Details

sample85.0ms

Algorithm

intervals

Results

46.0ms

277×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1293
3	386
2	132
1	62
0	30

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)
0.1b	(fma (fma 3.13060547623 z 11.1667541262) z t)
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)
27.6b	(/ (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))

rewrite11.0ms

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` `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 → 59

Calls

4 calls:

0.0ms	(fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)
0.0ms	(fma (fma 3.13060547623 z 11.1667541262) z t)
0.0ms	(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)
8.0ms	(/ (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))

series1.8s

Counts

4 → 12

Calls

4 calls:

80.0ms	(fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)
38.0ms	(fma (fma 3.13060547623 z 11.1667541262) z t)
1.2s	(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)
443.0ms	(/ (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))

simplify4.9s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
3	2977
2	736
1	252
0	132

prune697.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

3.8b	(fma y (+ 3.13060547623 (/ t (* z z))) x)
8.6b	(/ t (* z z))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

0.0ms	(fma y (+ 3.13060547623 (/ t (* z z))) x)
6.0ms	(/ t (* z z))

series88.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(fma y (+ 3.13060547623 (/ t (* z z))) x)
25.0ms	(/ t (* z z))

simplify712.0ms

Counts

39 → 39

Iterations

Iter	Nodes
done	5001
2	714
1	148
0	65

prune340.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ t z) z)
3.8b	(fma (+ (/ (/ t z) z) 3.13060547623) y x)

rewrite12.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`clear-num` `frac-2neg` `fma-udef` `associate-/l/`

Counts

2 → 82

Calls

2 calls:

9.0ms	(/ (/ t z) z)
0.0ms	(fma (+ (/ (/ t z) z) 3.13060547623) y x)

series88.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (/ t z) z)
61.0ms	(fma (+ (/ (/ t z) z) 3.13060547623) y x)

simplify979.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1698
1	373
0	162

prune678.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (+ (* (* (cbrt (/ t z)) (cbrt (/ t z))) (/ (cbrt (/ t z)) z)) 3.13060547623) y x)
14.5b	(cbrt (/ t z))
14.5b	(cbrt (/ t z))
14.5b	(cbrt (/ t z))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 82

Calls

4 calls:

0.0ms	(fma (+ (* (* (cbrt (/ t z)) (cbrt (/ t z))) (/ (cbrt (/ t z)) z)) 3.13060547623) y x)
2.0ms	(cbrt (/ t z))
2.0ms	(cbrt (/ t z))
2.0ms	(cbrt (/ t z))

series327.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (+ (* (* (cbrt (/ t z)) (cbrt (/ t z))) (/ (cbrt (/ t z)) z)) 3.13060547623) y x)
85.0ms	(cbrt (/ t z))
85.0ms	(cbrt (/ t z))
86.0ms	(cbrt (/ t z))

simplify1.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
4	4689
3	1026
2	326
1	159
0	102

prune715.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes1.4s

Accuracy

97.1% (0.8b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 26.6b

bsearch748.0ms

Steps

Iters	Range		Point
9	1.0619574867451315e+27	3.808858172108706e+32	5.877344572473257e+29
9	-3.9628163174181575e+30	-3.9554820123738635e+22	-3.240660210645078e+30

simplify12.0ms

Iterations

Iter	Nodes
done	42
1	42
0	34

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.7s

8902×

body

valid