Details

sample41.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify575.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	119	31
3	593	31
done	5001	31

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

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))
3.9b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite143.0ms

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)
25.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
48.0ms	(/ (/ (/ (+ 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))
26.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
206.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
232.0ms	(/ (/ (/ (+ 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))
99.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify672.0ms

Counts

434 → 434

Iterations

Useful iterations: done (630.0ms)

Iter	Nodes	Cost
0	516	20618
1	1325	20002
done	5000	19199

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))) (fma 1.0 2.0 (+ alpha beta)))
0.1b	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta)))))
0.1b	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.9b	(/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

3610×	`times-frac`
2161×	`*-un-lft-identity`
1423×	`add-sqr-sqrt` `add-cube-cbrt`
369×	`distribute-lft-out`
246×	`associate-/l*`
146×	`associate-/r/`
89×	`div-inv`
64×	`add-exp-log`
63×	`flip3-+` `flip-+`
44×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/r*`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 1331

Calls

4 calls:

65.0ms	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))) (fma 1.0 2.0 (+ alpha beta)))
26.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta)))))
134.0ms	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
27.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))) (fma 1.0 2.0 (+ alpha beta)))
121.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta)))))
257.0ms	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
156.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify2.8s

Counts

1343 → 1343

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	1578	75417
1	4561	69723
done	5002	68932

prune3.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (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))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
76×	`sqrt-prod`
63×	`times-frac`
58×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
14×	`associate-/l*`
13×	`distribute-lft-out`
9×	`associate-/r*`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 157

Calls

4 calls:

21.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
30.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
8.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
146.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
71.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
74.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify926.0ms

Counts

169 → 169

Iterations

Useful iterations: done (920.0ms)

Iter	Nodes	Cost
0	213	4211
1	436	3844
2	1448	3707
done	5000	3692

prune594.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (fma 1.0 2.0 (+ alpha beta))) (/ (/ (/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
0.5b	(/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta)))))
0.8b	(/ (/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
3.2b	(/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

10566×	`times-frac`
6366×	`*-un-lft-identity`
4247×	`add-sqr-sqrt`
4006×	`add-cube-cbrt`
2640×	`sqrt-prod`
2302×	`associate-r`
1163×	`distribute-lft-out`
230×	`associate-/r/`
197×	`add-exp-log`
137×	`div-inv`
128×	`div-exp`
104×	`associate-/l*`
99×	`flip3-+` `flip-+`
65×	`add-cbrt-cube`
48×	`unswap-sqr`
40×	`associate-/r*`
36×	`prod-exp`
35×	`cbrt-undiv`
21×	`rec-exp` `1-exp`
13×	`associate-l`
10×	`cbrt-unprod`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 3313

Calls

4 calls:

1.6s	(* (/ 1 (fma 1.0 2.0 (+ alpha beta))) (/ (/ (/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
22.0ms	(/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta)))))
69.0ms	(/ (/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
25.0ms	(/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(* (/ 1 (fma 1.0 2.0 (+ alpha beta))) (/ (/ (/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
129.0ms	(/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta)))))
95.0ms	(/ (/ 1 (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
197.0ms	(/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify5.1s

Counts

3325 → 3325

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	3049	161887
done	5000	148051

prune13.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

68.4% (1.1b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.6b

bsearch106.0ms

Steps

Iters	Range		Point
7	4.797381651173176e+149	1.9695734553503963e+151	1.833222038499473e+151

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	86
1	36	86
done	36	86

end0.0ms

sample1.3s

Algorithm

intervals

Results

727.0ms	8000×	body	80	valid
216.0ms	8000×	pre	80	true