Details

Time bar (total: 20.2s)

sample30.0ms

Algorithm
intervals
Results
10.0ms190×body80valid
4.0ms23×body640valid
3.0ms13×body1280valid
2.0ms14×body320valid
2.0ms16×body160valid

simplify4.1s

Counts
1 → 1
Iterations
IterNodes
done5002
134169
123568
113113
102621
92078
81683
71107
6562
5259
4129
373
233
116
08

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ 1.0 y))
15.7b
(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

rewrite42.0ms

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/ insert-posit16 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 → 60
Calls
2 calls:
39.0ms
(/ (- x 1.0) (+ 1.0 y))
0.0ms
(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

series192.0ms

Counts
2 → 6
Calls
2 calls:
72.0ms
(/ (- x 1.0) (+ 1.0 y))
120.0ms
(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

simplify2.7s

Counts
66 → 66
Iterations
IterNodes
done5000
33563
2882
1284
0116

prune308.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
4.2b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.8b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite77.0ms

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* insert-posit16 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 → 105
Calls
3 calls:
31.0ms
(* (- 1.0 x) y)
19.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
25.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series278.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(* (- 1.0 x) y)
145.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
72.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.3s

Counts
114 → 114
Iterations
IterNodes
done5003
21821
1554
0205

prune557.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
0.0b
(/ y (+ y 1.0))
4.2b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
30×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt
18×associate-*r*
10×add-cbrt-cube add-exp-log
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×expm1-log1p-u flip3-- fma-neg prod-diff insert-posit16 log1p-expm1-u flip-- associate-/l*
2×frac-times cbrt-undiv flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×clear-num sub-neg frac-2neg diff-log pow-prod-down associate-*r/ *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 103
Calls
3 calls:
36.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
9.0ms
(/ y (+ y 1.0))
5.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series241.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
49.0ms
(/ y (+ y 1.0))
107.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.8s

Counts
112 → 112
Iterations
IterNodes
done5002
21749
1469
0175

prune413.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma y (* y y) (* (* 1.0 1.0) 1.0))
7.4b
(- 1.0 (* (/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
9.2b
(/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0)))
15.1b
(* (/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
7×associate-*l*
6×pow1 times-frac add-log-exp
5×prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp associate-*r/ insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-*r* prod-diff
2×distribute-rgt-in frac-times distribute-lft-in flip3-+ flip3-- flip-+ div-inv flip-- associate--r+ associate-/l/
1×clear-num sub-neg frac-2neg diff-log pow-prod-down associate-*l/ *-commutative fma-udef associate-/l* unswap-sqr
Counts
4 → 96
Calls
4 calls:
0.0ms
(fma y (* y y) (* (* 1.0 1.0) 1.0))
6.0ms
(- 1.0 (* (/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
30.0ms
(/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0)))
128.0ms
(* (/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series748.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(fma y (* y y) (* (* 1.0 1.0) 1.0))
328.0ms
(- 1.0 (* (/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
162.0ms
(/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0)))
110.0ms
(* (/ (* y (- 1.0 x)) (fma y (* y y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify3.2s

Counts
108 → 108
Iterations
IterNodes
done5010
23222
1648
0192

prune635.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes245.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 13.6b

bsearch165.0ms

Steps
ItersRangePoint
9
45027090.2690009
11120271688924408.0
4005471382996.025
9
-9.169070498365897e+20
-3361471310457274.5
-3480617740589270.5

simplify10.0ms

Iterations
IterNodes
done37
137
027

end0.0ms

sample1.8s

Algorithm
intervals
Results
618.0ms6204×body80valid
581.0ms497×body320valid
212.0ms676×body640valid
198.0ms342×body1280valid
44.0ms281×body160valid