Details

sample25.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	119	31
3	586	31
4	4387	31
done	5000	31

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
0.0b	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.8b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

736×	`times-frac`
551×	`*-un-lft-identity`
321×	`add-sqr-sqrt` `add-cube-cbrt`
115×	`distribute-lft-out`
72×	`associate-/l*`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`fma-def` `frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`associate-/r/`
1×	`+-commutative` `associate-+l+` `sum-log` `fma-udef`

Counts

4 → 422

Calls

4 calls:

6.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
24.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
47.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
18.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
152.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
163.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
86.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.4s

Counts

434 → 434

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	516	20618
1	1175	20002
2	3277	19166
done	5000	18557

prune882.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
0.0b	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b	(/ (expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.8b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
114×	`*-un-lft-identity`
72×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
2×	`associate-/r/`
1×	`+-commutative` `associate-+l+` `div-sub` `sum-log` `fma-udef` `expm1-udef`

Counts

4 → 173

Calls

4 calls:

5.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
26.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
11.0ms	(/ (expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
18.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
146.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
286.0ms	(/ (expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
86.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify747.0ms

Counts

185 → 185

Iterations

Useful iterations: done (740.0ms)

Iter	Nodes	Cost
0	262	6157
1	575	5900
2	1544	5496
done	5000	5357

prune525.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
0.5b	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
3.8b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.8b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

612×	`times-frac`
516×	`sqrt-prod`
421×	`*-un-lft-identity`
325×	`add-sqr-sqrt`
319×	`add-cube-cbrt`
53×	`associate-/l*`
51×	`distribute-lft-out`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1` `sqrt-div`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-undiv` `flip3-+` `flip-+` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`

Counts

4 → 456

Calls

4 calls:

35.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
16.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
7.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
7.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
115.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
55.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
54.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify1.9s

Counts

468 → 468

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	421	20141
1	930	17784
2	1768	16794
3	4486	16207
done	5000	16201

prune828.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ (sqrt (sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (sqrt (fma 1.0 2.0 (+ alpha beta))))) (/ (sqrt (sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (pow (sqrt (sqrt (fma 1.0 2.0 (+ alpha beta)))) 3)))
3.8b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.8b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.8b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

1515×	`sqrt-prod`
1152×	`add-sqr-sqrt`
795×	`times-frac`
280×	`*-un-lft-identity`
250×	`unswap-sqr`
244×	`associate-r`
208×	`add-cube-cbrt`
180×	`unpow-prod-down` `cube-prod`
94×	`associate-l`
40×	`sqr-pow`
36×	`distribute-lft-out`
28×	`add-exp-log`
16×	`add-cbrt-cube`
10×	`cube-mult` `unpow3` `div-exp`
9×	`pow1`
8×	`prod-exp`
6×	`sqrt-div`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
2×	`pow-to-exp` `pow-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 671

Calls

4 calls:

367.0ms	(* (/ (sqrt (sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (sqrt (fma 1.0 2.0 (+ alpha beta))))) (/ (sqrt (sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (pow (sqrt (sqrt (fma 1.0 2.0 (+ alpha beta)))) 3)))
7.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
7.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series563.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (/ (sqrt (sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (sqrt (fma 1.0 2.0 (+ alpha beta))))) (/ (sqrt (sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (pow (sqrt (sqrt (fma 1.0 2.0 (+ alpha beta)))) 3)))
49.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
265.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
51.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify1.5s

Counts

683 → 683

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	413	39555
1	1141	36642
2	3678	35132
done	5001	29292

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

regimes87.0ms

Accuracy

35.5% (1.6b remaining)

Error of 2.7b against oracle of 1.1b and baseline of 3.6b

bsearch61.0ms

Steps

Iters	Range		Point
9	3.346468434766734e+140	7.57674529381864e+146	7.494253796401252e+146

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	56
1	23	56
done	23	56

end0.0ms

sample611.0ms

Algorithm

intervals

Results

321.0ms	8000×	body	80	valid
92.0ms	8000×	pre	80	true