Details

sample150.0ms

Algorithm

intervals

Results

104.0ms

505×

body

valid

simplify5.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4998
4	2295
3	723
2	217
1	67
0	28

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
0.2b	(* 27.0 (* k j))
4.9b	(* (* t x) (* y 18.0))
5.4b	(* z (* (* t x) (* y 18.0)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

322×	`add-sqr-sqrt`
288×	`associate-r`
142×	`unswap-sqr`
138×	`prod-diff`
130×	`associate-l`
108×	`*-un-lft-identity`
104×	`add-cube-cbrt`
46×	`fma-neg`
39×	`pow1` `add-cbrt-cube` `add-exp-log`
25×	`*-commutative`
24×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--` `associate--r+`

Counts

4 → 360

Calls

4 calls:

1.2s	(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
55.0ms	(* 27.0 (* k j))
68.0ms	(* (* t x) (* y 18.0))
245.0ms	(* z (* (* t x) (* y 18.0)))

series935.0ms

Counts

4 → 12

Calls

4 calls:

753.0ms	(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
37.0ms	(* 27.0 (* k j))
49.0ms	(* (* t x) (* y 18.0))
95.0ms	(* z (* (* t x) (* y 18.0)))

simplify3.0s

Counts

372 → 372

Iterations

Iter	Nodes
done	5000
2	3954
1	1121
0	428

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 27.0 (* k j))
0.3b	(* (* (* t x) y) 18.0)
4.8b	(* (* t x) y)
5.4b	(* z (* (* (* t x) y) 18.0))

rewrite721.0ms

Algorithm

rewrite-expression-head

Rules

98×	`associate-l`
86×	`add-sqr-sqrt`
72×	`associate-r`
38×	`unswap-sqr`
37×	`pow1` `add-cbrt-cube` `add-exp-log`
26×	`*-un-lft-identity` `add-cube-cbrt`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`*-commutative`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 179

Calls

4 calls:

38.0ms	(* 27.0 (* k j))
188.0ms	(* (* (* t x) y) 18.0)
49.0ms	(* (* t x) y)
435.0ms	(* z (* (* (* t x) y) 18.0))

series192.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* 27.0 (* k j))
45.0ms	(* (* (* t x) y) 18.0)
45.0ms	(* (* t x) y)
62.0ms	(* z (* (* (* t x) y) 18.0))

simplify1.7s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
2	2354
1	649
0	245

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (* z x) (* (* t y) 18.0)) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
0.2b	(* (* t y) 18.0)
0.2b	(* 27.0 (* k j))
9.5b	(* (* z x) (* (* t y) 18.0))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

294×	`add-sqr-sqrt`
176×	`associate-r`
174×	`associate-l`
135×	`prod-diff`
123×	`unswap-sqr`
107×	`*-un-lft-identity`
101×	`add-cube-cbrt`
45×	`fma-neg`
35×	`pow1` `add-cbrt-cube` `add-exp-log`
24×	`*-commutative`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`difference-of-squares`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--` `associate--r+`

Counts

4 → 343

Calls

4 calls:

845.0ms	(- (* (* z x) (* (* t y) 18.0)) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
58.0ms	(* (* t y) 18.0)
49.0ms	(* 27.0 (* k j))
173.0ms	(* (* z x) (* (* t y) 18.0))

series896.0ms

Counts

4 → 12

Calls

4 calls:

747.0ms	(- (* (* z x) (* (* t y) 18.0)) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
43.0ms	(* (* t y) 18.0)
31.0ms	(* 27.0 (* k j))
75.0ms	(* (* z x) (* (* t y) 18.0))

simplify3.9s

Counts

355 → 355

Iterations

Iter	Nodes
done	5002
2	3501
1	1082
0	411

prune4.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))
0.2b	(* x (* y 18.0))
0.2b	(* 27.0 (* k j))
3.9b	(fma (* z t) (* x (* y 18.0)) (- (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

30×	`associate-r`
26×	`add-sqr-sqrt`
14×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`unswap-sqr`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`

Counts

4 → 90

Calls

4 calls:

1.0ms	(fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))
46.0ms	(* x (* y 18.0))
39.0ms	(* 27.0 (* k j))
1.0ms	(fma (* z t) (* x (* y 18.0)) (- (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

175.0ms	(fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))
36.0ms	(* x (* y 18.0))
23.0ms	(* 27.0 (* k j))
787.0ms	(fma (* z t) (* x (* y 18.0)) (- (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1213
1	411
0	176

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes2.9s

Accuracy

54.2% (1.8b remaining)

Error of 2.0b against oracle of 0.2b and baseline of 4.1b

bsearch525.0ms

Steps

Iters	Range		Point
8	1.5527117352057856e+75	1.1194713229601033e+78	4.287180086893717e+76
9	-1.2314991742055574e-91	-5.3981115325820594e-98	-7.4130880817628e-93

simplify38.0ms

Iterations

Iter	Nodes
done	67
1	67
0	45

end0.0ms

sample6.6s

Algorithm

intervals

Results

5.3s

16007×

body

valid