Details

Time bar (total: 15.9s)

sample20.0ms

Algorithm
intervals
Results
6.0ms56×body1280valid
3.0ms42×body640valid
3.0ms127×body80valid
1.0ms20×body320valid
0.0ms11×body160valid

simplify122.0ms

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: 30.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
3.6b
(- (/ 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))
81.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series214.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ x (+ x 1.0))
39.0ms
(/ (+ x 1.0) (- x 1.0))
138.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.6s

Counts
605 → 605
Iterations

Useful iterations: done (1.5s)

IterNodesCost
052334216
1118730851
2302723635
done500022921

prune619.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.1b
(/ (/ 1.0 x) x)
0.2b
(/ 3.0 (pow x 3))
5.4b
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite549.0ms

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)
5.0ms
(/ 3.0 (pow x 3))
312.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series194.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
29.0ms
(/ (/ 1.0 x) x)
37.0ms
(/ 3.0 (pow x 3))
41.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify1.4s

Counts
1476 → 1476
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0151182096
1324766843
done500066088

prune2.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1.0 x) x)
0.2b
(* (/ (cbrt 3.0) x) (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
0.4b
(/ (cbrt 3.0) x)
5.4b
(- (- (/ (/ 1.0 x) x)) (* (/ (cbrt 3.0) x) (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
377×times-frac
225×add-sqr-sqrt
217×add-cube-cbrt *-un-lft-identity
90×fma-neg prod-diff
86×distribute-lft-neg-in distribute-rgt-neg-in
23×div-inv
22×cbrt-prod associate-*l*
19×associate-/l*
16×add-exp-log
14×add-cbrt-cube
8×add-log-exp
6×pow1 associate-/r* distribute-neg-frac
5×cbrt-undiv div-exp frac-sub
4×expm1-log1p-u frac-times flip3-+ associate-*r/ flip-+ log1p-expm1-u
3×associate-*r* associate-*l/ unswap-sqr
2×distribute-rgt-in neg-mul-1 frac-2neg distribute-lft-in diff-log prod-exp clear-num cbrt-unprod associate--r+
1×associate--l- neg-sub0 sub-neg flip3-- pow-prod-down neg-log *-commutative flip-- associate-/l/ sub-div
Counts
4 → 367
Calls
4 calls:
6.0ms
(/ (/ 1.0 x) x)
56.0ms
(* (/ (cbrt 3.0) x) (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
3.0ms
(/ (cbrt 3.0) x)
133.0ms
(- (- (/ (/ 1.0 x) x)) (* (/ (cbrt 3.0) x) (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (/ 1.0 x) x)
278.0ms
(* (/ (cbrt 3.0) x) (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
53.0ms
(/ (cbrt 3.0) x)
96.0ms
(- (- (/ (/ 1.0 x) x)) (* (/ (cbrt 3.0) x) (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))))

simplify2.4s

Counts
379 → 379
Iterations

Useful iterations: done (2.3s)

IterNodesCost
049312880
1134212115
242867609
done50007509

prune905.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

5.4b
(- (- (/ (/ 1.0 x) x)) (* (* (/ (cbrt 3.0) x) (* (cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))) (cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))))) (cbrt (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))))
14.5b
(cbrt (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
14.5b
(cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
14.5b
(cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
264×times-frac
149×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
90×fma-neg prod-diff
86×distribute-lft-neg-in distribute-rgt-neg-in
16×div-inv
9×cbrt-prod
8×add-log-exp
6×cbrt-div associate-*l/ distribute-neg-frac
5×frac-sub
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-+ pow1/3 flip-+
2×frac-times neg-mul-1 diff-log associate-*r/
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip-- sub-div
Counts
4 → 243
Calls
4 calls:
134.0ms
(- (- (/ (/ 1.0 x) x)) (* (* (/ (cbrt 3.0) x) (* (cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))) (cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))))) (cbrt (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))))
11.0ms
(cbrt (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
0.0ms
(cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
1.0ms
(cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))

series1.6s

Counts
4 → 12
Calls
4 calls:
604.0ms
(- (- (/ (/ 1.0 x) x)) (* (* (/ (cbrt 3.0) x) (* (cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))) (cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x))))) (cbrt (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))))
309.0ms
(cbrt (+ (* (cbrt 3.0) (cbrt 3.0)) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
326.0ms
(cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))
322.0ms
(cbrt (fma (cbrt 3.0) (cbrt 3.0) (/ (/ (* (cbrt 3.0) (cbrt 3.0)) x) x)))

simplify1.3s

Counts
255 → 255
Iterations

Useful iterations: done (1.3s)

IterNodesCost
043524493
1109122561
2319110227
done500010093

prune767.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.3b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02261
12661
22861
done2861

end0.0ms

sample530.0ms

Algorithm
intervals
Results
178.0ms1697×body1280valid
101.0ms1273×body640valid
94.0ms4049×body80valid
39.0ms636×body320valid
14.0ms345×body160valid