Details

sample76.0ms

Algorithm

intervals

Results

20.0ms	208×	body	80	valid
8.0ms	256×	pre	80	true
8.0ms	15×	body	1280	valid
6.0ms	15×	body	640	valid
4.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	15	405
1	31	405
2	106	380
3	478	355
4	2747	355
done	5000	355

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))

0.0b

(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))

2.3b

(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
7×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`distribute-lft-out--` `difference-of-squares` `associate-/l/`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `fma-udef` `flip--`

Counts

3 → 92

Calls

3 calls:

14.0ms

(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))

25.0ms

(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))

0.0ms

(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series549.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms

(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))

110.0ms

(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))

338.0ms

(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.7s

Counts

101 → 101

Iterations

Useful iterations: 2 (407.0ms)

Iter	Nodes	Cost
0	176	33186
1	406	30534
2	1725	30157
done	5002	30157

prune691.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
9.1b	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

6.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
6.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
6.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
1.0ms	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

477.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
404.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
445.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
135.0ms	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	100	30582
1	224	27140
2	603	26385
3	2631	23975
done	5001	22679

prune640.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
9.4b	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (* (cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`sqrt-div`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

7.0ms	(cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
6.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
7.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
1.0ms	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (* (cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

429.0ms	(cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))
420.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
467.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
113.0ms	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (* (cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta))))) (cbrt (sqrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify3.9s

Counts

73 → 73

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	153	34678
1	328	31271
2	881	30461
3	3573	29731
done	5001	28667

prune741.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.6b	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
8.4b	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (* (cbrt (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (cbrt (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
4.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
3.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.0ms	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (* (cbrt (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (cbrt (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

439.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
443.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
395.0ms	(cbrt (+ 2.0 (fma 2.0 i (+ alpha beta))))
147.0ms	(fma (* (/ 1 (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (/ (+ alpha beta) (* (cbrt (* (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))) (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))) (cbrt (cbrt (+ 2.0 (fma 2.0 i (+ alpha beta)))))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify3.0s

Counts

70 → 70

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	101	32582
1	228	29140
2	609	28385
3	2722	27905
done	5002	26519

prune759.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.5b

regimes363.0ms

Accuracy

13.7% (5.9b remaining)

Error of 11.9b against oracle of 5.9b and baseline of 12.8b

bsearch126.0ms

Steps

Iters	Range		Point
9	2.5571677378596085e+141	6.851744006698495e+147	3.5065776138048876e+145

simplify16.0ms

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	34	1169
1	41	1169
done	41	1169

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	6316×	body	80	valid
293.0ms	8000×	pre	80	true
290.0ms	519×	body	1280	valid
271.0ms	582×	body	640	valid
94.0ms	385×	body	320	valid
31.0ms	198×	body	160	valid