Details

sample109.0ms

Algorithm

intervals

Results

35.0ms	204×	body	80	valid
15.0ms	17×	body	1280	valid
13.0ms	256×	pre	80	true
9.0ms	12×	body	640	valid
8.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
4	2469
3	468
2	104
1	32
0	16

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize43.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
0.3b	(/ (- beta alpha) (+ 2.0 (+ (fma 2 i alpha) beta)))
1.8b	(fma (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) (/ (- beta alpha) (+ 2.0 (+ (fma 2 i alpha) beta))) 1.0)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
41×	`times-frac`
37×	`add-sqr-sqrt`
28×	`distribute-lft-out`
25×	`add-cube-cbrt`
9×	`associate-/r` `associate-/l`
7×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/r/` `associate-/l/`
3×	`expm1-log1p-u` `pow1` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`flip3--` `div-sub` `fma-udef` `flip--`

Counts

3 → 109

Calls

3 calls:

24.0ms	(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
45.0ms	(/ (- beta alpha) (+ 2.0 (+ (fma 2 i alpha) beta)))
1.0ms	(fma (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) (/ (- beta alpha) (+ 2.0 (+ (fma 2 i alpha) beta))) 1.0)

series349.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
95.0ms	(/ (- beta alpha) (+ 2.0 (+ (fma 2 i alpha) beta)))
159.0ms	(fma (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) (/ (- beta alpha) (+ 2.0 (+ (fma 2 i alpha) beta))) 1.0)

simplify1.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	5010
2	1414
1	444
0	180

prune716.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ alpha beta) (fma i 2 (+ alpha beta)))
0.3b	(/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0))
1.8b	(fma (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
4.3b	(log (fma (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
32×	`times-frac`
25×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/l*`
8×	`add-cbrt-cube`
7×	`associate-/r*`
5×	`pow1` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`log-prod`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `rem-log-exp` `log-pow` `fma-udef` `flip--`

Counts

4 → 111

Calls

4 calls:

31.0ms	(/ (+ alpha beta) (fma i 2 (+ alpha beta)))
15.0ms	(/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0))
0.0ms	(fma (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
1.0ms	(log (fma (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))

series772.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ alpha beta) (fma i 2 (+ alpha beta)))
112.0ms	(/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0))
279.0ms	(fma (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
287.0ms	(log (fma (/ (+ alpha beta) (fma i 2 (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))

simplify1.2s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
2	1452
1	493
0	214

prune744.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0))
0.5b	(/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta)))
1.8b	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
4.3b	(log (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
113×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
22×	`associate-/r*`
18×	`add-exp-log` `distribute-lft-out`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `associate-/l*`
6×	`pow1` `div-inv`
5×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`flip3--` `div-sub` `rem-log-exp` `log-pow` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

4 → 174

Calls

4 calls:

21.0ms	(/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0))
11.0ms	(/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta)))
0.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
1.0ms	(log (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))

series470.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0))
119.0ms	(/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta)))
107.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
136.0ms	(log (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))

simplify1.8s

Counts

186 → 186

Iterations

Iter	Nodes
done	5001
2	2003
1	686
0	286

prune986.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize68.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
1.8b	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
1.8b	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
4.3b	(log (cbrt (* (* (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0) (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)) (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`log-pow`
1×	`cbrt-prod` `pow1/3` `rem-log-exp`

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
0.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
0.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
12.0ms	(log (cbrt (* (* (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0) (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)) (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
78.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
109.0ms	(fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)
138.0ms	(log (cbrt (* (* (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0) (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0)) (fma (/ 1 (/ (fma i 2 (+ alpha beta)) (+ alpha beta))) (/ (- beta alpha) (+ (fma i 2 (+ alpha beta)) 2.0)) 1.0))))

simplify2.8s

Counts

62 → 62

Iterations

Iter	Nodes
done	5004
4	3180
3	612
2	178
1	91
0	56

prune430.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

regimes227.0ms

Accuracy

11.4% (6.8b remaining)

Error of 11.8b against oracle of 5.0b and baseline of 12.7b

bsearch109.0ms

Steps

Iters	Range		Point
6	1.3474617902510972e+184	1.1199388218060782e+185	8.434843859125862e+184

simplify10.0ms

Iterations

Iter	Nodes
done	42
1	42
0	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

985.0ms	6317×	body	80	valid
521.0ms	368×	body	320	valid
456.0ms	521×	body	1280	valid
436.0ms	8000×	pre	80	true
406.0ms	597×	body	640	valid
52.0ms	197×	body	160	valid