Details

Time bar (total: 36.4s)

sample54.0ms

Algorithm
intervals
Results
16.0ms46×body1280valid
11.0ms27×body320valid
9.0ms37×body640valid
9.0ms135×body80valid
1.0ms11×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
143644
13892
12339
11229
10177
9109
855
742
632
526
423
322
219
115
07

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite163.0ms

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:
11.0ms
(/ x (+ x 1))
21.0ms
(/ (+ x 1) (- x 1))
99.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(/ x (+ x 1))
28.0ms
(/ (+ x 1) (- x 1))
102.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.8s

Counts
762 → 762
Iterations
IterNodes
done5000
24887
11388
0584

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite711.0ms

Algorithm
rewrite-expression-head
Rules
3664×*-un-lft-identity
2832×times-frac
2392×add-sqr-sqrt
1836×prod-diff
1492×add-cube-cbrt
717×distribute-lft-out
444×difference-of-squares
318×associate-/r/
255×distribute-lft-out--
216×difference-of-sqr-1
159×div-inv
105×flip3-+ flip3-- flip-+ flip--
81×frac-times
63×cbrt-div
54×fma-neg
51×frac-sub
27×associate-*l/
15×associate-*r/
10×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×sub-neg diff-log
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 2053
Calls
4 calls:
378.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
56.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
72.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
76.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
80.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
390.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
107.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.6s

Counts
2065 → 2065
Iterations
IterNodes
done5000
11767
0763

prune6.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

13.7b
(/ (+ x 1) (- (* x x) (* 1 1)))
13.7b
(/ (+ x 1) (- (* x x) (* 1 1)))
28.7b
(fma x (/ 1 (+ x 1)) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
31.3b
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
32×times-frac
24×add-sqr-sqrt add-cube-cbrt
10×distribute-lft-out difference-of-squares
8×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ fma-udef div-inv flip--
Counts
4 → 108
Calls
4 calls:
25.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))
36.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))
0.0ms
(fma x (/ 1 (+ x 1)) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
0.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))
43.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))
158.0ms
(fma x (/ 1 (+ x 1)) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
175.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

simplify1.3s

Counts
120 → 120
Iterations
IterNodes
done5000
21540
1310
0122

prune657.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.6b
(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))))))
28.3b
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
2444×*-un-lft-identity
1888×times-frac
1596×add-sqr-sqrt
1224×prod-diff
996×add-cube-cbrt
478×distribute-lft-out
296×difference-of-squares
212×associate-/r/
170×distribute-lft-out--
144×difference-of-sqr-1
106×div-inv
70×flip3-+ flip-+
38×flip3-- flip--
36×fma-neg
8×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×sub-neg diff-log frac-sub fma-udef
Counts
4 → 1340
Calls
4 calls:
74.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
56.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0ms
(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))))))
0.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))

series864.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
109.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
448.0ms
(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))))))
204.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))

simplify3.8s

Counts
1352 → 1352
Iterations
IterNodes
done5000
24513
11436
0603

prune8.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes151.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.9b

bsearch179.0ms

Steps
ItersRangePoint
7
986.1969312707462
23716.851585869685
11803.399742628724
9
-209901990.47645873
-0.28008678268591264
-13258.447866903614

simplify24.0ms

Iterations
IterNodes
done59
259
154
035

end0.0ms

sample2.5s

Algorithm
intervals
Results
973.0ms1331×body640valid
797.0ms1701×body1280valid
322.0ms4038×body80valid
232.0ms621×body320valid
49.0ms309×body160valid