Details

sample73.0ms

Algorithm

intervals

Results

37.0ms

258×

body

valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2165
3	512
2	154
1	62
0	29

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.5b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
3.0b	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
20.8b	(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
104×	`add-sqr-sqrt` `*-un-lft-identity`
72×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`

Counts

4 → 163

Calls

4 calls:

0.0ms	(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
15.0ms	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
30.0ms	(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series736.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
42.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
132.0ms	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
418.0ms	(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify1.8s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	3550
1	700
0	293

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
11.7b	(sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))
11.7b	(sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))
20.8b	(/ (fma x (fma x (* (sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)) (sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
108×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
74×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
6×	`pow1` `sqrt-prod` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 173

Calls

4 calls:

12.0ms	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
1.0ms	(sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))
2.0ms	(sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))
23.0ms	(/ (fma x (fma x (* (sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)) (sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series672.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
105.0ms	(sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))
103.0ms	(sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))
360.0ms	(/ (fma x (fma x (* (sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)) (sqrt (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416))) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify1.3s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	3424
1	737
0	311

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x (fma 4.16438922228 x 78.6994924154) 137.519416416)
12.0b	(* (/ (* 1 (- (pow x 3) (pow 2.0 3))) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)) (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x))))
18.3b	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x)))
20.5b	(/ (* 1 (- (pow x 3) (pow 2.0 3))) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
32×	`add-cbrt-cube`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`*-un-lft-identity` `add-cube-cbrt`
14×	`div-exp` `prod-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
7×	`associate-l`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`1-exp` `associate-*r/`
2×	`clear-num` `frac-2neg` `unswap-sqr` `associate-/l/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `flip--`

Counts

4 → 115

Calls

4 calls:

0.0ms	(fma x (fma 4.16438922228 x 78.6994924154) 137.519416416)
105.0ms	(* (/ (* 1 (- (pow x 3) (pow 2.0 3))) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)) (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x))))
4.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x)))
82.0ms	(/ (* 1 (- (pow x 3) (pow 2.0 3))) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))

series879.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma x (fma 4.16438922228 x 78.6994924154) 137.519416416)
494.0ms	(* (/ (* 1 (- (pow x 3) (pow 2.0 3))) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)) (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x))))
248.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x)))
103.0ms	(/ (* 1 (- (pow x 3) (pow 2.0 3))) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))

simplify2.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	4000
1	642
0	236

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize119.0ms

Local error

Found 4 expressions with local error:

12.0b	(* (/ (/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x))))
12.2b	(/ (/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))
17.0b	(/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))
18.3b	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

3993×	`times-frac`
3533×	`add-sqr-sqrt`
2288×	`*-un-lft-identity`
1990×	`sqrt-prod`
1438×	`add-cube-cbrt`
1360×	`difference-of-squares`
1020×	`unpow-prod-down` `cube-prod`
928×	`associate-l`
680×	`sqr-pow`
425×	`distribute-lft-out--`
182×	`associate-/l*`
85×	`difference-cubes`
34×	`add-cbrt-cube` `add-exp-log`
18×	`div-inv`
15×	`associate-/r*`
14×	`cbrt-undiv` `div-exp` `unswap-sqr`
13×	`associate-r`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `div-sub` `associate-/l/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 2310

Calls

4 calls:

586.0ms	(* (/ (/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x))))
128.0ms	(/ (/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))
86.0ms	(/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))
5.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

485.0ms	(* (/ (/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x))))
104.0ms	(/ (/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))
223.0ms	(/ (- (pow x 3) (pow 2.0 3)) (sqrt (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))
237.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (fma 2.0 (+ x 2.0) (* x x)))

simplify2.8s

Counts

2322 → 2322

Iterations

Iter	Nodes
done	5002
1	3725
0	1272

prune12.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes437.0ms

Accuracy

94.8% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 25.1b

bsearch279.0ms

Steps

Iters	Range		Point
9	488997712.5877659	631776370996477.2	620615997107907.6
3	-6.376815652518718e+28	-5.267362834597857e+28	-6.168793249158557e+28

simplify6.0ms

Iterations

Iter	Nodes
done	42
1	42
0	36

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.2s

8010×

body

valid