Details

sample320.0ms

Algorithm

intervals

Results

120.0ms	61×	body	10240	exit
66.0ms	65×	body	1280	valid
59.0ms	319×	body	80	valid
37.0ms	48×	body	640	valid
10.0ms	17×	body	320	valid
4.0ms	10×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
5	3313
4	892
3	314
2	124
1	49
0	19

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
0.0b	(exp (- (* (- 1 eps) x)))
0.0b	(exp (- (* (+ 1 eps) x)))
1.2b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-l/` `associate-r/`
30×	`flip3-+` `flip-+`
28×	`flip3--` `flip--`
19×	`un-div-inv`
12×	`exp-prod`
11×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube`
5×	`associate-l` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log` `distribute-lft-out`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 170

Calls

4 calls:

48.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
15.0ms	(exp (- (* (- 1 eps) x)))
11.0ms	(exp (- (* (+ 1 eps) x)))
45.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
29.0ms	(exp (- (* (- 1 eps) x)))
24.0ms	(exp (- (* (+ 1 eps) x)))
145.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.5s

Counts

182 → 182

Iterations

Iter	Nodes
2	3105
1	1220
0	366

prune2.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 2/3 (* (* x x) x) 2)
0.1b	(* (* x x) x)
5.0b	(- (fma 2/3 (* (* x x) x) 2) (* x x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
6×	`*-un-lft-identity` `pow-plus` `pow-prod-up` `add-cube-cbrt`
5×	`add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `associate--l+` `*-commutative` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 65

Calls

3 calls:

0.0ms	(fma 2/3 (* (* x x) x) 2)
15.0ms	(* (* x x) x)
6.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))

series244.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(fma 2/3 (* (* x x) x) 2)
52.0ms	(* (* x x) x)
55.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))

simplify885.0ms

Counts

74 → 74

Iterations

Iter	Nodes
3	2095
2	537
1	214
0	84

prune632.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 2 (* x x))
0.3b	(* 2/3 x)
5.0b	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

rewrite21.0ms

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`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

10.0ms	(- 2 (* x x))
10.0ms	(* 2/3 x)
1.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(- 2 (* x x))
28.0ms	(* 2/3 x)
71.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

simplify4.8s

Counts

63 → 63

Iterations

Iter	Nodes
4	7194
3	1739
2	469
1	188
0	88

prune599.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2/3 (posit16->real (real->posit16 (* (* x x) x))) 2)
0.1b	(* (* x x) x)
5.0b	(- (fma 2/3 (posit16->real (real->posit16 (* (* x x) x))) 2) (* x x))
17.3b	(posit16->real (real->posit16 (* (* x x) x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `associate--l+` `*-commutative` `remove-posit16` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma 2/3 (posit16->real (real->posit16 (* (* x x) x))) 2)
15.0ms	(* (* x x) x)
8.0ms	(- (fma 2/3 (posit16->real (real->posit16 (* (* x x) x))) 2) (* x x))
1.0ms	(posit16->real (real->posit16 (* (* x x) x)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(fma 2/3 (posit16->real (real->posit16 (* (* x x) x))) 2)
46.0ms	(* (* x x) x)
52.0ms	(- (fma 2/3 (posit16->real (real->posit16 (* (* x x) x))) 2) (* x x))
64.0ms	(posit16->real (real->posit16 (* (* x x) x)))

simplify5.3s

Counts

88 → 88

Iterations

Iter	Nodes
4	8042
3	1760
2	518
1	220
0	95

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

regimes259.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.1b

bsearch288.0ms

Steps

Iters	Range		Point
10	1.6697130628152668	353170825925.37476	171.1161917239734

simplify25.0ms

Iterations

Iter	Nodes
4	59
3	59
2	57
1	48
0	31

end0.0ms

sample11.3s

Algorithm

intervals

Results

4.0s	1914×	body	10240	exit
2.4s	1818×	body	1280	valid
2.2s	9982×	body	80	valid
1.4s	1169×	body	640	valid
778.0ms	643×	body	320	valid
128.0ms	298×	body	160	valid