Details

Time bar (total: 4.3s)

sample16.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify131.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0919
11918
23918
38018
413418
518918
621818
722218
done22218

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
2.6b
(- (* x x) (* (* y 4.0) y))
32.0b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
times-frac
add-log-exp
add-exp-log add-cbrt-cube
pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
3.0ms
(+ (* x x) (* (* y 4.0) y))
3.0ms
(- (* x x) (* (* y 4.0) y))
11.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series157.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ (* x x) (* (* y 4.0) y))
46.0ms
(- (* x x) (* (* y 4.0) y))
71.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify531.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
0981510
12531408
211741266
done50001266

prune240.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune10.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune11.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (pow x 2) (* 4.0 (pow y 2)))))
0.0b
(* 4.0 (pow y 2))
2.6b
(- (pow x 2) (* 4.0 (pow y 2)))
32.0b
(/ (fma x x (* (* y 4.0) y)) (- (pow x 2) (* 4.0 (pow y 2))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
69×add-sqr-sqrt
63×add-cube-cbrt *-un-lft-identity
22×add-exp-log
18×associate-/r*
13×add-cbrt-cube
11×associate-/r/
10×unpow-prod-down
fma-neg div-exp associate-*r* prod-diff
flip3-- flip-- div-inv associate-/l* add-log-exp
pow1
cbrt-undiv expm1-log1p-u log1p-expm1-u unpow2 unswap-sqr sqr-pow
associate-*l* prod-exp
rec-exp frac-2neg 1-exp clear-num
pow-to-exp sub-neg pow-flip diff-log pow-exp *-commutative cbrt-unprod inv-pow
Counts
4 → 176
Calls
4 calls:
12.0ms
(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (pow x 2) (* 4.0 (pow y 2)))))
5.0ms
(* 4.0 (pow y 2))
9.0ms
(- (pow x 2) (* 4.0 (pow y 2)))
9.0ms
(/ (fma x x (* (* y 4.0) y)) (- (pow x 2) (* 4.0 (pow y 2))))

series233.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (pow x 2) (* 4.0 (pow y 2)))))
28.0ms
(* 4.0 (pow y 2))
50.0ms
(- (pow x 2) (* 4.0 (pow y 2)))
79.0ms
(/ (fma x x (* (* y 4.0) y)) (- (pow x 2) (* 4.0 (pow y 2))))

simplify1.7s

Counts
188 → 188
Iterations

Useful iterations: 2 (252.0ms)

IterNodesCost
02594655
15704346
224093916
done50003916

prune483.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes131.0ms

Accuracy

62.8% (11.8b remaining)

Error of 12.2b against oracle of 0.4b and baseline of 32.1b

bsearch174.0ms

Steps
ItersRangePoint
7
4.7789019538112153e+104
1.591151741636895e+106
2.70835173311075e+105
6
2.542334140773719e-97
3.55820370252485e-96
3.3095785565051797e-97
9
-1.4109009987990789e-130
-4.102798577199621e-136
-7.055703835942177e-134
8
-5.294872751913314e+157
-4.107841816162241e+153
-1.1020932357029451e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02865
13565
23765
done3765

end0.0ms

sample371.0ms

Algorithm
intervals
Results
234.0ms8000×body80valid