Details

Time bar (total: 12.9s)

sample21.0ms

Algorithm
intervals
Results
6.0ms60×body1280valid
3.0ms124×body80valid
3.0ms31×body640valid
2.0ms34×body320valid
0.0ms7×body160valid

simplify113.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
75813
87613
99713
1012713
1113713
1214113
1314313
done14313

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
3.4b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
11.0ms
(/ (+ x 1.0) (- x 1.0))
79.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series201.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
39.0ms
(/ (+ x 1.0) (- x 1.0))
129.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.2s

Counts
605 → 605
Iterations

Useful iterations: done (1.2s)

IterNodesCost
052334216
1115730851
2296722735
done500022021

prune607.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.1b
(/ 3.0 (pow x 3))
0.1b
(/ (/ 1.0 x) x)
6.8b
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite526.0ms

Algorithm
rewrite-expression-head
Rules
3245×times-frac
2816×*-un-lft-identity
1528×add-sqr-sqrt
1526×add-cube-cbrt
1170×prod-diff
605×distribute-rgt-neg-in
602×distribute-lft-neg-in
459×unpow3
458×distribute-lft-out
364×distribute-rgt-out
301×div-inv
91×distribute-rgt1-in
90×fma-neg
16×associate-/l* add-log-exp
15×associate-/r*
14×add-exp-log neg-mul-1
13×fma-def
12×unpow-prod-down cube-prod
11×add-cbrt-cube
6×div-exp
5×distribute-lft-out--
4×pow1 cbrt-undiv expm1-log1p-u cube-mult diff-log log1p-expm1-u sqr-pow
3×sum-log frac-sub distribute-neg-frac
2×frac-2neg flip3-+ neg-log frac-add clear-num flip-+
1×+-commutative associate--l- neg-sub0 pow-to-exp sub-neg flip3-- pow-exp flip-- associate-/l/ associate--r+ difference-of-squares
Counts
4 → 1464
Calls
4 calls:
36.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
4.0ms
(/ 3.0 (pow x 3))
6.0ms
(/ (/ 1.0 x) x)
287.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series176.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
35.0ms
(/ 3.0 (pow x 3))
24.0ms
(/ (/ 1.0 x) x)
39.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify1.1s

Counts
1476 → 1476
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0151182096
1284166843
done500066062

prune2.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
2.4b
(+ (fma (- (/ (/ (sqrt 1.0) (cbrt x)) (cbrt x))) (/ (/ (sqrt 1.0) x) (cbrt x)) (* (/ 3.0 x) (+ -1 (/ (/ -1 x) x)))) (fma (+ -1 (/ (/ -1 x) x)) (/ 3.0 x) (* (/ 3.0 x) (+ 1 (/ 1 (* x x))))))
2.6b
(fma (- (/ (/ (sqrt 1.0) (cbrt x)) (cbrt x))) (/ (/ (sqrt 1.0) x) (cbrt x)) (* (/ 3.0 x) (+ -1 (/ (/ -1 x) x))))
29.8b
(fma (+ -1 (/ (/ -1 x) x)) (/ 3.0 x) (* (/ 3.0 x) (+ 1 (/ 1 (* x x)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u
3×cbrt-prod fma-def
1×+-commutative associate-+l+ associate-+r+ flip3-+ pow1/3 sum-log flip-+ distribute-lft-out
Counts
4 → 52
Calls
4 calls:
0.0ms
(cbrt x)
3.0ms
(+ (fma (- (/ (/ (sqrt 1.0) (cbrt x)) (cbrt x))) (/ (/ (sqrt 1.0) x) (cbrt x)) (* (/ 3.0 x) (+ -1 (/ (/ -1 x) x)))) (fma (+ -1 (/ (/ -1 x) x)) (/ 3.0 x) (* (/ 3.0 x) (+ 1 (/ 1 (* x x))))))
0.0ms
(fma (- (/ (/ (sqrt 1.0) (cbrt x)) (cbrt x))) (/ (/ (sqrt 1.0) x) (cbrt x)) (* (/ 3.0 x) (+ -1 (/ (/ -1 x) x))))
0.0ms
(fma (+ -1 (/ (/ -1 x) x)) (/ 3.0 x) (* (/ 3.0 x) (+ 1 (/ 1 (* x x)))))

series687.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt x)
242.0ms
(+ (fma (- (/ (/ (sqrt 1.0) (cbrt x)) (cbrt x))) (/ (/ (sqrt 1.0) x) (cbrt x)) (* (/ 3.0 x) (+ -1 (/ (/ -1 x) x)))) (fma (+ -1 (/ (/ -1 x) x)) (/ 3.0 x) (* (/ 3.0 x) (+ 1 (/ 1 (* x x))))))
177.0ms
(fma (- (/ (/ (sqrt 1.0) (cbrt x)) (cbrt x))) (/ (/ (sqrt 1.0) x) (cbrt x)) (* (/ 3.0 x) (+ -1 (/ (/ -1 x) x))))
97.0ms
(fma (+ -1 (/ (/ -1 x) x)) (/ 3.0 x) (* (/ 3.0 x) (+ 1 (/ 1 (* x x)))))

simplify1.4s

Counts
64 → 64
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0992030
12181888
25971569
330381288
done50011148

prune246.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

15.7b
(/ x (- (* x x) (* 1.0 1.0)))
15.8b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.8b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
31.7b
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
44×times-frac
33×add-sqr-sqrt add-cube-cbrt
14×difference-of-squares
12×associate-/r*
11×associate-/l*
10×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/r/
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
2×flip3-+ flip-+
1×fma-udef
Counts
4 → 129
Calls
4 calls:
5.0ms
(/ x (- (* x x) (* 1.0 1.0)))
10.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
11.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ x (- (* x x) (* 1.0 1.0)))
35.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
40.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
178.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify2.6s

Counts
141 → 141
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01692601
13912521
212032066
347841896
done50001896

prune404.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch118.0ms

Steps
ItersRangePoint
11
4368.076441928604
1.2360357871274782e+23
10746.126747103617
8
-133622.27441454158
-436.72743869654124
-10924.794683009177

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
043160
166110
272110
done72110

end0.0ms

sample527.0ms

Algorithm
intervals
Results
174.0ms1668×body1280valid
107.0ms1254×body640valid
97.0ms4085×body80valid
43.0ms652×body320valid
14.0ms341×body160valid