Details

Time bar (total: 18.5s)

sample73.0ms

Algorithm
intervals
Results
36.0ms287×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
03037
16230
213230
338629
4130129
done500029

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma z 3.13060547623 11.1667541262) z t)
0.0b
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
2.3b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
25.5b
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
1.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
0.0ms
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
5.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series1.4s

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
125.0ms
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
158.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.1s
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

simplify2.4s

Counts
71 → 71
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01451496
12761478
28321320
339961308
done50001301

prune568.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z (fma z 3.13060547623 11.1667541262) t)
0.0b
(fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b)
2.3b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
25.5b
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b) x)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma z (fma z 3.13060547623 11.1667541262) t)
0.0ms
(fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b)
6.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b) x)

series1.4s

Counts
4 → 12
Calls
4 calls:
46.0ms
(fma z (fma z 3.13060547623 11.1667541262) t)
133.0ms
(fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b)
164.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.1s
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b) x)

simplify2.1s

Counts
71 → 71
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01451496
12761478
28321320
339961308
done50001301

prune507.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize48.0ms

Local error

Found 4 expressions with local error:

17.7b
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
17.7b
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
17.7b
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
25.5b
(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series1.6s

Counts
4 → 12
Calls
4 calls:
223.0ms
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
180.0ms
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
159.0ms
(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.1s
(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

simplify1.4s

Counts
61 → 61
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0911782
11841749
25181258
320931202
done50021200

prune600.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 3.13060547623 (/ t (pow z 2)))
4.0b
(/ t (pow z 2))
4.5b
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down
8×add-exp-log associate-/r*
5×add-cbrt-cube add-log-exp
4×unpow2 sqr-pow
3×pow1 expm1-log1p-u fma-def div-exp log1p-expm1-u associate-/l*
1×cbrt-undiv +-commutative pow-to-exp frac-2neg flip3-+ pow-exp clear-num sum-log flip-+ fma-udef div-inv distribute-lft-out
Counts
3 → 78
Calls
3 calls:
19.0ms
(+ 3.13060547623 (/ t (pow z 2)))
8.0ms
(/ t (pow z 2))
0.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)

series135.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ 3.13060547623 (/ t (pow z 2)))
24.0ms
(/ t (pow z 2))
64.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)

simplify646.0ms

Counts
87 → 87
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
0133915
1268848
21013738
done5000738

prune344.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes917.0ms

Accuracy

97.7% (0.6b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 27.8b

bsearch415.0ms

Steps
ItersRangePoint
9
1.3536085459735286e+44
2.162692372244929e+50
1.228915962873731e+45
10
-1.0775147056867349e+62
-1.5008917160976862e+47
-1.4587735366083961e+48

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03571
14155
done4155

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.7s8861×body80valid