Details

Time bar (total: 17.3s)

sample36.0ms

Algorithm
intervals
Results
11.0ms50×body1280valid
6.0ms137×body80valid
6.0ms33×body640valid
3.0ms21×body320valid
1.0ms15×body160valid

simplify171.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
4.1b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite137.0ms

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:
7.0ms
(/ x (+ x 1))
23.0ms
(/ (+ x 1) (- x 1))
83.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series429.0ms

Counts
3 → 9
Calls
3 calls:
295.0ms
(/ x (+ x 1))
24.0ms
(/ (+ x 1) (- x 1))
111.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.2s

Counts
762 → 762
Iterations
IterNodes
done5002
23248
11369
0584

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x 1) (- x 1))
0.0b
(log1p (expm1 (/ (+ x 1) (- x 1))))
0.5b
(expm1 (/ (+ x 1) (- x 1)))
4.1b
(- (/ x (+ x 1)) (log1p (expm1 (/ (+ x 1) (- x 1)))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
124×*-un-lft-identity
92×add-sqr-sqrt
77×times-frac
67×add-cube-cbrt
54×prod-diff
20×distribute-lft-out
18×fma-neg
12×difference-of-squares
10×associate-/r/
7×associate-/r* add-log-exp
6×add-cbrt-cube add-exp-log distribute-lft-out--
5×flip3-+ difference-of-sqr-1 flip-+ log1p-expm1-u div-inv
4×expm1-log1p-u pow1 insert-posit16 associate-/l*
2×log1p-udef flip3-- diff-log flip-- associate-/l/
1×cbrt-undiv expm1-log1p clear-num sub-neg frac-2neg div-exp log1p-expm1 expm1-udef
Counts
4 → 173
Calls
4 calls:
25.0ms
(/ (+ x 1) (- x 1))
0.0ms
(log1p (expm1 (/ (+ x 1) (- x 1))))
1.0ms
(expm1 (/ (+ x 1) (- x 1)))
43.0ms
(- (/ x (+ x 1)) (log1p (expm1 (/ (+ x 1) (- x 1)))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (+ x 1) (- x 1))
124.0ms
(log1p (expm1 (/ (+ x 1) (- x 1))))
79.0ms
(expm1 (/ (+ x 1) (- x 1)))
219.0ms
(- (/ x (+ x 1)) (log1p (expm1 (/ (+ x 1) (- x 1)))))

simplify3.0s

Counts
185 → 185
Iterations
IterNodes
done5000
34817
21435
1562
0257

prune615.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x 1) (- x 1))
0.5b
(+ 1 (expm1 (/ (+ x 1) (- x 1))))
0.5b
(expm1 (/ (+ x 1) (- x 1)))
4.1b
(- (/ x (+ x 1)) (log (+ 1 (expm1 (/ (+ x 1) (- x 1))))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
145×*-un-lft-identity
102×add-sqr-sqrt
89×times-frac
77×add-cube-cbrt
72×prod-diff
25×distribute-lft-out
23×pow1
19×log-pow
18×fma-neg
12×associate-/r/ difference-of-squares
8×flip3-+ flip-+
7×associate-/r* distribute-lft-out-- add-log-exp
6×add-cbrt-cube add-exp-log div-inv
5×difference-of-sqr-1 log1p-expm1-u
4×expm1-log1p-u log-prod insert-posit16 associate-/l* associate--r+
3×fma-def
2×log-div flip3-- flip-- expm1-udef associate--r- associate-/l/
1×cbrt-undiv +-commutative expm1-log1p clear-num associate-+r- sum-log sub-neg frac-2neg diff-log div-exp
Counts
4 → 204
Calls
4 calls:
27.0ms
(/ (+ x 1) (- x 1))
7.0ms
(+ 1 (expm1 (/ (+ x 1) (- x 1))))
1.0ms
(expm1 (/ (+ x 1) (- x 1)))
59.0ms
(- (/ x (+ x 1)) (log (+ 1 (expm1 (/ (+ x 1) (- x 1))))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (+ x 1) (- x 1))
75.0ms
(+ 1 (expm1 (/ (+ x 1) (- x 1))))
53.0ms
(expm1 (/ (+ x 1) (- x 1)))
240.0ms
(- (/ x (+ x 1)) (log (+ 1 (expm1 (/ (+ x 1) (- x 1))))))

simplify1.7s

Counts
216 → 216
Iterations
IterNodes
done5001
21737
1646
0281

prune777.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ 1 (expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))))
0.5b
(expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1))))
4.1b
(- (/ x (+ x 1)) (log (+ 1 (expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))))))
12.7b
(/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
103×*-un-lft-identity
72×prod-diff
71×add-sqr-sqrt
66×add-cube-cbrt
65×times-frac
23×pow1
19×log-pow
18×fma-neg associate-/r/
17×distribute-lft-out
9×add-cbrt-cube add-exp-log
8×flip3-- flip--
7×flip3-+ flip-+ add-log-exp
6×div-inv
5×log1p-expm1-u
4×expm1-log1p-u frac-times log-prod insert-posit16 associate-/l* associate--r+ difference-of-squares
3×fma-def
2×cbrt-undiv log-div div-exp associate-*l/ associate-*r/ distribute-lft-out-- expm1-udef associate--r- associate-/l/
1×+-commutative expm1-log1p clear-num associate-+r- associate-/r* sum-log sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod
Counts
4 → 183
Calls
4 calls:
6.0ms
(+ 1 (expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))))
1.0ms
(expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1))))
57.0ms
(- (/ x (+ x 1)) (log (+ 1 (expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))))))
24.0ms
(/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(+ 1 (expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))))
81.0ms
(expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1))))
273.0ms
(- (/ x (+ x 1)) (log (+ 1 (expm1 (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))))))
47.0ms
(/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))

simplify2.0s

Counts
195 → 195
Iterations
IterNodes
done5003
22169
1717
0282

prune790.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.1b

bsearch115.0ms

Steps
ItersRangePoint
9
68.55102067575892
801012902.7811656
10076.446968341284
9
-17438.246738609338
-0.0018335887134067947
-1.0028494934768706

simplify9.0ms

Iterations
IterNodes
done50
250
143
028

end0.0ms

sample1.5s

Algorithm
intervals
Results
872.0ms1695×body1280valid
257.0ms1221×body640valid
168.0ms4115×body80valid
73.0ms641×body320valid
25.0ms328×body160valid