Details

Time bar (total: 20.4s)

sample19.0ms

Algorithm
intervals
Results
5.0ms48×body1280valid
4.0ms52×body640valid
3.0ms134×body80valid
1.0ms14×body320valid
0.0ms8×body160valid

simplify118.0ms

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: 28.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
2.3b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
963×*-un-lft-identity
724×times-frac
575×add-sqr-sqrt
468×prod-diff
409×add-cube-cbrt
185×distribute-lft-out
92×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
46×div-inv
28×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
5×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
2×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num frac-sub
Counts
2 → 561
Calls
2 calls:
11.0ms
(/ (+ x 1.0) (- x 1.0))
76.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series165.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(/ (+ x 1.0) (- x 1.0))
126.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts
567 → 567
Iterations

Useful iterations: done (1.3s)

IterNodesCost
050233838
1115030506
2334922406
done500122212

prune634.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (/ (+ x 1.0) (- x 1.0)))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.3b
(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
1024×*-un-lft-identity
773×times-frac
638×add-sqr-sqrt
540×prod-diff
494×exp-prod
487×log-pow
471×add-cube-cbrt
194×distribute-lft-out
102×associate-/r/
83×distribute-lft-out-- difference-of-squares
51×div-inv
32×flip3-+ flip-+
22×pow1
21×flip3-- flip--
18×fma-neg
5×add-exp-log associate-/r* add-cbrt-cube add-log-exp
4×associate-/l*
3×expm1-log1p-u log-prod log1p-expm1-u associate--r+
2×associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num rem-exp-log
Counts
3 → 662
Calls
3 calls:
19.0ms
(exp (/ (+ x 1.0) (- x 1.0)))
11.0ms
(/ (+ x 1.0) (- x 1.0))
128.0ms
(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

series246.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(exp (/ (+ x 1.0) (- x 1.0)))
40.0ms
(/ (+ x 1.0) (- x 1.0))
134.0ms
(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

simplify1.7s

Counts
671 → 671
Iterations

Useful iterations: done (1.6s)

IterNodesCost
062642235
1132833649
2363425574
done500125436

prune671.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
0.5b
(/ 1.0 (* x x))
0.9b
(/ 3.0 (pow x 3))
7.2b
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
493×*-un-lft-identity
425×times-frac
234×prod-diff
219×add-sqr-sqrt
217×add-cube-cbrt
102×unpow3
100×distribute-rgt-neg-in
98×distribute-lft-neg-in
97×distribute-lft-out
76×distribute-rgt-out
69×div-inv
40×fma-def
21×unpow-prod-down cube-prod
19×distribute-lft1-in
18×fma-neg
16×add-log-exp
14×add-exp-log neg-mul-1
13×associate-/r*
11×add-cbrt-cube
7×cube-mult sqr-pow
6×associate-/l*
5×div-exp
4×pow1 expm1-log1p-u diff-log log1p-expm1-u distribute-lft-out--
3×cbrt-undiv 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 prod-exp flip-- cbrt-unprod associate--r+ difference-of-squares
Counts
4 → 433
Calls
4 calls:
44.0ms
(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
3.0ms
(/ 1.0 (* x x))
4.0ms
(/ 3.0 (pow x 3))
164.0ms
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

series181.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
27.0ms
(/ 1.0 (* x x))
35.0ms
(/ 3.0 (pow x 3))
37.0ms
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify2.6s

Counts
445 → 445
Iterations

Useful iterations: 2 (417.0ms)

IterNodesCost
048516713
1115513694
2458110584
done500010584

prune520.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

12.3b
(- (* (- 1.0) (- (/ 3.0 (pow x 3)) (/ 3.0 x))) (* (- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x))) (pow x 2)))
14.2b
(- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x)))
30.4b
(* (- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x))) (pow x 2))
35.9b
(* (* x x) (- (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite786.0ms

Algorithm
rewrite-expression-head
Rules
3358×times-frac
2326×add-sqr-sqrt
2295×*-un-lft-identity
2282×add-cube-cbrt
2092×prod-diff
1044×distribute-rgt-in distribute-lft-in associate--l+
482×unpow-prod-down
470×cube-prod
216×div-inv
164×sqr-pow
160×unpow3
156×cube-mult
36×frac-sub
30×associate-*r*
25×associate-*l/
23×associate-*r/
18×difference-of-squares
14×add-exp-log
12×flip3-- fma-neg flip--
11×add-cbrt-cube
9×pow1
8×associate-*l* add-log-exp
6×sub-neg prod-exp
5×frac-times distribute-lft-out-- unswap-sqr
4×expm1-log1p-u distribute-rgt-out-- cbrt-unprod log1p-expm1-u
3×pow-prod-down
2×diff-log *-commutative unpow2
1×pow-to-exp pow-exp
Counts
4 → 2243
Calls
4 calls:
202.0ms
(- (* (- 1.0) (- (/ 3.0 (pow x 3)) (/ 3.0 x))) (* (- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x))) (pow x 2)))
19.0ms
(- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x)))
53.0ms
(* (- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x))) (pow x 2))
227.0ms
(* (* x x) (- (/ 3.0 (pow x 3)) (/ 3.0 x)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* (- 1.0) (- (/ 3.0 (pow x 3)) (/ 3.0 x))) (* (- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x))) (pow x 2)))
138.0ms
(- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x)))
190.0ms
(* (- (/ (* 3.0 3.0) (pow x 6)) (* (/ 3.0 x) (/ 3.0 x))) (pow x 2))
138.0ms
(* (* x x) (- (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify1.6s

Counts
2255 → 2255
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01741111150
1484898307
done500098290

prune8.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch97.0ms

Steps
ItersRangePoint
10
5.968040026638966e-05
117627206.70733242
14618.947191620917
10
-64880754058.88788
-2.651420353119469e-05
-13801.088468895898

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02555
13240
done3240

end0.0ms

sample520.0ms

Algorithm
intervals
Results
177.0ms1719×body1280valid
103.0ms1224×body640valid
98.0ms4124×body80valid
38.0ms618×body320valid
13.0ms315×body160valid