Details

sample326.0ms

Algorithm

intervals

Results

88.0ms	312×	body	80	valid
75.0ms	67×	body	1280	valid
72.0ms	58×	body	10240	exit
51.0ms	34×	body	640	valid
11.0ms	24×	body	320	valid
5.0ms	15×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1436
3	398
2	124
1	49
0	19

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma eps x x))
0.0b	(* x (+ -1 eps))
0.0b	(* x (+ -1 eps))
4.1b	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

316×	`add-sqr-sqrt`
241×	`*-un-lft-identity` `times-frac`
180×	`prod-diff`
127×	`add-cube-cbrt`
74×	`difference-of-squares`
44×	`fma-udef`
43×	`exp-sum`
36×	`difference-of-sqr-1`
25×	`distribute-lft-out--`
15×	`div-inv`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
7×	`add-log-exp`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `fma-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `div-sub` `associate--l+` `flip--` `associate--r-` `rem-exp-log`

Counts

4 → 270

Calls

4 calls:

2.0ms	(exp (fma eps x x))
14.0ms	(* x (+ -1 eps))
14.0ms	(* x (+ -1 eps))
43.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (fma eps x x))
53.0ms	(* x (+ -1 eps))
53.0ms	(* x (+ -1 eps))
165.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

simplify2.3s

Counts

282 → 282

Iterations

Iter	Nodes
done	5001
2	3334
1	1319
0	506

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

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:

21.0ms	(* (* x x) x)
1.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* (* x x) x)
51.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

simplify1.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	1580
3	616
2	267
1	122
0	55

prune176.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

5.0b	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
8.3b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
8.3b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
8.3b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

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

series347.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))
117.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
89.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
106.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))

simplify1.6s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	1796
2	441
1	156
0	77

prune374.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 4 expressions with local error:

8.3b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
8.3b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
8.3b	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
8.3b	(cbrt (* (* (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x)))) (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))) (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow3` `rem-cbrt-cube`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
1.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
28.0ms	(cbrt (* (* (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x)))) (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))) (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
89.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
97.0ms	(cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))
102.0ms	(cbrt (* (* (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x)))) (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))) (cbrt (fma (* (* x x) x) 2/3 (- 2 (* x x))))))

simplify1.8s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	1282
2	377
1	152
0	77

prune418.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes121.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.4b

bsearch269.0ms

Steps

Iters	Range		Point
8	0.006928851504795399	123.90859695911298	1.9890182023189888

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample12.0s

Algorithm

intervals

Results

4.4s	1955×	body	10240	exit
2.9s	9896×	body	80	valid
2.4s	1760×	body	1280	valid
1.3s	1227×	body	640	valid
445.0ms	616×	body	320	valid
234.0ms	342×	body	160	valid