Details

sample105.0ms

Algorithm

intervals

Results

38.0ms	212×	body	80	valid
14.0ms	256×	pre	80	true
13.0ms	18×	body	640	valid
12.0ms	12×	body	1280	valid
5.0ms	9×	body	320	valid
2.0ms	5×	body	160	valid

simplify685.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2315
3	458
2	99
1	32
0	16

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
1.2b	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
20.3b	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-/l/`
7×	`fma-def`
6×	`times-frac` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `fma-udef` `flip--`
2×	`cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `div-inv`
1×	`pow2` `distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow-plus` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

0.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
12.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
19.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
33.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series858.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
111.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
258.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
349.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify4.9s

Counts

107 → 107

Iterations

Iter	Nodes
3	8533
2	1757
1	493
0	175

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.7b

localize63.0ms

Local error

Found 4 expressions with local error:

10.6b	(/ (+ beta alpha) (* (cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))))
28.3b	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))
28.3b	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))
28.3b	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

39.0ms	(/ (+ beta alpha) (* (cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))))
1.0ms	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))
1.0ms	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))
1.0ms	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series1.2m

Counts

4 → 12

Calls

4 calls:

1.2m	(/ (+ beta alpha) (* (cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))))
410.0ms	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))
376.0ms	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))
434.0ms	(cbrt (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify1.1s

Counts

82 → 82

Iterations

Iter	Nodes
3	2685
2	927
1	349
0	145

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
10.4b	(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
16.2b	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/l*`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `swap-sqr` `associate-r` `associate-l*`
2×	`associate-/l/`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `pow-plus` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
11.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
0.0ms	(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
17.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series839.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
115.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
280.0ms	(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
293.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify1.7s

Counts

105 → 105

Iterations

Iter	Nodes
3	3458
2	1028
1	369
0	169

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0)))
4.5b	(log (fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0))
10.4b	(fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0)
16.2b	(/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

3.0ms	(exp (log (fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0)))
2.0ms	(log (fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0))
0.0ms	(fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0)
24.0ms	(/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha))))

series1.4s

Counts

4 → 12

Calls

4 calls:

355.0ms	(exp (log (fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0)))
435.0ms	(log (fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0))
385.0ms	(fma (+ alpha beta) (/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha)))) 1.0)
247.0ms	(/ (- beta alpha) (fma 2.0 (+ (fma i 2 beta) alpha) (* (+ (fma i 2 beta) alpha) (+ (fma i 2 beta) alpha))))

simplify874.0ms

Counts

97 → 97

Iterations

Iter	Nodes
3	3084
2	883
1	370
0	173

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

regimes280.0ms

Accuracy

12.7% (7.3b remaining)

Error of 11.3b against oracle of 4.0b and baseline of 12.3b

bsearch153.0ms

Steps

Iters	Range		Point
9	6.994450312263042e+191	3.1988988901785705e+198	9.569473321706742e+195

simplify8.0ms

Iterations

Iter	Nodes
2	36
1	36
0	32

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	6367×	body	80	valid
441.0ms	600×	body	640	valid
426.0ms	485×	body	1280	valid
373.0ms	8000×	pre	80	true
246.0ms	355×	body	320	valid
82.0ms	193×	body	160	valid