Details

Time bar (total: 22.8s)

sample39.0ms

Algorithm
intervals
Results
12.0ms207×body80valid
4.0ms19×body640valid
3.0ms12×body1280valid
2.0ms12×body320valid
1.0ms6×body160valid

simplify5.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (60.0ms)

IterNodesCost
08203
116203
233203
373203
4129178
5259178
6562178
71107178
81683178
92078178
102621178
113113178
123568178
134169178
done5002178

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
11.8b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×associate-/r* add-cbrt-cube add-exp-log
2×expm1-log1p-u pow1 associate-/r/ log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-sub div-exp flip-+ fma-udef div-inv flip--
Counts
2 → 58
Calls
2 calls:
19.0ms
(/ (- x 1.0) (+ y 1.0))
0.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series124.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (- x 1.0) (+ y 1.0))
75.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.3s

Counts
64 → 64
Iterations

Useful iterations: done (2.3s)

IterNodesCost
011417009
128115623
287015344
3348515159
done500115111

prune295.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (+ y 1.0))
0.0b
(/ x (+ y 1.0))
11.8b
(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
24×times-frac
21×add-sqr-sqrt add-cube-cbrt
8×associate-/r* distribute-lft-out
7×add-cbrt-cube add-exp-log
6×associate-/l*
4×associate-/r/
3×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ div-inv
1×fma-udef
Counts
3 → 80
Calls
3 calls:
14.0ms
(/ 1.0 (+ y 1.0))
14.0ms
(/ x (+ y 1.0))
0.0ms
(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

series149.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 1.0 (+ y 1.0))
38.0ms
(/ x (+ y 1.0))
75.0ms
(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

simplify2.4s

Counts
89 → 89
Iterations

Useful iterations: done (2.4s)

IterNodesCost
014521872
131918623
2103718024
3405217806
done500017758

prune444.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
1.3b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
11.3b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
30×add-sqr-sqrt prod-diff
24×add-cube-cbrt
16×times-frac
10×add-cbrt-cube add-exp-log
8×associate-/r/
5×pow1 associate-*l* distribute-lft-out add-log-exp
4×associate-/r* flip3-+ associate-*l/ flip-+ div-inv
3×expm1-log1p-u flip3-- fma-neg associate-*r* log1p-expm1-u flip--
2×cbrt-undiv div-exp prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares associate-/l/
1×clear-num sub-neg frac-2neg diff-log pow-prod-down *-commutative associate-/l* unswap-sqr
Counts
3 → 102
Calls
3 calls:
24.0ms
(* (- 1.0 x) y)
21.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
19.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series203.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(* (- 1.0 x) y)
98.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
52.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.8s

Counts
111 → 111
Iterations

Useful iterations: done (2.8s)

IterNodesCost
020244825
155139464
2181335256
done500435206

prune520.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

14.7b
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
17.2b
(* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
17.2b
(* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
33.2b
(fma (- (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))))

rewrite485.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
30×associate-*r*
27×times-frac add-cbrt-cube add-exp-log
20×distribute-lft-out
16×add-sqr-sqrt unpow-prod-down cube-prod
12×add-cube-cbrt
9×associate-/r* prod-exp cbrt-unprod
8×pow1
7×flip3-+ flip-+
6×cbrt-undiv div-exp associate-*l* associate-*l/ associate-/r/
4×expm1-log1p-u frac-times sum-cubes log1p-expm1-u add-log-exp
3×div-inv
2×pow-prod-down associate-*r/ *-commutative unswap-sqr associate-/l/
1×clear-num frac-2neg flip3-- fma-udef flip-- associate-/l*
Counts
4 → 131
Calls
4 calls:
68.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
180.0ms
(* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
231.0ms
(* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
1.0ms
(fma (- (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))))

series628.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
109.0ms
(* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
103.0ms
(* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
280.0ms
(fma (- (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (* (+ (* y y) (- (* 1.0 1.0) (* y 1.0))) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))))

simplify3.6s

Counts
143 → 143
Iterations

Useful iterations: done (3.5s)

IterNodesCost
0162104942
150962469
2219558977
done500258657

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes167.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.3b

bsearch165.0ms

Steps
ItersRangePoint
10
9.61659873327403e-09
11867636368.965105
115501974.66236675
10
-1.0339559943375677e+17
-822.3940084488386
-159699341.56246573

simplify40.0ms

Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
0321492
1491492
2571492
3621492
done621492

end0.0ms

sample1.1s

Algorithm
intervals
Results
438.0ms6112×body80valid
177.0ms737×body640valid
128.0ms394×body1280valid
71.0ms494×body320valid
29.0ms263×body160valid