Details

Time bar (total: 11.1s)

sample38.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify286.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0919
11918
23918
37718
413118
519318
623418
724218
done24218

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize30.0ms

Local error

Found 2 expressions with local error:

2.2b
(- (* x x) (* (* y 4.0) y))
29.5b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff clear-num flip-+ div-inv
Counts
2 → 50
Calls
2 calls:
9.0ms
(- (* x x) (* (* y 4.0) y))
48.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series179.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(- (* x x) (* (* y 4.0) y))
102.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify1.6s

Counts
56 → 56
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0911282
12551209
214931096
done50001090

prune296.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (pow y 2))
1.4b
(log1p (/ (- (pow x 2) (* 4.0 (pow y 2))) (fma x x (* (* y 4.0) y))))
2.2b
(- (pow x 2) (* 4.0 (pow y 2)))
29.5b
(/ (- (pow x 2) (* 4.0 (pow y 2))) (fma x x (* (* y 4.0) y)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
11×add-exp-log
10×unpow-prod-down
9×times-frac
8×fma-neg associate-*r* prod-diff add-cbrt-cube
6×add-log-exp
5×expm1-log1p-u
4×pow1 log1p-expm1-u unpow2 unswap-sqr sqr-pow
3×associate-*l* prod-exp associate-/r* associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv pow-to-exp sub-neg log1p-udef frac-2neg diff-log div-sub log1p-expm1 div-exp pow-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 102
Calls
4 calls:
13.0ms
(* 4.0 (pow y 2))
1.0ms
(log1p (/ (- (pow x 2) (* 4.0 (pow y 2))) (fma x x (* (* y 4.0) y))))
41.0ms
(- (pow x 2) (* 4.0 (pow y 2)))
55.0ms
(/ (- (pow x 2) (* 4.0 (pow y 2))) (fma x x (* (* y 4.0) y)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* 4.0 (pow y 2))
224.0ms
(log1p (/ (- (pow x 2) (* 4.0 (pow y 2))) (fma x x (* (* y 4.0) y))))
61.0ms
(- (pow x 2) (* 4.0 (pow y 2)))
155.0ms
(/ (- (pow x 2) (* 4.0 (pow y 2))) (fma x x (* (* y 4.0) y)))

simplify1.4s

Counts
114 → 114
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01681931
13801851
215991664
done50001642

prune592.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (pow x 2) (fma x x (* (* y 4.0) y))) (/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y))))
1.4b
(log1p (- (/ (pow x 2) (fma x x (* (* y 4.0) y))) (/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y)))))
20.6b
(/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y)))
20.8b
(/ (pow x 2) (fma x x (* (* y 4.0) y)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
307×times-frac
211×add-sqr-sqrt
201×*-un-lft-identity
199×add-cube-cbrt
196×prod-diff
85×unpow-prod-down
40×div-inv
29×unpow2 sqr-pow
28×fma-neg
19×add-exp-log
11×add-cbrt-cube
9×associate-/l*
7×div-exp
6×associate-/r* add-log-exp
5×expm1-log1p-u difference-of-squares
4×pow1 log1p-expm1-u
3×cbrt-undiv prod-exp
2×pow-to-exp frac-2neg pow-exp clear-num
1×sub-neg log1p-udef flip3-- distribute-rgt-out-- diff-log log1p-expm1 frac-sub flip-- cbrt-unprod distribute-lft-out-- sub-div
Counts
4 → 334
Calls
4 calls:
82.0ms
(- (/ (pow x 2) (fma x x (* (* y 4.0) y))) (/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y))))
2.0ms
(log1p (- (/ (pow x 2) (fma x x (* (* y 4.0) y))) (/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y)))))
13.0ms
(/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y)))
18.0ms
(/ (pow x 2) (fma x x (* (* y 4.0) y)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(- (/ (pow x 2) (fma x x (* (* y 4.0) y))) (/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y))))
281.0ms
(log1p (- (/ (pow x 2) (fma x x (* (* y 4.0) y))) (/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y)))))
91.0ms
(/ (* 4.0 (pow y 2)) (fma x x (* (* y 4.0) y)))
85.0ms
(/ (pow x 2) (fma x x (* (* y 4.0) y)))

simplify2.6s

Counts
346 → 346
Iterations

Useful iterations: done (2.5s)

IterNodesCost
041824963
192320334
2351416369
done500016366

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes86.0ms

Accuracy

63.3% (11.5b remaining)

Error of 11.8b against oracle of 0.3b and baseline of 31.7b

bsearch203.0ms

Steps
ItersRangePoint
7
8.877180743642542e+106
1.7404810338668972e+108
7.812277400687208e+107
8
3.7161142089086124e-124
4.927184641861187e-121
1.5244723395464041e-122
6
-2.1564359723426472e-113
-3.259432699068069e-114
-1.7519615191246815e-113
8
-1.1188035785773677e+138
-2.8785927817889844e+133
-4.452213238363226e+134

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03484
13984
done3984

end0.0ms

sample837.0ms

Algorithm
intervals
Results
567.0ms8000×body80valid