Details

sample343.0ms

Algorithm

intervals

Results

121.0ms	60×	body	10240	exit
73.0ms	326×	body	80	valid
71.0ms	54×	body	1280	valid
39.0ms	42×	body	640	valid
9.0ms	15×	body	320	valid
3.0ms	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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.2b

localize46.0ms

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)))))

rewrite39.0ms

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)))
14.0ms	(* x (+ -1 eps))
19.0ms	(* x (+ -1 eps))
0.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (* x (+ -1 eps)))
35.0ms	(* x (+ -1 eps))
43.0ms	(* x (+ -1 eps))
165.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

simplify1.3s

Counts

90 → 90

Iterations

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

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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:

26.0ms	(* x (* x x))
1.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series95.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* x (* x x))
47.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify1.0s

Counts

44 → 44

Iterations

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

prune384.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

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)))

rewrite7.0ms

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)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
79.0ms	(sqrt (fma 2/3 (* x (* x x)) (- 2 (* x x))))
44.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
42.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify1.2s

Counts

66 → 66

Iterations

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

prune696.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize68.0ms

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)))))

rewrite73.0ms

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:

17.0ms	(exp (* x (+ -1 eps)))
27.0ms	(* x (+ -1 eps))
27.0ms	(* x (+ -1 eps))
1.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (* x (+ -1 eps)))
54.0ms	(* x (+ -1 eps))
50.0ms	(* x (+ -1 eps))
169.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

simplify1.0s

Counts

90 → 90

Iterations

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

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes175.0ms

Accuracy

96.5% (0.6b remaining)

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

bsearch253.0ms

Steps

Iters	Range		Point
9	0.008390766330885046	8718.24681470488	100.06482820348397

simplify8.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample12.3s

Algorithm

intervals

Results

4.0s	2056×	body	10240	exit
3.1s	9988×	body	80	valid
2.7s	1750×	body	1280	valid
1.6s	1266×	body	640	valid
380.0ms	621×	body	320	valid
125.0ms	328×	body	160	valid