Details

Time bar (total: 14.7s)

sample44.0ms

Algorithm
intervals
Results
20.0ms295×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 3 (36.0ms)

IterNodesCost
03037
16230
213130
329429
476429
5216029
6499729
done500029

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
0.1b
(fma (fma z 3.13060547623 11.1667541262) z t)
1.3b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.7b
(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)

rewrite4.0ms

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 (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
0.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
2.0ms
(/ 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)

series959.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
30.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
118.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
751.0ms
(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)

simplify1.4s

Counts
71 → 71
Iterations

Useful iterations: 3 (529.0ms)

IterNodesCost
01391485
12701466
27911299
332211295
done50011295

prune415.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

2.7b
(fma (/ t (pow z 2)) y (fma 3.13060547623 y x))
7.7b
(/ t (pow z 2))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
8×associate-/r*
7×add-exp-log
4×add-cbrt-cube unpow2 sqr-pow
3×div-exp associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num fma-udef div-inv
Counts
2 → 61
Calls
2 calls:
0.0ms
(fma (/ t (pow z 2)) y (fma 3.13060547623 y x))
4.0ms
(/ t (pow z 2))

series85.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(fma (/ t (pow z 2)) y (fma 3.13060547623 y x))
26.0ms
(/ t (pow z 2))

simplify2.3s

Counts
67 → 67
Iterations

Useful iterations: 3 (355.0ms)

IterNodesCost
0111736
1191687
2693586
33464573
done5000573

prune209.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

7.7b
(/ t (pow z 2))
12.1b
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
12.1b
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
12.1b
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
9×add-exp-log cbrt-prod
8×associate-/r*
6×add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×pow1/3 div-exp associate-/l*
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 90
Calls
4 calls:
4.0ms
(/ t (pow z 2))
0.0ms
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
1.0ms
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
1.0ms
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))

series949.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ t (pow z 2))
311.0ms
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
309.0ms
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
306.0ms
(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))

simplify491.0ms

Counts
102 → 102
Iterations

Useful iterations: done (487.0ms)

IterNodesCost
01501398
12861328
210341194
done50011185

prune410.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
8.0b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
8.0b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.7b
(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (sqrt (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)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
3.0ms
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms
(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (sqrt (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)

series1.1s

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
103.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
104.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
759.0ms
(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (sqrt (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)

simplify1.6s

Counts
93 → 93
Iterations

Useful iterations: 3 (563.0ms)

IterNodesCost
01592368
13162013
29461874
340071852
done50001852

prune431.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes655.0ms

Accuracy

96.8% (0.9b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 27.2b

bsearch292.0ms

Steps
ItersRangePoint
8
1.2564570459059827e+18
1.9712404559034665e+21
1.497253047305232e+19
10
-6.6313037056385885e+35
-1.88993376364928e+24
-1.7503197233736622e+25

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
04167
16157
done6157

end0.0ms

sample912.0ms

Algorithm
intervals
Results
595.0ms8906×body80valid