Details

Time bar (total: 23.5s)

sample52.0ms

Algorithm
intervals
Results
19.0ms55×body1280valid
10.0ms140×body80valid
9.0ms32×body640valid
3.0ms16×body320valid
2.0ms13×body160valid

simplify168.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
3.7b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite162.0ms

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:
16.0ms
(/ x (+ x 1))
31.0ms
(/ (+ x 1) (- x 1))
64.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series214.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ x (+ x 1))
40.0ms
(/ (+ x 1) (- x 1))
138.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify3.2s

Counts
762 → 762
Iterations
IterNodes
done5002
23248
11369
0584

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
3.7b
(+ (/ x (+ x 1)) (- (/ (+ x 1) (- x 1))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
68×times-frac
53×add-sqr-sqrt
33×add-cube-cbrt distribute-lft-out
18×fma-def
11×associate-/r*
10×difference-of-squares
9×distribute-rgt-neg-in distribute-lft-out--
7×add-cbrt-cube add-exp-log associate-/l* add-log-exp
6×associate-/r/
5×difference-of-sqr-1
4×flip3-+ flip-+
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u div-inv
2×cbrt-undiv clear-num sum-log frac-2neg div-exp associate-/l/
1×neg-sub0 +-commutative associate-+r- flip3-- unsub-neg neg-log frac-add flip-- distribute-neg-frac
Counts
3 → 141
Calls
3 calls:
13.0ms
(/ x (+ x 1))
29.0ms
(/ (+ x 1) (- x 1))
92.0ms
(+ (/ x (+ x 1)) (- (/ (+ x 1) (- x 1))))

series183.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ x (+ x 1))
34.0ms
(/ (+ x 1) (- x 1))
113.0ms
(+ (/ x (+ x 1)) (- (/ (+ x 1) (- x 1))))

simplify2.4s

Counts
150 → 150
Iterations
IterNodes
done5000
34391
21356
1442
0185

prune397.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))
0.0b
(/ (+ 1 x) (- x 1))
3.7b
(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
3.7b
(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
3683×*-un-lft-identity
2836×times-frac
2412×add-sqr-sqrt
1836×prod-diff
1492×add-cube-cbrt
1228×exp-sum
719×distribute-lft-out
617×log-prod
454×difference-of-squares
316×associate-/r/
260×distribute-lft-out--
221×difference-of-sqr-1
158×div-inv
104×flip3-+ flip-+
56×flip3-- flip--
32×exp-prod
18×fma-neg
17×log-pow
9×add-log-exp
7×associate-/r*
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×sub-neg
2×exp-diff diff-log rem-exp-log associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg div-exp rem-log-exp frac-sub
Counts
4 → 2006
Calls
4 calls:
182.0ms
(exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))
25.0ms
(/ (+ 1 x) (- x 1))
175.0ms
(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
77.0ms
(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))
32.0ms
(/ (+ 1 x) (- x 1))
82.0ms
(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
85.0ms
(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

simplify3.1s

Counts
2018 → 2018
Iterations
IterNodes
done5000
24309
12123
01299

prune4.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1)))))
0.0b
(/ (+ 1 x) (- x 1))
8.1b
(log (exp (fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1))))))
27.7b
(fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
40×add-sqr-sqrt
28×times-frac
20×add-cube-cbrt
10×difference-of-squares
8×distribute-lft-out
7×associate-/r*
6×exp-prod add-cbrt-cube add-exp-log
5×pow1 difference-of-sqr-1 distribute-lft-out-- add-log-exp
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u associate-/l*
3×fma-udef
2×exp-sum associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp rem-log-exp flip-+ div-inv flip-- rem-exp-log
Counts
4 → 103
Calls
4 calls:
2.0ms
(exp (fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1)))))
22.0ms
(/ (+ 1 x) (- x 1))
3.0ms
(log (exp (fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1))))))
0.0ms
(fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(exp (fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1)))))
29.0ms
(/ (+ 1 x) (- x 1))
103.0ms
(log (exp (fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1))))))
81.0ms
(fma x (/ 1 (+ 1 x)) (- (/ (+ 1 x) (- x 1))))

simplify2.1s

Counts
115 → 115
Iterations
IterNodes
done5000
33663
2968
1370
0170

prune432.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch104.0ms

Steps
ItersRangePoint
9
2842.495256040047
513310621636.50653
11033.995023478727
8
-29345360.474346694
-7508.589471958369
-13498.121057699798

simplify7.0ms

Iterations
IterNodes
done37
337
235
130
022

end0.0ms

sample2.2s

Algorithm
intervals
Results
810.0ms1269×body640valid
709.0ms1762×body1280valid
364.0ms4063×body80valid
124.0ms593×body320valid
66.0ms313×body160valid