Details

Time bar (total: 22.6s)

sample48.0ms

Algorithm
intervals
Results
15.0ms65×body640valid
7.0ms133×body80valid
6.0ms38×body320valid
2.0ms20×body160valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21511
done1511

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize18.0ms

Local error

Found 1 expressions with local error:

2.4b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
625×*-un-lft-identity
562×times-frac
467×add-sqr-sqrt
378×prod-diff
347×add-cube-cbrt
82×associate-/r/
75×distribute-lft-out--
72×distribute-lft-out
58×difference-of-squares
42×div-inv
23×flip-+
22×flip3-+
20×flip--
19×flip3--
18×fma-neg
3×add-log-exp
1×pow1 add-exp-log expm1-log1p-u sub-neg diff-log frac-sub add-cbrt-cube log1p-expm1-u
Counts
1 → 430
Calls
1 calls:
188.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series283.0ms

Counts
1 → 3
Calls
1 calls:
283.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify2.6s

Counts
433 → 433
Iterations

Useful iterations: done (2.5s)

IterNodesCost
047823493
1110121056
2346316280
done500016278

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
16.1b
(+ (- (fma x x (* (+ x 1.0) 1.0))) (fma x x (* (+ x 1.0) 1.0)))
20.9b
(* (fma x x (* (+ x 1.0) 1.0)) (- (/ 1.0 (- (pow x 3) (pow 1.0 3)))))
30.2b
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (fma x x (* 1.0 (- 1.0 x))) (* (fma x x (* (+ x 1.0) 1.0)) (- (/ 1.0 (- (pow x 3) (pow 1.0 3))))))

rewrite595.0ms

Algorithm
rewrite-expression-head
Rules
231×add-sqr-sqrt
189×*-un-lft-identity
177×times-frac
166×associate-*r*
96×difference-of-squares
88×distribute-lft-neg-in unpow-prod-down cube-prod
87×distribute-rgt-neg-in
85×add-cube-cbrt
48×sqr-pow
30×distribute-lft-out--
24×distribute-lft-out
10×fma-def
9×associate-/r*
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1 difference-cubes associate-/r/
4×expm1-log1p-u neg-mul-1 distribute-rgt-out sum-cubes log1p-expm1-u
3×associate-*l* fma-udef div-inv associate-/l*
2×flip3-- distribute-lft1-in flip3-+ sum-log flip-- flip-+
1×cbrt-undiv +-commutative neg-sub0 associate-+l- associate-+l+ associate-+r+ distribute-neg-in frac-2neg associate-*r/ div-exp pow-prod-down neg-log prod-exp clear-num *-commutative distribute-rgt-neg-out cbrt-unprod distribute-neg-frac unswap-sqr
Counts
4 → 287
Calls
4 calls:
75.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
26.0ms
(+ (- (fma x x (* (+ x 1.0) 1.0))) (fma x x (* (+ x 1.0) 1.0)))
450.0ms
(* (fma x x (* (+ x 1.0) 1.0)) (- (/ 1.0 (- (pow x 3) (pow 1.0 3)))))
1.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (fma x x (* 1.0 (- 1.0 x))) (* (fma x x (* (+ x 1.0) 1.0)) (- (/ 1.0 (- (pow x 3) (pow 1.0 3))))))

series803.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
3.0ms
(+ (- (fma x x (* (+ x 1.0) 1.0))) (fma x x (* (+ x 1.0) 1.0)))
112.0ms
(* (fma x x (* (+ x 1.0) 1.0)) (- (/ 1.0 (- (pow x 3) (pow 1.0 3)))))
558.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (fma x x (* 1.0 (- 1.0 x))) (* (fma x x (* (+ x 1.0) 1.0)) (- (/ 1.0 (- (pow x 3) (pow 1.0 3))))))

simplify1.1s

Counts
299 → 299
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04186036
111185242
done50004886

prune2.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 4)))
0.2b
(/ 2.0 (pow x 6))
0.3b
(/ 2.0 (pow x 4))
1.1b
(/ 2.0 (* x x))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×*-un-lft-identity
40×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×add-exp-log
15×associate-/r*
13×add-cbrt-cube
9×associate-/l*
8×div-exp sqr-pow
7×fma-def
6×div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×pow-to-exp pow-exp distribute-lft-out
1×+-commutative flip3-+ frac-add prod-exp sum-log cbrt-unprod flip-+
Counts
4 → 140
Calls
4 calls:
76.0ms
(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 4)))
14.0ms
(/ 2.0 (pow x 6))
13.0ms
(/ 2.0 (pow x 4))
14.0ms
(/ 2.0 (* x x))

series383.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 4)))
84.0ms
(/ 2.0 (pow x 6))
71.0ms
(/ 2.0 (pow x 4))
47.0ms
(/ 2.0 (* x x))

simplify2.9s

Counts
152 → 152
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02171559
14811433
229711348
done50001314

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))
0.1b
(/ (/ 2.0 x) x)
0.2b
(/ 2.0 (pow x 6))
0.3b
(/ 2.0 (pow x 4))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
185×times-frac
119×*-un-lft-identity
113×add-sqr-sqrt add-cube-cbrt
43×fma-def
24×unpow-prod-down
19×add-exp-log associate-/l*
17×associate-/r*
13×add-cbrt-cube
11×div-inv
9×div-exp
8×sqr-pow
6×add-log-exp
5×cbrt-undiv
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×pow-to-exp pow-exp distribute-lft-out
1×+-commutative flip3-+ frac-add sum-log flip-+ associate-/l/
Counts
4 → 225
Calls
4 calls:
172.0ms
(+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))
23.0ms
(/ (/ 2.0 x) x)
15.0ms
(/ 2.0 (pow x 6))
15.0ms
(/ 2.0 (pow x 4))

series430.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))
59.0ms
(/ (/ 2.0 x) x)
107.0ms
(/ 2.0 (pow x 6))
73.0ms
(/ 2.0 (pow x 4))

simplify3.0s

Counts
237 → 237
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03072234
16832060
232721905
done50011893

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes114.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.4b

bsearch265.0ms

Steps
ItersRangePoint
10
2.8868360106527892e-08
453261925.93168354
226.65001029383706
8
-3934.6710789005906
-4.26929226401081
-213.48879909880657

simplify28.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
040110
15893
26193
36293
done6293

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.1s1926×body640valid
299.0ms4175×body80valid
245.0ms1239×body320valid
131.0ms660×body160valid