Details

sample78.0ms

Algorithm

intervals

Results

30.0ms

280×

body

valid

simplify5.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	3129
4	1167
3	380
2	130
1	62
0	30

prune75.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.4b

localize96.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma 3.13060547623 z 11.1667541262) z t)
0.1b	(fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
0.1b	(fma y (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) x)
29.5b	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 63

Calls

4 calls:

1.0ms	(fma (fma 3.13060547623 z 11.1667541262) z t)
1.0ms	(fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
1.0ms	(fma y (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) x)
7.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))

series2.0s

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma (fma 3.13060547623 z 11.1667541262) z t)
66.0ms	(fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
1.5s	(fma y (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) x)
441.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))

simplify4.2s

Counts

75 → 75

Iterations

Iter	Nodes
done	5004
3	2087
2	645
1	256
0	139

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ t z) z)
2.6b	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
44×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/l*`
7×	`add-cbrt-cube` `add-exp-log`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`clear-num` `frac-2neg` `fma-udef` `associate-/l/`

Counts

2 → 84

Calls

2 calls:

30.0ms	(/ (/ t z) z)
2.0ms	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

series155.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (/ t z) z)
107.0ms	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

simplify7.5s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
3	4747
2	893
1	360
0	164

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize126.0ms

Local error

Found 4 expressions with local error:

9.1b	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
9.1b	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
19.4b	(* (/ 1 (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))
25.6b	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
22×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 160

Calls

4 calls:

5.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
5.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
91.0ms	(* (/ 1 (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))
14.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

series1.7s

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
193.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
555.0ms	(* (/ 1 (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))
758.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

simplify9.1s

Counts

172 → 172

Iterations

Iter	Nodes
done	5000
3	4993
2	1796
1	587
0	227

prune3.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize216.0ms

Local error

Found 4 expressions with local error:

17.5b	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
17.5b	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
17.5b	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
24.1b	(* (/ 1 (* (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
22×	`associate-r` `add-cube-cbrt`
21×	`cbrt-prod`
20×	`prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 115

Calls

4 calls:

2.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
2.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
2.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
111.0ms	(* (/ 1 (* (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))

series1.3s

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
311.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
254.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
480.0ms	(* (/ 1 (* (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))

simplify5.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	2226
1	600
0	214

prune2.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes3.9s

Accuracy

96.4% (0.9b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 27.0b

bsearch545.0ms

Steps

Iters	Range		Point
9	22024.647857286567	2590629949647.022	2533004793734.77
8	-2.5854171655697825e+36	-4.020641651017867e+32	-1.0275167136366416e+34

simplify25.0ms

Iterations

Iter	Nodes
done	44
1	44
0	36

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.1s

8932×

body

valid