Details

sample363.0ms

Algorithm

intervals

Results

142.0ms	70×	body	10240	exit
68.0ms	57×	body	1280	valid
66.0ms	332×	body	80	valid
50.0ms	40×	body	640	valid
9.0ms	12×	body	320	valid
2.0ms	6×	body	160	valid

simplify2.2s

Counts: 1 → 1

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.3b

localize100.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
31×	`flip3-+` `flip-+`
29×	`flip3--` `flip--`
19×	`add-sqr-sqrt` `un-div-inv`
18×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-cube-cbrt`
9×	`associate-r` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
2×	`difference-of-squares`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `distribute-lft-out--`

Counts

4 → 180

Calls

4 calls:

Slowest

44.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))
41.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
20.0ms	(* (- 1 eps) x)
17.0ms	(* (+ 1 eps) x)

series286.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))
38.0ms	(* (- 1 eps) x)
34.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
27.0ms	(* (+ 1 eps) x)

simplify1.7s

Counts: 192 → 192

prune3.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

8.6b	(fma 2/3 (* (* x x) x) (- 2 (* x x)))
0.1b	(* (* x x) x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`pow2` `expm1-log1p-u` `pow-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 42

Calls

2 calls:

Slowest

21.0ms	(* (* x x) x)
0.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

58.0ms	(* (* x x) x)
44.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

simplify1.5s

Counts: 48 → 48

prune561.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

3.1b	(fma (exp (- (* x eps) x)) (/ 1 eps) (- (exp (- (* x eps) x)) (/ (- (/ 1 eps) 1) (exp (fma x eps x)))))
0.0b	(/ (- (/ 1 eps) 1) (exp (fma x eps x)))
0.0b	(- (* x eps) x)
0.0b	(- (* x eps) x)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
86×	`times-frac`
71×	`*-un-lft-identity`
30×	`difference-of-squares`
26×	`add-cube-cbrt`
16×	`fma-udef`
15×	`difference-of-sqr-1` `exp-sum`
14×	`associate-/l*`
10×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`add-cbrt-cube` `prod-diff` `div-inv`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`sub-neg` `fma-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp`

Counts

4 → 141

Calls

4 calls:

Slowest

27.0ms	(/ (- (/ 1 eps) 1) (exp (fma x eps x)))
19.0ms	(- (* x eps) x)
15.0ms	(- (* x eps) x)
0.0ms	(fma (exp (- (* x eps) x)) (/ 1 eps) (- (exp (- (* x eps) x)) (/ (- (/ 1 eps) 1) (exp (fma x eps x)))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(fma (exp (- (* x eps) x)) (/ 1 eps) (- (exp (- (* x eps) x)) (/ (- (/ 1 eps) 1) (exp (fma x eps x)))))
49.0ms	(- (* x eps) x)
46.0ms	(- (* x eps) x)
32.0ms	(/ (- (/ 1 eps) 1) (exp (fma x eps x)))

simplify1.4s

Counts: 153 → 153

prune2.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes106.0ms

Accuracy

96% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.1b

bsearch306.0ms

end0.0ms

sample11.7s

Algorithm

intervals

Results

3.6s	1883×	body	10240	exit
3.1s	9879×	body	80	valid
2.6s	1780×	body	1280	valid
1.1s	1231×	body	640	valid
773.0ms	623×	body	320	valid
132.0ms	349×	body	160	valid