Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	118	31
3	515	31
4	2648	31
done	5001	31

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma alpha beta (+ alpha beta))
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))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
3.6b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

872×	`times-frac`
766×	`*-un-lft-identity`
361×	`add-sqr-sqrt` `add-cube-cbrt`
229×	`distribute-lft-out`
72×	`associate-/l*`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`fma-udef`

Counts

4 → 467

Calls

4 calls:

0.0ms	(fma alpha beta (+ alpha beta))
13.0ms	(/ (/ (+ 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))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
8.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(fma alpha beta (+ alpha beta))
143.0ms	(/ (/ (+ 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))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
86.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.2s

Counts

479 → 479

Iterations

Useful iterations: 2 (701.0ms)

Iter	Nodes	Cost
0	513	23562
1	1222	22869
2	3844	21908
done	5000	21908

prune978.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* alpha beta) (+ alpha beta))
0.0b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

872×	`times-frac`
766×	`*-un-lft-identity`
361×	`add-sqr-sqrt` `add-cube-cbrt`
229×	`distribute-lft-out`
72×	`associate-/l*`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`
2×	`associate-/r/`
1×	`+-commutative` `associate-+r+` `fma-def`

Counts

4 → 473

Calls

4 calls:

8.0ms	(+ (* alpha beta) (+ alpha beta))
78.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
107.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
72.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (* alpha beta) (+ alpha beta))
146.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
161.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
84.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.3s

Counts

485 → 485

Iterations

Useful iterations: 2 (737.0ms)

Iter	Nodes	Cost
0	529	24361
1	1305	22934
2	4274	21973
done	5000	21973

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma alpha beta (+ alpha beta))
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))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
3.6b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

872×	`times-frac`
766×	`*-un-lft-identity`
361×	`add-sqr-sqrt` `add-cube-cbrt`
229×	`distribute-lft-out`
72×	`associate-/l*`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`fma-udef`

Counts

4 → 467

Calls

4 calls:

0.0ms	(fma alpha beta (+ alpha beta))
12.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
46.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
8.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(fma alpha beta (+ alpha beta))
153.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
167.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
79.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.2s

Counts

479 → 479

Iterations

Useful iterations: 2 (685.0ms)

Iter	Nodes	Cost
0	513	23562
1	1222	22869
2	3844	21908
done	5000	21908

prune995.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize18.0ms

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))))
3.6b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.6b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite75.0ms

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:

26.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
9.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
4.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
119.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
49.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
57.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify2.4s

Counts

468 → 468

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	421	20141
1	944	17784
2	1931	16796
3	4972	16211
done	5000	16211

prune879.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes70.0ms

Accuracy

56.4% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch51.0ms

Steps

Iters	Range		Point
8	4.8266542845792594e+173	1.0069133071674746e+178	8.48564295701033e+177

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	46
1	24	46
done	24	46

end0.0ms

sample557.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
104.0ms	8000×	pre	80	true