Details

sample122.0ms

Algorithm

intervals

Results

51.0ms	210×	body	80	valid
16.0ms	256×	pre	80	true
14.0ms	19×	body	640	valid
12.0ms	12×	body	1280	valid
6.0ms	10×	body	320	valid
2.0ms	5×	body	160	valid

simplify916.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2067
4	2067
3	458
2	99
1	32
0	16

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2 i (+ beta alpha))
0.0b	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
1.5b	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
26.6b	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-cube-cbrt` `associate-/l/`
7×	`fma-def`
6×	`times-frac` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `pow1` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `flip3--` `flip--`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `fma-udef` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma 2 i (+ beta alpha))
0.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
25.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
19.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

series915.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma 2 i (+ beta alpha))
185.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
308.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
387.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	2013
3	2013
2	1545
1	429
0	148

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2 i (+ beta alpha))
0.0b	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
11.0b	(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
20.6b	(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
14×	`add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r*` `fma-udef`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma 2 i (+ beta alpha))
0.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
0.0ms	(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
16.0ms	(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma 2 i (+ beta alpha))
167.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
248.0ms	(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
225.0ms	(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

simplify1.1s

Counts

86 → 86

Iterations

Iter	Nodes
done	2011
3	2011
2	812
1	304
0	142

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0)))
2.7b	(log (fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0))
11.0b	(fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0)
20.6b	(/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

3.0ms	(exp (log (fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0)))
1.0ms	(log (fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0))
0.0ms	(fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0)
19.0ms	(/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

218.0ms	(exp (log (fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0)))
415.0ms	(log (fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0))
239.0ms	(fma (+ beta alpha) (/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0))) 1.0)
239.0ms	(/ (- beta alpha) (* (fma 2 i (+ beta alpha)) (+ (fma 2 i (+ beta alpha)) 2.0)))

simplify1.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	2000
3	2000
2	1385
1	367
0	156

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0))
0.2b	(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0)))
2.7b	(log (fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0))
11.0b	(fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

151×	`times-frac`
142×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
20×	`distribute-lft-out`
19×	`associate-/l*`
15×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1` `log-prod` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `exp-sum`
2×	`div-sub` `associate-/r/` `log-pow`
1×	`clear-num` `frac-2neg` `flip3-+` `rem-log-exp` `flip-+` `fma-udef` `rem-exp-log` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

21.0ms	(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0))
3.0ms	(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0)))
1.0ms	(log (fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0))
0.0ms	(fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0))
197.0ms	(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0)))
388.0ms	(log (fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0))
245.0ms	(fma (+ beta alpha) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (fma 2 i (+ beta alpha)) 2.0)) 1.0)

simplify1.8s

Counts

176 → 176

Iterations

Iter	Nodes
done	2006
3	2006
2	1771
1	619
0	275

prune2.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.5b

regimes473.0ms

Accuracy

0% (0.3b remaining)

Error of 12.8b against oracle of 12.5b and baseline of 12.8b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	6299×	body	80	valid
896.0ms	8000×	pre	80	true
518.0ms	596×	body	640	valid
449.0ms	527×	body	1280	valid
177.0ms	378×	body	320	valid
64.0ms	200×	body	160	valid