Details

Time bar (total: 10.6s)

sample40.0ms

Algorithm
intervals
Results
19.0ms286×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
03037
16230
213130
328629
474429
5205729
6468929
done500029

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.1b
(fma (fma z 3.13060547623 11.1667541262) z t)
2.1b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.9b
(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 (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
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)

series903.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
29.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
117.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
721.0ms
(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)

simplify653.0ms

Counts
71 → 71
Iterations

Useful iterations: done (651.0ms)

IterNodesCost
01441442
12721423
26561262
318151252
done50021249

prune418.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y 3.13060547623 (fma (/ t (pow z 2)) y x))
4.6b
(fma (/ t (pow z 2)) y x)
7.6b
(/ t (pow z 2))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
8×add-exp-log associate-/r*
5×add-cbrt-cube
4×unpow2 sqr-pow
3×pow1 expm1-log1p-u div-exp log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
3 → 71
Calls
3 calls:
0.0ms
(fma y 3.13060547623 (fma (/ t (pow z 2)) y x))
0.0ms
(fma (/ t (pow z 2)) y x)
4.0ms
(/ t (pow z 2))

series136.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(fma y 3.13060547623 (fma (/ t (pow z 2)) y x))
52.0ms
(fma (/ t (pow z 2)) y x)
23.0ms
(/ t (pow z 2))

simplify667.0ms

Counts
80 → 80
Iterations

Useful iterations: 3 (236.0ms)

IterNodesCost
0122872
1198818
2542704
31538691
done5001691

prune246.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma y 3.13060547623 (fma (* t (/ 1 (pow z 2))) y x))
0.5b
(/ 1 (pow z 2))
4.6b
(fma (* t (/ 1 (pow z 2))) y x)
7.2b
(* t (/ 1 (pow z 2)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
55×add-sqr-sqrt
41×*-un-lft-identity
37×add-cube-cbrt
33×add-exp-log
28×associate-*r*
23×unpow-prod-down
12×div-exp
11×add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×associate-/r*
6×pow1 pow-to-exp rec-exp 1-exp pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* associate-/l*
2×cbrt-undiv cbrt-unprod fma-udef div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 144
Calls
4 calls:
0.0ms
(fma y 3.13060547623 (fma (* t (/ 1 (pow z 2))) y x))
4.0ms
(/ 1 (pow z 2))
0.0ms
(fma (* t (/ 1 (pow z 2))) y x)
15.0ms
(* t (/ 1 (pow z 2)))

series158.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(fma y 3.13060547623 (fma (* t (/ 1 (pow z 2))) y x))
17.0ms
(/ 1 (pow z 2))
52.0ms
(fma (* t (/ 1 (pow z 2))) y x)
23.0ms
(* t (/ 1 (pow z 2)))

simplify905.0ms

Counts
156 → 156
Iterations

Useful iterations: 2 (131.0ms)

IterNodesCost
01821666
13781275
27321035
320311035
done50011035

prune364.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y 3.13060547623 (+ (/ (* t y) (pow z 2)) x))
0.0b
(+ (/ (* t y) (pow z 2)) x)
13.7b
(/ (* t y) (pow z 2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log times-frac
12×fma-def *-un-lft-identity
10×add-sqr-sqrt add-cube-cbrt
9×unpow-prod-down
8×associate-/r* add-cbrt-cube
6×div-exp
5×add-log-exp
3×pow1 expm1-log1p-u prod-exp log1p-expm1-u unpow2 sqr-pow
2×cbrt-undiv pow-to-exp pow-exp div-inv
1×+-commutative frac-2neg flip3-+ clear-num sum-log cbrt-unprod flip-+ fma-udef distribute-lft-out associate-/l*
Counts
3 → 73
Calls
3 calls:
0.0ms
(fma y 3.13060547623 (+ (/ (* t y) (pow z 2)) x))
15.0ms
(+ (/ (* t y) (pow z 2)) x)
5.0ms
(/ (* t y) (pow z 2))

series144.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(fma y 3.13060547623 (+ (/ (* t y) (pow z 2)) x))
54.0ms
(+ (/ (* t y) (pow z 2)) x)
31.0ms
(/ (* t y) (pow z 2))

simplify1.9s

Counts
82 → 82
Iterations

Useful iterations: 3 (676.0ms)

IterNodesCost
0118840
1266785
2886687
34708657
done5000657

prune224.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes694.0ms

Accuracy

95.9% (1.1b remaining)

Error of 1.4b against oracle of 0.3b and baseline of 26.7b

bsearch129.0ms

Steps
ItersRangePoint
3
523651629958845.9
721716784511977.2
706881567136002.4
5
-1.5939472764859622e+18
-4.5045000713410016e+17
-1.5611661787177866e+18

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03665
14453
done4453

end0.0ms

sample918.0ms

Algorithm
intervals
Results
614.0ms8872×body80valid