Details

Time bar (total: 17.2s)

sample42.0ms

Algorithm
intervals
Results
13.0ms45×body1280valid
9.0ms44×body640valid
8.0ms149×body80valid
2.0ms13×body320valid
0.0ms5×body160valid

simplify186.0ms

Counts
1 → 1
Iterations
IterNodes
done168
15168
14165
13136
12114
1199
1089
969
853
742
632
526
423
322
219
115
07

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
1.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
1284×*-un-lft-identity
984×times-frac
841×add-sqr-sqrt
612×prod-diff
521×add-cube-cbrt
251×distribute-lft-out
158×difference-of-squares
110×associate-/r/
90×distribute-lft-out--
77×difference-of-sqr-1
55×div-inv
37×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 753
Calls
3 calls:
23.0ms
(/ x (+ x 1))
51.0ms
(/ (+ x 1) (- x 1))
188.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series171.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ x (+ x 1))
30.0ms
(/ (+ x 1) (- x 1))
106.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.9s

Counts
762 → 762
Iterations
IterNodes
done5002
23248
11369
0584

prune2.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (/ (+ x 1) (- x 1)))
0.0b
(cbrt (/ (+ x 1) (- x 1)))
2.7b
(fma (- (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))))
25.5b
(fma x (/ 1 (+ x 1)) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
80×*-un-lft-identity
68×cbrt-prod
60×add-sqr-sqrt
56×times-frac
28×add-cube-cbrt
16×difference-of-squares
14×distribute-lft-out
8×difference-of-sqr-1 distribute-lft-out--
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-div flip3-- pow1/3 fma-udef div-inv flip--
Counts
4 → 114
Calls
4 calls:
11.0ms
(cbrt (/ (+ x 1) (- x 1)))
17.0ms
(cbrt (/ (+ x 1) (- x 1)))
1.0ms
(fma (- (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))))
1.0ms
(fma x (/ 1 (+ x 1)) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))

series821.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(cbrt (/ (+ x 1) (- x 1)))
92.0ms
(cbrt (/ (+ x 1) (- x 1)))
515.0ms
(fma (- (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))))
114.0ms
(fma x (/ 1 (+ x 1)) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))

simplify1.9s

Counts
126 → 126
Iterations
IterNodes
done5000
33720
21034
1383
0192

prune752.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ x (+ x 1)) (- (fma 2 (+ x (* x x)) 1)))
0.0b
(/ x (+ x 1))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
231×*-un-lft-identity
180×prod-diff
158×add-sqr-sqrt
153×add-cube-cbrt
145×times-frac
55×distribute-rgt-neg-in
54×distribute-lft-neg-in
37×distribute-lft-out
24×associate-/r/
18×neg-mul-1 fma-neg
12×flip3-+ flip-+ div-inv
6×add-log-exp
4×associate-/r* add-cbrt-cube add-exp-log
3×associate-/l*
2×expm1-log1p-u pow1 diff-log insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
1×neg-sub0 cbrt-undiv distribute-neg-in clear-num sub-neg frac-2neg flip3-- div-exp neg-log fma-udef flip-- associate--r+ associate--r-
Counts
2 → 256
Calls
2 calls:
104.0ms
(- (/ x (+ x 1)) (- (fma 2 (+ x (* x x)) 1)))
19.0ms
(/ x (+ x 1))

series103.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(- (/ x (+ x 1)) (- (fma 2 (+ x (* x x)) 1)))
42.0ms
(/ x (+ x 1))

simplify2.0s

Counts
262 → 262
Iterations
IterNodes
done5001
21580
1686
0294

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 (* x x)) (/ 3 x))
0.5b
(/ 1 (* x x))
0.5b
(/ 1 (* x x))
10.6b
(fma (/ 3 x) (/ 1 (* x x)) (+ (/ 1 (* x x)) (/ 3 x)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
20×pow1
14×*-un-lft-identity add-cbrt-cube
12×pow-flip
10×add-sqr-sqrt times-frac add-cube-cbrt
8×div-exp
7×fma-def
6×prod-exp associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u cbrt-undiv rec-exp 1-exp insert-posit16 log1p-expm1-u
2×pow2 clear-num associate-/r* frac-2neg pow-plus pow-prod-down pow-sqr pow-prod-up cbrt-unprod distribute-lft-out inv-pow
1×+-commutative sum-log flip3-+ distribute-rgt-out frac-add flip-+ fma-udef
Counts
4 → 106
Calls
4 calls:
46.0ms
(+ (/ 1 (* x x)) (/ 3 x))
32.0ms
(/ 1 (* x x))
24.0ms
(/ 1 (* x x))
1.0ms
(fma (/ 3 x) (/ 1 (* x x)) (+ (/ 1 (* x x)) (/ 3 x)))

series167.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (/ 1 (* x x)) (/ 3 x))
21.0ms
(/ 1 (* x x))
26.0ms
(/ 1 (* x x))
33.0ms
(fma (/ 3 x) (/ 1 (* x x)) (+ (/ 1 (* x x)) (/ 3 x)))

simplify1.9s

Counts
118 → 118
Iterations
IterNodes
done5000
21226
1281
099

prune323.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.0b

bsearch115.0ms

Steps
ItersRangePoint
10
1.508099977930646e-06
2590629949647.022
1.020834055947729
10
-26711381.42537418
-6.803810524357175e-07
-1.311384526318253

simplify10.0ms

Iterations
IterNodes
done38
238
134
023

end0.0ms

sample1.2s

Algorithm
intervals
Results
460.0ms1713×body1280valid
275.0ms1254×body640valid
243.0ms4072×body80valid
119.0ms639×body320valid
27.0ms322×body160valid