Details

sample60.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize18.0ms

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))
4.3b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite157.0ms

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)
28.0ms	(/ (/ (+ 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))
27.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
218.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
280.0ms	(/ (/ (/ (+ 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))
110.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.5s

Counts

434 → 434

Iterations

Useful iterations: done (2.4s)

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

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 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))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
4.3b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

600×	`times-frac`
383×	`*-un-lft-identity`
279×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`associate-/l*`
52×	`distribute-lft-out`
23×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
6×	`sum-log`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`associate-/r/`
1×	`+-commutative` `associate-+r+` `fma-def`

Counts

4 → 368

Calls

4 calls:

92.0ms	(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
38.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
192.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
19.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
244.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
218.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
119.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.8s

Counts

380 → 380

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	529	18010
1	1230	17218
2	3843	16397
done	5000	15894

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ (* (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
4.6b	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.6b	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.6b	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
17×	`*-un-lft-identity`
12×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log` `flip3-+` `flip-+`
8×	`associate-/l/`
7×	`add-cbrt-cube`
6×	`times-frac` `associate-/r*` `sqrt-prod`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 85

Calls

4 calls:

35.0ms	(/ (* (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
7.0ms	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
6.0ms	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series591.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(/ (* (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
75.0ms	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
81.0ms	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
107.0ms	(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify2.4s

Counts

97 → 97

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	188	2561
1	465	2345
2	1237	2156
3	4081	2069
done	5000	2064

prune686.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
0.5b	(/ (/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
4.3b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.3b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

1482×	`times-frac`
816×	`*-un-lft-identity`
678×	`add-sqr-sqrt`
672×	`add-cube-cbrt`
552×	`sqrt-prod`
86×	`associate-/l*`
72×	`distribute-lft-out`
30×	`div-inv`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `sqrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`
1×	`sqrt-undiv`

Counts

4 → 688

Calls

4 calls:

35.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
100.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
28.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
16.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series1.3s

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
577.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
488.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
81.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify2.8s

Counts

700 → 700

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	881	41492
1	1910	38729
2	4640	37572
done	5002	36415

prune2.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.6b

regimes139.0ms

Accuracy

55.9% (1.2b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.9b

bsearch34.0ms

Steps

Iters	Range		Point
3	2.964554085996149e+160	3.844672684397608e+160	3.789665271997516e+160

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	23	37
done	23	37

end0.0ms

sample1.3s

Algorithm

intervals

Results

747.0ms	8000×	body	80	valid
257.0ms	8000×	pre	80	true