Details

sample66.0ms

Algorithm

intervals

Results

25.0ms

279×

body

valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	30	37
1	62	30
2	132	30
3	376	29
4	1053	29
5	3174	29
done	5001	29

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)
0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
3.8b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
27.5b	(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)

rewrite7.0ms

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 3.13060547623 11.1667541262) z t) z a)
0.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
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:

95.0ms	(fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)
47.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
217.0ms	(/ 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)

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	145	1459
1	273	1441
2	633	1279
3	1691	1266
done	5001	1258

prune694.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
3.6b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
8.9b	(/ t (pow z 2))

rewrite51.0ms

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:

31.0ms	(+ 3.13060547623 (/ t (pow z 2)))
0.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
8.0ms	(/ t (pow z 2))

series174.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ 3.13060547623 (/ t (pow z 2)))
73.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
42.0ms	(/ t (pow z 2))

simplify1.4s

Counts

87 → 87

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	133	915
1	255	848
2	595	738
3	1907	738
done	5000	738

prune367.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize48.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
27.5b	(fma (* (/ 1 (* (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)))) (/ y (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)

rewrite8.0ms

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:

2.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
2.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
2.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(fma (* (/ 1 (* (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)))) (/ y (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)

series1.3s

Counts

4 → 12

Calls

4 calls:

236.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
214.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
214.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
683.0ms	(fma (* (/ 1 (* (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)))) (/ y (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)

simplify1.5s

Counts

61 → 61

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	92	1808
1	189	1775
2	472	1544
3	1530	1202
done	5000	1200

prune681.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize51.0ms

Local error

Found 4 expressions with local error:

4.4b	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
9.8b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
9.8b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
27.5b	(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (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)

rewrite23.0ms

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:

12.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
3.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
3.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (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)

series1.3s

Counts

4 → 12

Calls

4 calls:

282.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
142.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
152.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
699.0ms	(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (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)

simplify2.0s

Counts

93 → 93

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	159	2394
1	317	2226
2	782	2039
3	2277	1852
done	5000	1848

prune792.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.5b

regimes988.0ms

Accuracy

94.8% (1.4b remaining)

Error of 1.8b against oracle of 0.4b and baseline of 27.5b

bsearch389.0ms

Steps

Iters	Range		Point
8	58161725028366.24	1.3010483917410328e+17	1.2853526268829621e+17
7	-1.915538204409738e+58	-3.0309842811750995e+56	-3.0768108824136354e+56

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	41	65
1	62	56
done	62	56

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.0s

8886×

body

valid