Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	213×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	13×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	105	27
3	433	26
4	1600	26
done	5000	26

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

2.1b

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

rewrite24.0ms

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×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`associate-/l/` `distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

3 → 92

Calls

3 calls:

11.0ms

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

9.0ms

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

0.0ms

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

series400.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms

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

77.0ms

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

247.0ms

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

simplify1.7s

Counts

101 → 101

Iterations

Useful iterations: 3 (924.0ms)

Iter	Nodes	Cost
0	176	1908
1	395	1852
2	1068	1716
3	3510	1713
done	5000	1713

prune304.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
8.2b	(fma (* (/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

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

series1.0s

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
303.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
305.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
82.0ms	(fma (* (/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify839.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (199.0ms)

Iter	Nodes	Cost
0	100	1728
1	225	1682
2	550	1503
3	1847	1164
done	5001	1164

prune290.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
7.9b	(fma (* (/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (* (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-div`
15×	`add-exp-log`
12×	`pow1` `*-un-lft-identity`
9×	`pow-flip`
8×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `pow1/3` `associate-/r/` `flip-+`
7×	`add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `distribute-lft-out`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 87

Calls

4 calls:

17.0ms	(/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
2.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
2.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0ms	(fma (* (/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (* (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
317.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
312.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
85.0ms	(fma (* (/ 1 (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (* (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.1s

Counts

99 → 99

Iterations

Useful iterations: 3 (464.0ms)

Iter	Nodes	Cost
0	189	2608
1	434	2458
2	998	2182
3	3214	2025
done	5000	2025

prune417.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
8.4b	(fma (/ (/ (+ alpha beta) (* (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `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:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

319.0ms	(cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
310.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
314.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
259.0ms	(fma (/ (/ (+ alpha beta) (* (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (cbrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (* (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify856.0ms

Counts

73 → 73

Iterations

Useful iterations: 3 (331.0ms)

Iter	Nodes	Cost
0	164	1993
1	362	1936
2	894	1744
3	2709	1638
done	5001	1638

prune385.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.2b

regimes204.0ms

Accuracy

14.3% (5.7b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 12.5b

bsearch91.0ms

Steps

Iters	Range		Point
9	2.4649659853731173e+247	8.03398024326001e+253	1.7553714861944655e+248

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	83
1	38	83
done	38	83

end0.0ms

sample823.0ms

Algorithm

intervals

Results

247.0ms	6353×	body	80	valid
131.0ms	8000×	pre	80	true
106.0ms	511×	body	1280	valid
88.0ms	572×	body	640	valid
45.0ms	375×	body	320	valid
14.0ms	189×	body	160	valid