Details

Time bar (total: 2.9m)

sample52.0ms

Algorithm
intervals
Results
16.0ms61×body640valid
10.0ms137×body80valid
6.0ms30×body320valid
4.0ms11×body1280valid
2.0ms17×body160valid

simplify231.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010283
118283
231283
341283
460283
572283
683283
7103283
8170283
9198283
done198283

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize18.0ms

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))
2.4b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite668.0ms

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-cbrt-cube add-exp-log
6×associate-/l*
4×expm1-log1p-u pow1 log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv clear-num sum-log sub-neg frac-2neg diff-log div-exp frac-sub
1×+-commutative associate-+l-
Counts
4 → 618
Calls
4 calls:
16.0ms
(/ 1.0 (+ x 1.0))
16.0ms
(/ 1.0 (- x 1.0))
93.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
495.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series832.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1.0 (+ x 1.0))
30.0ms
(/ 1.0 (- x 1.0))
56.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
709.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify4.0s

Counts
630 → 630
Iterations

Useful iterations: done (3.9s)

IterNodesCost
0501324510
11189285410
23147250026
done5001222346

prune3.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))
2.4b
(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
32×add-sqr-sqrt
27×times-frac
24×add-cube-cbrt
9×associate-/r* add-log-exp
8×add-cbrt-cube add-exp-log
7×distribute-lft-out
6×associate-/l*
4×expm1-log1p-u pow1 associate-/r/ log1p-expm1-u distribute-lft-out-- difference-of-squares
3×sum-log fma-def
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ fma-udef div-inv
1×+-commutative associate-+l+ associate-+r+ flip3-- flip--
Counts
4 → 105
Calls
4 calls:
19.0ms
(/ 1.0 (+ x 1.0))
16.0ms
(/ 1.0 (- x 1.0))
0.0ms
(fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))
96.0ms
(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))

series635.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 1.0 (+ x 1.0))
36.0ms
(/ 1.0 (- x 1.0))
87.0ms
(fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))
464.0ms
(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))

simplify2.3s

Counts
117 → 117
Iterations

Useful iterations: done (2.2s)

IterNodesCost
019138051
147631168
2150128951
done500128749

prune836.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))
0.3b
(* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))))
2.4b
(- (* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))) (* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0)))))
15.8b
(/ (- (* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))) (* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))) (- (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0)))))

rewrite430.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
38×add-sqr-sqrt
24×times-frac add-cube-cbrt
18×pow1
13×difference-of-squares
11×distribute-lft-out
10×add-cbrt-cube add-exp-log distribute-lft-out--
9×swap-sqr
7×associate-*r* associate-*l*
6×associate-/r* flip3-+ flip-+ add-log-exp
4×distribute-rgt-in expm1-log1p-u frac-times distribute-lft-in fma-udef log1p-expm1-u associate-/l*
3×flip3-- flip--
2×pow2 pow-plus pow-prod-down associate-*l/ prod-exp associate--l+ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod associate--r+ unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 145
Calls
4 calls:
175.0ms
(* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))
10.0ms
(* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))))
13.0ms
(- (* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))) (* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0)))))
228.0ms
(/ (- (* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))) (* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))) (- (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0)))))

series5.1s

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))
126.0ms
(* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))))
2.0s
(- (* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))) (* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0)))))
2.9s
(/ (- (* (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))) (* (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))) (- (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0)))))

simplify4.8s

Counts
157 → 157
Iterations

Useful iterations: done (4.8s)

IterNodesCost
0248109964
174188323
2266682076
done500082042

prune904.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize103.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.4b
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.4b
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
20.5b
(cbrt (* (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))))))

rewrite14.2s

Algorithm
rewrite-expression-head
Rules
26325×frac-add
10693×frac-times
6864×flip3-+ flip-+
5831×cbrt-div
4875×flip3-- frac-sub flip--
2925×distribute-neg-frac
1216×*-un-lft-identity
1032×times-frac
708×associate-+r+
702×prod-diff
697×add-sqr-sqrt add-cube-cbrt
629×associate-*r/
323×associate-*l/
240×distribute-lft-out
94×add-log-exp
93×div-inv
78×associate-/r/
54×sum-log
33×distribute-lft-out--
27×distribute-rgt-neg-in
24×fma-def
12×diff-log
6×associate-+r- neg-log associate-+l-
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×neg-sub0 +-commutative associate-+l+ sub-neg
1×cbrt-prod pow1/3 cube-unmult rem-cbrt-cube
Counts
4 → 6725
Calls
4 calls:
1.7s
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
1.7s
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
1.6s
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
6.7s
(cbrt (* (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
272.0ms
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
311.0ms
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
306.0ms
(+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
342.0ms
(cbrt (* (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (+ (+ (/ 1.0 (- x 1.0)) (+ (- (/ 2.0 x)) (/ 2.0 x))) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))))))

simplify49.6s

Counts
6737 → 6737
Iterations

Useful iterations: 0 (32.5s)

IterNodesCost
02308220008054
done2308220008054

prune1.4m

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 9.8b

bsearch117.0ms

Steps
ItersRangePoint
9
0.1909160003853501
166131308.15705827
144.7677165249174
10
-27652538170.40468
-0.18371106458419734
-111.13785993607881

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0361729
1561729
2581729
done581729

end0.0ms

sample1.1s

Algorithm
intervals
Results
355.0ms549×body1280valid
304.0ms1879×body640valid
207.0ms4139×body80valid
120.0ms946×body320valid
59.0ms489×body160valid