Details

Time bar (total: 5.2s)

sample22.0ms

Algorithm
intervals
Results
6.0ms60×body640valid
4.0ms132×body80valid
2.0ms16×body1280valid
2.0ms25×body320valid
1.0ms23×body160valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097
done2097

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.9b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite488.0ms

Algorithm
rewrite-expression-head
Rules
725×*-un-lft-identity
703×times-frac
524×add-sqr-sqrt
492×add-cube-cbrt
468×prod-diff
236×associate-+l+
95×distribute-lft-out
65×div-inv
58×associate-/r/
29×flip3-+ flip-+
18×fma-neg
17×distribute-lft-out--
12×difference-of-squares
11×add-log-exp
10×fma-def
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num sum-log frac-sub
1×+-commutative associate-+l-
Counts
4 → 618
Calls
4 calls:
12.0ms
(/ 1.0 (- x 1.0))
11.0ms
(/ 1.0 (+ x 1.0))
78.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
334.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ 1.0 (- x 1.0))
29.0ms
(/ 1.0 (+ x 1.0))
40.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
220.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify148.0ms

Counts
630 → 630
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
0115610955
136078288
250017670
done50017670

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt 1.0) (+ x 1.0))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0)))
1.9b
(+ (fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
40×add-sqr-sqrt
39×times-frac
32×add-cube-cbrt
15×sqrt-prod
9×associate-/r* associate-/l*
8×add-exp-log add-cbrt-cube distribute-lft-out
6×add-log-exp
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u distribute-lft-out-- difference-of-squares
3×fma-def fma-udef
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
1×+-commutative associate-+l+ associate-+r+ flip3-- sum-log flip--
Counts
4 → 118
Calls
4 calls:
14.0ms
(/ (sqrt 1.0) (+ x 1.0))
10.0ms
(/ 1.0 (- x 1.0))
0.0ms
(fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0)))
6.0ms
(+ (fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (sqrt 1.0) (+ x 1.0))
26.0ms
(/ 1.0 (- x 1.0))
99.0ms
(fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0)))
156.0ms
(+ (fma (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

simplify56.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05121149
121441050
25003999
done5003999

prune359.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.1b
(* (* (+ x 1.0) x) (- x 1.0))
31.5b
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt prod-diff
11×pow1 add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
10×associate-*l/
8×associate-*r*
6×add-log-exp
5×associate-*l*
4×expm1-log1p-u frac-times flip3-- flip3-+ pow-prod-down prod-exp flip-- cbrt-unprod flip-+ log1p-expm1-u
3×sub-neg
2×associate-*r/ *-commutative
1×fma-neg diff-log fma-udef distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 101
Calls
4 calls:
19.0ms
(* (+ x 1.0) x)
8.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
57.0ms
(* (* (+ x 1.0) x) (- x 1.0))
0.0ms
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series338.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (+ x 1.0) x)
39.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
90.0ms
(* (* (+ x 1.0) x) (- x 1.0))
169.0ms
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify71.0ms

Counts
113 → 113
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
0510907
12772711
25001711
done5001711

prune209.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.1b
(* (* (+ x 1.0) x) (- x 1.0))
0.1b
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×add-exp-log add-cbrt-cube
18×prod-diff associate-*l/
11×distribute-rgt-in distribute-lft-in
10×pow1
8×frac-times associate-*r* associate-/r/
7×flip3-+ prod-exp cbrt-unprod flip-+
6×flip3-- flip--
5×associate-*l*
4×associate-*r/ pow-prod-down
3×cbrt-undiv expm1-log1p-u times-frac div-exp log1p-expm1-u associate-/l* add-log-exp
2×sub-neg *-commutative
1×frac-2neg clear-num associate-/r* div-inv distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 108
Calls
3 calls:
20.0ms
(* (+ x 1.0) x)
46.0ms
(* (* (+ x 1.0) x) (- x 1.0))
35.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series229.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(* (+ x 1.0) x)
96.0ms
(* (* (+ x 1.0) x) (- x 1.0))
85.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify75.0ms

Counts
117 → 117
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0565948
12962739
25001737
done5001737

prune171.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes17.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0156
1156
done156

end0.0ms

sample590.0ms

Algorithm
intervals
Results
182.0ms1796×body640valid
118.0ms4215×body80valid
74.0ms564×body1280valid
73.0ms952×body320valid
24.0ms473×body160valid