Details

Time bar (total: 20.9s)

sample24.0ms

Algorithm
intervals
Results
6.0ms54×body1280valid
6.0ms123×body80valid
4.0ms49×body640valid
2.0ms27×body320valid
0.0ms3×body160valid

simplify119.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
76013
87813
99913
1014713
1119013
1220513
done20513

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
1.3b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite154.0ms

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))
80.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series216.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(/ x (+ x 1.0))
45.0ms
(/ (+ x 1.0) (- x 1.0))
137.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.5s

Counts
605 → 605
Iterations

Useful iterations: done (1.4s)

IterNodesCost
052334216
1120330851
2365922683
done500022489

prune925.0ms

Pruning

4 alts after pruning (4 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
(/ (/ 1.0 x) x)
0.3b
(/ 3.0 (pow x 3))
6.4b
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite535.0ms

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)))
6.0ms
(/ (/ 1.0 x) x)
4.0ms
(/ 3.0 (pow x 3))
297.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series189.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
25.0ms
(/ (/ 1.0 x) x)
44.0ms
(/ 3.0 (pow x 3))
33.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify1.0s

Counts
1476 → 1476
Iterations

Useful iterations: done (917.0ms)

IterNodesCost
0151182096
1327666843
done500066296

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
21.4b
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite618.0ms

Algorithm
rewrite-expression-head
Rules
4521×times-frac
3679×*-un-lft-identity
2605×add-sqr-sqrt
2412×prod-diff
1976×add-cube-cbrt
1780×cbrt-div
1482×cbrt-prod
1458×associate-/r/
891×flip3-- flip--
580×frac-times
550×distribute-lft-out
304×difference-of-squares
299×distribute-lft-out--
297×div-inv
290×associate-*r/ associate-*l/
135×flip3-+ flip-+
18×fma-neg
11×pow1
10×swap-sqr
8×pow1/3 associate-*r* associate-*l*
6×add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus diff-log prod-exp *-commutative frac-sub cbrt-unprod
Counts
4 → 2550
Calls
4 calls:
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
19.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
213.0ms
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(cbrt (- x 1.0))
103.0ms
(cbrt (- x 1.0))
146.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
187.0ms
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify1.4s

Counts
2562 → 2562
Iterations

Useful iterations: done (882.0ms)

IterNodesCost
02513324147
done5000311619

prune7.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0)))
7.6b
(/ x (+ (pow x 3) (pow 1.0 3)))
32.2b
(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (- 1.0 x)) (* x x)) (- (* (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1)))))
33.8b
(fma (- (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0)))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1)) (* (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
619×times-frac
583×*-un-lft-identity
399×add-sqr-sqrt
375×cbrt-prod
249×add-cube-cbrt
92×distribute-lft-out
75×distribute-lft-out-- difference-of-squares
41×associate-/l*
22×associate-/r/
20×cbrt-div
17×associate-/r*
16×unpow-prod-down cube-prod
11×add-exp-log div-inv
10×flip3-- flip--
8×add-cbrt-cube
4×pow1 cbrt-undiv expm1-log1p-u div-exp sum-cubes log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
1×flip3-+ flip-+ associate-/l/
Counts
4 → 444
Calls
4 calls:
30.0ms
(/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0)))
28.0ms
(/ x (+ (pow x 3) (pow 1.0 3)))
0.0ms
(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (- 1.0 x)) (* x x)) (- (* (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1)))))
0.0ms
(fma (- (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0)))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1)) (* (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1))))

series1.0s

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0)))
100.0ms
(/ x (+ (pow x 3) (pow 1.0 3)))
235.0ms
(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (- 1.0 x)) (* x x)) (- (* (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1)))))
509.0ms
(fma (- (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0)))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1)) (* (/ (/ (+ x 1.0) (cbrt (- x 1.0))) (cbrt (- x 1.0))) (/ (/ 1 (cbrt (- x 1.0))) (cbrt 1))))

simplify501.0ms

Counts
456 → 456
Iterations

Useful iterations: done (469.0ms)

IterNodesCost
059112637
1139312137
done500111566

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.7b

bsearch125.0ms

Steps
ItersRangePoint
11
0.08347146558812443
3.320253512051989e+22
6357.975922070107
8
-14583263.309321204
-1162.6651869185068
-7667.570022826935

simplify8.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
040131
159116
267116
372116
done72116

end0.0ms

sample549.0ms

Algorithm
intervals
Results
191.0ms1731×body1280valid
108.0ms1265×body640valid
97.0ms4084×body80valid
40.0ms618×body320valid
15.0ms302×body160valid