Details

Time bar (total: 20.8s)

sample24.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
057
176
done76

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize10.0ms

Local error

Found 1 expressions with local error:

15.3b
(/ x (fma x x 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
10.0ms
(/ x (fma x x 1.0))

series130.0ms

Counts
1 → 3
Calls
1 calls:
130.0ms
(/ x (fma x x 1.0))

simplify2.3s

Counts
32 → 32
Iterations

Useful iterations: 2 (124.0ms)

IterNodesCost
068377
1140362
2492332
32678332
done5000332

prune189.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
0.0b
(/ x (sqrt (fma x x 1.0)))
15.2b
(sqrt (fma x x 1.0))
15.2b
(sqrt (fma x x 1.0))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×add-cube-cbrt *-un-lft-identity
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 248
Calls
4 calls:
32.0ms
(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
17.0ms
(/ x (sqrt (fma x x 1.0)))
3.0ms
(sqrt (fma x x 1.0))
3.0ms
(sqrt (fma x x 1.0))

series532.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
222.0ms
(/ x (sqrt (fma x x 1.0)))
84.0ms
(sqrt (fma x x 1.0))
93.0ms
(sqrt (fma x x 1.0))

simplify2.2s

Counts
260 → 260
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03045985
17195190
230584876
done50014661

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 1 expressions with local error:

19.7b
(- (+ x (pow x 5)) (pow x 3))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
48×prod-diff
33×add-sqr-sqrt
26×add-cube-cbrt
14×distribute-lft-out
13×unpow-prod-down cube-prod
6×add-log-exp
5×sqr-pow
4×cube-mult fma-neg unpow3 difference-of-squares
2×diff-log distribute-lft-out--
1×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- associate--l+ sum-log add-cbrt-cube flip-- log1p-expm1-u
Counts
1 → 74
Calls
1 calls:
179.0ms
(- (+ x (pow x 5)) (pow x 3))

series80.0ms

Counts
1 → 3
Calls
1 calls:
80.0ms
(- (+ x (pow x 5)) (pow x 3))

simplify3.2s

Counts
77 → 77
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01202299
12961547
214451242
done5000970

prune206.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1 x) (/ 1.0 (pow x 3)))
0.1b
(/ 1.0 (pow x 5))
0.3b
(/ 1.0 (pow x 3))
18.7b
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
1773×times-frac
1273×add-sqr-sqrt
1222×*-un-lft-identity
1185×add-cube-cbrt
1040×prod-diff
522×associate-+l+
264×unpow-prod-down
252×cube-prod
112×div-inv
92×sqr-pow
82×cube-mult unpow3
30×difference-of-squares
21×fma-def
19×associate-/r*
14×add-exp-log
13×fma-neg
11×add-log-exp
9×distribute-lft-out--
8×add-cbrt-cube
6×div-exp associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out
3×frac-add
2×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log pow-exp clear-num sum-log frac-sub flip--
1×+-commutative associate-+l- flip3-+ flip-+
Counts
4 → 1245
Calls
4 calls:
138.0ms
(- (/ 1 x) (/ 1.0 (pow x 3)))
16.0ms
(/ 1.0 (pow x 5))
17.0ms
(/ 1.0 (pow x 3))
791.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (/ 1 x) (/ 1.0 (pow x 3)))
95.0ms
(/ 1.0 (pow x 5))
74.0ms
(/ 1.0 (pow x 3))
91.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

simplify1.7s

Counts
1257 → 1257
Iterations

Useful iterations: done (1.5s)

IterNodesCost
079751194
1186441009
done500132962

prune6.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes62.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch95.0ms

Steps
ItersRangePoint
10
2.8868360106527892e-08
453261925.93168354
742.6193916240435
6
-3.251690204975706e+154
-5.320162488446726e+153
-1.3440694370491086e+154

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02251
12837
done2837

end0.0ms

sample619.0ms

Algorithm
intervals
Results
406.0ms8000×body80valid