Details

sample92.0ms

Algorithm

intervals

Results

58.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
4	2384
3	459
2	104
1	33
0	15

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
2.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite574.0ms

Algorithm

rewrite-expression-head

Rules

4338×	`*-un-lft-identity`
2696×	`times-frac`
2176×	`distribute-lft-out`
779×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
5×	`fma-def`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1234

Calls

4 calls:

113.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
91.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
230.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
29.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
187.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
205.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
141.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.5s

Counts

1246 → 1246

Iterations

Iter	Nodes
2	4034
1	1422
0	612

prune14.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
2.5b	(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

228×	`*-un-lft-identity`
123×	`times-frac`
118×	`distribute-lft-out`
50×	`add-sqr-sqrt` `add-exp-log`
43×	`add-cube-cbrt`
32×	`add-cbrt-cube`
22×	`div-exp`
21×	`associate-r`
20×	`associate-/r/`
15×	`flip3-+` `flip-+`
13×	`cbrt-undiv` `add-log-exp`
12×	`prod-exp` `associate-/l*`
11×	`associate-/r*`
10×	`div-inv`
7×	`associate-/l/`
6×	`pow1` `sum-log` `cbrt-unprod`
5×	`fma-def`
4×	`expm1-log1p-u` `frac-times` `associate-l` `associate-*l/` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv`
1×	`+-commutative` `associate-+l+` `pow-prod-down` `*-commutative`

Counts

4 → 226

Calls

4 calls:

88.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
43.0ms	(/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
187.0ms	(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
93.0ms	(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
176.0ms	(/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
204.0ms	(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
96.0ms	(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

simplify1.3s

Counts

238 → 238

Iterations

Iter	Nodes
2	3059
1	853
0	300

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ 2 (+ beta alpha)))
0.0b	(/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ (+ beta alpha) 1.0)))
2.5b	(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

243×	`*-un-lft-identity`
138×	`times-frac`
121×	`distribute-lft-out`
59×	`add-sqr-sqrt`
54×	`add-exp-log`
52×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
22×	`associate-/r/`
21×	`associate-r`
16×	`associate-/r*`
15×	`flip3-+` `flip-+` `associate-/l*`
14×	`cbrt-undiv`
12×	`prod-exp`
11×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 245

Calls

4 calls:

18.0ms	(/ 1 (+ 2 (+ beta alpha)))
56.0ms	(/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
146.0ms	(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ (+ beta alpha) 1.0)))
99.0ms	(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1 (+ 2 (+ beta alpha)))
207.0ms	(/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
237.0ms	(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ (+ beta alpha) 1.0)))
109.0ms	(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

simplify2.4s

Counts

257 → 257

Iterations

Iter	Nodes
2	3565
1	863
0	297

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (* (- 2 (+ beta alpha)) (+ (+ beta alpha) 2))) (/ (- 2 (+ beta alpha)) (+ (+ (+ beta alpha) 2) 1.0)))
0.0b	(/ (- 2 (+ beta alpha)) (+ (+ (+ beta alpha) 2) 1.0))
0.8b	(/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (* (- 2 (+ beta alpha)) (+ (+ beta alpha) 2)))
2.4b	(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2))

rewrite791.0ms

Algorithm

rewrite-expression-head

Rules

382×	`*-un-lft-identity`
205×	`times-frac`
163×	`distribute-lft-out`
104×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
61×	`add-cbrt-cube` `add-exp-log`
42×	`associate-r`
38×	`associate-l`
36×	`associate-/l*`
28×	`associate-/r/`
26×	`distribute-lft-out--`
25×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
13×	`flip3-+` `flip-+` `difference-of-squares`
12×	`associate-/r*`
9×	`frac-times`
8×	`div-inv`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`associate-l/` `associate-r/` `associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`unswap-sqr`
1×	`div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 316

Calls

4 calls:

489.0ms	(* (/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (* (- 2 (+ beta alpha)) (+ (+ beta alpha) 2))) (/ (- 2 (+ beta alpha)) (+ (+ (+ beta alpha) 2) 1.0)))
157.0ms	(/ (- 2 (+ beta alpha)) (+ (+ (+ beta alpha) 2) 1.0))
99.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (* (- 2 (+ beta alpha)) (+ (+ beta alpha) 2)))
32.0ms	(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2))

series686.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (* (- 2 (+ beta alpha)) (+ (+ beta alpha) 2))) (/ (- 2 (+ beta alpha)) (+ (+ (+ beta alpha) 2) 1.0)))
78.0ms	(/ (- 2 (+ beta alpha)) (+ (+ (+ beta alpha) 2) 1.0))
191.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (* (- 2 (+ beta alpha)) (+ (+ beta alpha) 2)))
134.0ms	(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2))

simplify2.8s

Counts

328 → 328

Iterations

Iter	Nodes
2	5971
1	1204
0	370

prune3.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes93.0ms

Accuracy

53% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.5b

bsearch106.0ms

Steps

Iters	Range		Point
10	3.3838621513037655e+153	2.0577599465650627e+167	1.8207254528844126e+167

simplify5.0ms

Iterations

Iter	Nodes
2	37
1	37
0	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
753.0ms	8000×	pre	80	true