Details

sample110.0ms

Algorithm

intervals

Results

31.0ms	206×	body	80	valid
28.0ms	21×	body	640	valid
13.0ms	256×	pre	80	true
8.0ms	11×	body	1280	valid
8.0ms	17×	body	320	valid
0.0ms	1×	body	160	valid

simplify698.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.7b

localize37.0ms

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)))
0.7b	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
21.4b	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite91.0ms

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))))
13.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
37.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
39.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series854.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
95.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
291.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
331.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify4.7s

Counts

107 → 107

Iterations

Iter	Nodes
3	8699
2	1759
1	493
0	175

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.7b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
0.1b	(* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
0.7b	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))
3.1b	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)

rewrite430.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-cbrt-cube` `add-exp-log`
73×	`*-un-lft-identity`
69×	`prod-exp` `cbrt-unprod`
45×	`add-sqr-sqrt` `pow1`
44×	`cbrt-undiv` `times-frac` `div-exp`
27×	`associate-r` `associate-l`
25×	`add-cube-cbrt`
22×	`distribute-lft-out`
18×	`frac-times` `pow-prod-down`
12×	`associate-l/` `associate-r/`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`prod-diff`
2×	`flip3-+` `pow-plus` `*-commutative` `flip-+` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `fma-neg` `diff-log` `swap-sqr` `fma-udef` `flip--`

Counts

4 → 203

Calls

4 calls:

114.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
240.0ms	(* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
1.0ms	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))
66.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)

series5.2s

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
2.0s	(* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
2.6s	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))
380.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)

simplify1.7s

Counts

215 → 215

Iterations

Iter	Nodes
2	3760
1	970
0	324

prune4.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.7b

localize108.0ms

Local error

Found 4 expressions with local error:

0.7b	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))
3.1b	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
3.1b	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
3.1b	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)

rewrite478.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`prod-diff`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`
1×	`fma-udef`

Counts

4 → 68

Calls

4 calls:

0.0ms	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))
48.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
402.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
27.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)

series3.7s

Counts

4 → 12

Calls

4 calls:

2.5s	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))
336.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
410.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
432.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)

simplify931.0ms

Counts

80 → 80

Iterations

Iter	Nodes
3	2052
2	562
1	220
0	95

prune1.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.7b

localize46.0ms

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)))
12.1b	(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)
17.1b	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite20.0ms

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))))
6.0ms	(* (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)
13.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
100.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
260.0ms	(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)
231.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify1.8s

Counts

105 → 105

Iterations

Iter	Nodes
3	3445
2	999
1	369
0	169

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.7b

regimes280.0ms

Accuracy

0% (0.3b remaining)

Error of 12.6b against oracle of 12.3b and baseline of 12.6b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
2	33
1	33
0	26

end0.0ms

sample3.2s

Algorithm

intervals

Results

991.0ms	6330×	body	80	valid
879.0ms	8000×	pre	80	true
493.0ms	527×	body	1280	valid
397.0ms	599×	body	640	valid
168.0ms	363×	body	320	valid
51.0ms	181×	body	160	valid