Details

sample319.0ms

Algorithm

intervals

Results

99.0ms	326×	body	80	valid
85.0ms	60×	body	10240	exit
64.0ms	54×	body	1280	valid
32.0ms	42×	body	640	valid
9.0ms	15×	body	320	valid
2.0ms	8×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2010
5	2010
4	1436
3	398
2	124
1	49
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (+ -1 eps)))
0.0b	(* x (+ -1 eps))
0.0b	(* x (+ -1 eps))
3.9b	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`flip3-+` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `fma-udef` `rem-exp-log`

Counts

4 → 78

Calls

4 calls:

5.0ms	(exp (* x (+ -1 eps)))
32.0ms	(* x (+ -1 eps))
13.0ms	(* x (+ -1 eps))
0.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(exp (* x (+ -1 eps)))
56.0ms	(* x (+ -1 eps))
54.0ms	(* x (+ -1 eps))
147.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

simplify1.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	2008
3	2008
2	917
1	284
0	111

prune555.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (* x x))
7.8b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

15.0ms	(* x (* x x))
0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series97.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(* x (* x x))
55.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify995.0ms

Counts

44 → 44

Iterations

Iter	Nodes
done	2018
4	2018
3	937
2	279
1	109
0	56

prune152.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

5.8b	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
5.8b	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
7.8b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
7.8b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

2.0ms	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
2.0ms	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
1.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
66.0ms	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
56.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
40.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	2004
4	2004
3	1174
2	310
1	107
0	57

prune333.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (exp (fma eps x x)))
0.0b	(* (- eps 1) x)
0.0b	(* (- eps 1) x)
3.2b	(- (+ (exp (* (- eps 1) x)) (+ (/ (exp (* (- eps 1) x)) eps) (/ 1 (exp (fma eps x x))))) (/ 1 (* eps (exp (fma eps x x)))))

rewrite931.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 172

Calls

4 calls:

12.0ms	(/ 1 (exp (fma eps x x)))
32.0ms	(* (- eps 1) x)
31.0ms	(* (- eps 1) x)
850.0ms	(- (+ (exp (* (- eps 1) x)) (+ (/ (exp (* (- eps 1) x)) eps) (/ 1 (exp (fma eps x x))))) (/ 1 (* eps (exp (fma eps x x)))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (exp (fma eps x x)))
31.0ms	(* (- eps 1) x)
38.0ms	(* (- eps 1) x)
225.0ms	(- (+ (exp (* (- eps 1) x)) (+ (/ (exp (* (- eps 1) x)) eps) (/ 1 (exp (fma eps x x))))) (/ 1 (* eps (exp (fma eps x x)))))

simplify1.6s

Counts

184 → 184

Iterations

Iter	Nodes
done	2007
3	2007
2	1668
1	577
0	238

prune988.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes105.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 16.2b

bsearch340.0ms

Steps

Iters	Range		Point
9	0.008390766330885046	8718.24681470488	100.06482820348397

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample12.2s

Algorithm

intervals

Results

3.7s	2056×	body	10240	exit
2.8s	9988×	body	80	valid
2.5s	1750×	body	1280	valid
1.7s	1266×	body	640	valid
864.0ms	621×	body	320	valid
126.0ms	328×	body	160	valid