Details

Time bar (total: 18.0s)

sample43.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01114
11613
22612
33312
done3312

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
37.8b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×rem-sqrt-square div-inv
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num fma-udef
Counts
3 → 66
Calls
3 calls:
0.0ms
(fma z z (fma x x (* y y)))
5.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
4.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series387.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(fma z z (fma x x (* y y)))
78.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
249.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify1.8s

Counts
75 → 75
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
01071274
11751215
24761106
325441106
done50011106

prune302.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.1b
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
37.9b
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt
5×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×sqrt-pow1 pow-prod-down
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 45
Calls
3 calls:
0.0ms
(fma z z (fma x x (* y y)))
7.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
5.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

series469.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(fma z z (fma x x (* y y)))
90.0ms
(* 0.3333333333333333 (fma z z (fma x x (* y y))))
309.0ms
(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

simplify4.7s

Counts
54 → 54
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
070723
1145689
2587613
34328605
done5000605

prune220.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.1b
(/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0)))
0.1b
(/ (/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
37.8b
(sqrt (/ (/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
72×add-sqr-sqrt
63×add-cube-cbrt *-un-lft-identity
47×cbrt-prod
46×sqrt-prod
18×add-exp-log
16×div-inv
11×add-cbrt-cube
10×associate-/l*
7×cbrt-undiv div-exp associate-/r*
5×pow1 rem-sqrt-square
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sqrt-pow1 pow1/2 sqrt-div fma-udef associate-/l/
Counts
4 → 170
Calls
4 calls:
0.0ms
(fma z z (fma x x (* y y)))
10.0ms
(/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0)))
44.0ms
(/ (/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
24.0ms
(sqrt (/ (/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
62.0ms
(fma z z (fma x x (* y y)))
340.0ms
(/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0)))
262.0ms
(/ (/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
511.0ms
(sqrt (/ (/ (fma z z (fma x x (* y y))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

simplify1.1s

Counts
182 → 182
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02554978
14654639
219734237
done50014114

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2)))
0.2b
(* (sqrt (/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2)))) (sqrt (/ 1 (* (cbrt (cbrt 3.0)) (pow (cbrt 3.0) 2)))))
1.0b
(/ 1 (* (cbrt (cbrt 3.0)) (pow (cbrt 3.0) 2)))
37.9b
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
158×cbrt-prod
150×times-frac
146×add-sqr-sqrt
121×sqrt-prod
95×add-cube-cbrt *-un-lft-identity
66×unpow-prod-down
49×associate-*l*
30×add-exp-log
16×unswap-sqr
15×associate-/r*
13×unpow2 sqr-pow
11×add-cbrt-cube
10×pow1 associate-*r* prod-exp
9×div-exp
7×rem-sqrt-square
6×associate-/l*
5×sqrt-div div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×cbrt-undiv pow-to-exp sqrt-pow1 pow1/2 pow-prod-down pow-exp
2×pow-flip frac-2neg clear-num cbrt-unprod
1×frac-times pow1/3 sqrt-unprod associate-*r/ associate-*l/ *-commutative pow-prod-up inv-pow
Counts
4 → 268
Calls
4 calls:
11.0ms
(/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2)))
129.0ms
(* (sqrt (/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2)))) (sqrt (/ 1 (* (cbrt (cbrt 3.0)) (pow (cbrt 3.0) 2)))))
23.0ms
(/ 1 (* (cbrt (cbrt 3.0)) (pow (cbrt 3.0) 2)))
15.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2))))

series2.1s

Counts
4 → 10
Calls
4 calls:
774.0ms
(/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2)))
471.0ms
(* (sqrt (/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2)))) (sqrt (/ 1 (* (cbrt (cbrt 3.0)) (pow (cbrt 3.0) 2)))))
0.0ms
(/ 1 (* (cbrt (cbrt 3.0)) (pow (cbrt 3.0) 2)))
844.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt (pow (cbrt 3.0) 2))))

simplify1.5s

Counts
278 → 278
Iterations

Useful iterations: 2 (570.0ms)

IterNodesCost
03607801
16587379
227386965
done50016965

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.3b

regimes336.0ms

Accuracy

59.5% (8.1b remaining)

Error of 26.2b against oracle of 18.0b and baseline of 38.1b

bsearch205.0ms

Steps
ItersRangePoint
8
2.076897170420828e+65
8.513147127683243e+68
1.3138979852720737e+67
9
-2.154144417514084e-248
-4.713895385524712e-257
-2.0033564760002915e-248
10
-2.004514806375514e-194
-4.7948385983044623e-206
-2.6727131427269115e-197
9
-1.593392701854085e+123
-2.829049393529762e+117
-2.6686434086554147e+122

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03768
14868
25068
done5068

end0.0ms

sample899.0ms

Algorithm
intervals
Results
573.0ms8000×body80valid