Details

sample346.0ms

Algorithm

intervals

Results

127.0ms	56×	body	10240	exit
75.0ms	64×	body	1280	valid
64.0ms	316×	body	80	valid
43.0ms	48×	body	640	valid
10.0ms	17×	body	320	valid
5.0ms	11×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1565
3	414
2	123
1	49
0	19

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- -1 eps) x)
0.0b	(/ (exp (* (- -1 eps) x)) eps)
0.0b	(/ (exp (* x (+ eps -1))) eps)
2.9b	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* (- -1 eps) x)) eps) (exp (* (- -1 eps) x))))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
95×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
63×	`prod-diff`
55×	`times-frac`
41×	`associate--r+`
16×	`add-log-exp`
11×	`distribute-lft-out--`
10×	`add-cbrt-cube` `difference-of-squares`
9×	`distribute-lft-out`
8×	`exp-sum` `add-exp-log` `associate-/l*`
6×	`pow1` `associate-/r*` `diff-log`
5×	`associate-l` `div-inv`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `flip3--` `fma-neg` `frac-sub` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-r`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `associate-*l/` `flip-+`
1×	`pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `associate--r-` `unswap-sqr`

Counts

4 → 191

Calls

4 calls:

26.0ms	(* (- -1 eps) x)
13.0ms	(/ (exp (* (- -1 eps) x)) eps)
10.0ms	(/ (exp (* x (+ eps -1))) eps)
208.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* (- -1 eps) x)) eps) (exp (* (- -1 eps) x))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (- -1 eps) x)
49.0ms	(/ (exp (* (- -1 eps) x)) eps)
44.0ms	(/ (exp (* x (+ eps -1))) eps)
151.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* (- -1 eps) x)) eps) (exp (* (- -1 eps) x))))

simplify2.8s

Counts

203 → 203

Iterations

Iter	Nodes
done	5002
2	3314
1	1017
0	391

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) (* x 2/3) 2)
0.3b	(* x 2/3)
5.6b	(- (fma (* x x) (* x 2/3) 2) (* x x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `prod-diff` `insert-posit16` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 55

Calls

3 calls:

0.0ms	(fma (* x x) (* x 2/3) 2)
7.0ms	(* x 2/3)
5.0ms	(- (fma (* x x) (* x 2/3) 2) (* x x))

series203.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(fma (* x x) (* x 2/3) 2)
17.0ms	(* x 2/3)
62.0ms	(- (fma (* x x) (* x 2/3) 2) (* x x))

simplify2.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
3	2768
2	628
1	206
0	84

prune253.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) 2)
0.3b	(* x 2/3)
5.6b	(- (fma (* x x) (posit16->real (real->posit16 (* x 2/3))) 2) (* x x))
60.2b	(posit16->real (real->posit16 (* x 2/3)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `remove-posit16` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) 2)
5.0ms	(* x 2/3)
5.0ms	(- (fma (* x x) (posit16->real (real->posit16 (* x 2/3))) 2) (* x x))
0.0ms	(posit16->real (real->posit16 (* x 2/3)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(fma (* x x) (posit16->real (real->posit16 (* x 2/3))) 2)
29.0ms	(* x 2/3)
43.0ms	(- (fma (* x x) (posit16->real (real->posit16 (* x 2/3))) 2) (* x x))
17.0ms	(posit16->real (real->posit16 (* x 2/3)))

simplify2.3s

Counts

78 → 78

Iterations

Iter	Nodes
done	5009
3	2750
2	625
1	215
0	95

prune654.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 4 expressions with local error:

5.6b	(- (fma (* x x) (* x 2/3) 2) (* x x))
8.5b	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))
8.5b	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))
8.5b	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`cbrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
3×	`fma-neg` `pow1/3` `prod-diff`
1×	`sub-neg` `diff-log` `associate--l+` `fma-udef`

Counts

4 → 74

Calls

4 calls:

11.0ms	(- (fma (* x x) (* x 2/3) 2) (* x x))
5.0ms	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))
5.0ms	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))
5.0ms	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (fma (* x x) (* x 2/3) 2) (* x x))
124.0ms	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))
126.0ms	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))
106.0ms	(cbrt (- (fma (* x x) (* x 2/3) 2) (* x x)))

simplify2.4s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
3	3046
2	672
1	235
0	107

prune525.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes140.0ms

Accuracy

96% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.5b

bsearch215.0ms

Steps

Iters	Range		Point
6	0.9820002734449668	5.220773054910798	1.9334006562055708

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample12.1s

Algorithm

intervals

Results

4.6s	1901×	body	10240	exit
2.6s	1680×	body	1280	valid
2.2s	10104×	body	80	valid
1.7s	1287×	body	640	valid
441.0ms	644×	body	320	valid
123.0ms	320×	body	160	valid