.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
63.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify2.2s

Counts
1090 → 1090
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
081244329
1179339950
2478830323
done500030323

prune2.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

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))
8.5b
(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite115.0ms

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:
51.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
4.0ms
(/ 0.125 (pow x 3))
1.0ms
(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series277.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
35.0ms
(/ 0.125 (pow x 3))
156.0ms
(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify1.7s

Counts
650 → 650
Iterations

Useful iterations: done (1.6s)

IterNodesCost
074231264
1161725431
2374816537
done500014860

prune451.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.6b

bsearch79.0ms

Steps
ItersRangePoint
9
0.00016167321766412214
1766.3470775505596
0.8894030106629419
10
-3752817.331716861
-5.670122129476186e-07
-1.0108746280769982

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13455
done3455

end0.0ms

sample1.8s

Algorithm
intervals
Results
919.0ms2299×body1280valid
372.0ms1555×body640valid
220.0ms822×body2560valid
106.0ms804×body320valid
70.0ms2139×body80valid
29.0ms381×body160valid