Details

sample74.0ms

Algorithm

intervals

Results

20.0ms	204×	body	80	valid
10.0ms	256×	pre	80	true
10.0ms	20×	body	1280	valid
10.0ms	24×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2315
3	458
2	99
1	32
0	16

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

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)))
12.5b	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
19.6b	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite33.0ms

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))))
7.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
0.0ms	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
24.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

531.0ms	(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)))
239.0ms	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
264.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify2.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	3884
2	1077
1	377
0	168

prune655.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
0.0b	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
1.2b	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
1.2b	(log (exp (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

33.0ms	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
35.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.0ms	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
3.0ms	(log (exp (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
101.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
213.0ms	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
218.0ms	(log (exp (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)))

simplify1.5s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1195
1	433
0	200

prune829.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.2b	(* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha))))
4.1b	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
4.1b	(log (exp (fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
27×	`times-frac`
24×	`add-cube-cbrt`
15×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
10×	`distribute-lft-out`
7×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `log-prod` `associate-/r` `prod-exp` `log-pow` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`exp-prod` `div-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `flip3-+` `flip3--` `associate-*l/` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `flip--` `associate-/l/`
1×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

37.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
34.0ms	(* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha))))
0.0ms	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
3.0ms	(log (exp (fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
106.0ms	(* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha))))
205.0ms	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
199.0ms	(log (exp (fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)))

simplify1.4s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1503
1	514
0	220

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (fma i 2 (+ beta alpha)))
0.0b	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.2b	(* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha))))
4.1b	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
36×	`times-frac`
30×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
10×	`distribute-lft-out`
7×	`pow1` `associate-/r` `associate-/l`
5×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `flip3--` `1-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `flip-+` `flip--` `associate-/l/`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 133

Calls

4 calls:

5.0ms	(/ 1 (fma i 2 (+ beta alpha)))
23.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
65.0ms	(* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha))))
1.0ms	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

series593.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ 1 (fma i 2 (+ beta alpha)))
122.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
124.0ms	(* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha))))
229.0ms	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

simplify1.4s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	1364
1	492
0	208

prune828.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

regimes288.0ms

Accuracy

0% (0.4b remaining)

Error of 12.1b against oracle of 11.8b and baseline of 12.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample2.3s

Algorithm

intervals

Results

984.0ms	6395×	body	80	valid
410.0ms	8000×	pre	80	true
321.0ms	547×	body	1280	valid
174.0ms	527×	body	640	valid
93.0ms	178×	body	160	valid
84.0ms	353×	body	320	valid