Details

sample34.0ms

Algorithm

intervals

Results

11.0ms	208×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	15×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	8×	body	160	valid

simplify934.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (30.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.1b

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

2.5b

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

rewrite23.0ms

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))

8.0ms

(/ (- 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)

series379.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms

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

73.0ms

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

235.0ms

(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 (876.0ms)

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

prune303.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.0b	(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.1b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
11.5b	(fma (expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))))
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 (expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series574.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))))
75.0ms	(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
73.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
316.0ms	(fma (expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.6s

Counts

115 → 115

Iterations

Useful iterations: 3 (798.0ms)

Iter	Nodes	Cost
0	189	2171
1	413	2061
2	1102	1895
3	3559	1891
done	5001	1891

prune412.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize22.0ms

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))
11.5b	(fma (expm1 (log1p (* (/ 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))
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 (expm1 (log1p (* (/ 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)

series1.1s

Counts

4 → 12

Calls

4 calls:

314.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
309.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
309.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
140.0ms	(fma (expm1 (log1p (* (/ 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)

simplify928.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (213.0ms)

Iter	Nodes	Cost
0	102	1754
1	225	1682
2	544	1503
3	1814	1164
done	5000	1164

prune353.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma 2.0 i (+ alpha beta)))
0.5b	(cbrt (fma 2.0 i (+ alpha beta)))
0.5b	(cbrt (fma 2.0 i (+ alpha beta)))
8.6b	(fma (expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (- beta alpha) (* (cbrt (fma 2.0 i (+ alpha beta))) (cbrt (fma 2.0 i (+ alpha beta))))) (cbrt (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (fma 2.0 i (+ alpha beta)))
0.0ms	(cbrt (fma 2.0 i (+ alpha beta)))
1.0ms	(cbrt (fma 2.0 i (+ alpha beta)))
0.0ms	(fma (expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (- beta alpha) (* (cbrt (fma 2.0 i (+ alpha beta))) (cbrt (fma 2.0 i (+ alpha beta))))) (cbrt (fma 2.0 i (+ alpha beta)))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

258.0ms	(cbrt (fma 2.0 i (+ alpha beta)))
255.0ms	(cbrt (fma 2.0 i (+ alpha beta)))
256.0ms	(cbrt (fma 2.0 i (+ alpha beta)))
320.0ms	(fma (expm1 (log1p (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (- beta alpha) (* (cbrt (fma 2.0 i (+ alpha beta))) (cbrt (fma 2.0 i (+ alpha beta))))) (cbrt (fma 2.0 i (+ alpha beta)))) 1.0)

simplify1.7s

Counts

61 → 61

Iterations

Useful iterations: 4 (699.0ms)

Iter	Nodes	Cost
0	85	1204
1	176	1158
2	429	847
3	1104	792
4	3590	772
done	5001	772

prune278.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

regimes174.0ms

Accuracy

6.4% (6.2b remaining)

Error of 12.1b against oracle of 5.8b and baseline of 12.5b

bsearch102.0ms

Steps

Iters	Range		Point
6	3.167500755513364e+261	1.714049986786729e+262	5.677121898437386e+261
5	1.595531751984622e+164	3.8953984883944915e+164	3.754408854930521e+164

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	91
1	45	91
done	45	91

end0.0ms

sample828.0ms

Algorithm

intervals

Results

256.0ms	6332×	body	80	valid
130.0ms	8000×	pre	80	true
111.0ms	531×	body	1280	valid
94.0ms	583×	body	640	valid
43.0ms	362×	body	320	valid
15.0ms	192×	body	160	valid