Details

sample215.0ms

Algorithm

intervals

Results

56.0ms	313×	body	80	valid
54.0ms	63×	body	10240	exit
40.0ms	51×	body	1280	valid
21.0ms	44×	body	640	valid
8.0ms	25×	body	320	valid
2.0ms	8×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	2356
3	395
2	124
1	47
0	19

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(exp (- (* (- 1.0 eps) x)))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.0b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
77×	`exp-neg`
76×	`frac-times`
58×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
38×	`associate-*r/`
31×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
19×	`un-div-inv`
18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
7×	`add-exp-log`
6×	`exp-prod` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr` `rem-exp-log`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `times-frac` `fma-neg` `diff-log` `prod-diff` `neg-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 171

Calls

4 calls:

25.0ms	(* (+ 1.0 eps) x)
12.0ms	(exp (- (* (- 1.0 eps) x)))
71.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
57.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (+ 1.0 eps) x)
51.0ms	(exp (- (* (- 1.0 eps) x)))
70.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
296.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.5s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
1	1386
0	405

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 0.6666666666666667 (* x (* x x)) 2.0)
0.1b	(* x (* x x))
5.4b	(- (fma 0.6666666666666667 (* x (* x x)) 2.0) (* 1.0 (* x x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

0.0ms	(fma 0.6666666666666667 (* x (* x x)) 2.0)
17.0ms	(* x (* x x))
5.0ms	(- (fma 0.6666666666666667 (* x (* x x)) 2.0) (* 1.0 (* x x)))

series190.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(fma 0.6666666666666667 (* x (* x x)) 2.0)
40.0ms	(* x (* x x))
53.0ms	(- (fma 0.6666666666666667 (* x (* x x)) 2.0) (* 1.0 (* x x)))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
2	1386
1	250
0	87

prune270.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 1 expressions with local error:

5.4b	(fma (* x 0.6666666666666667) (* x x) (- 2.0 (* 1.0 (* x x))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (* x 0.6666666666666667) (* x x) (- 2.0 (* 1.0 (* x x))))

series69.0ms

Counts

1 → 3

Calls

1 calls:

69.0ms

(fma (* x 0.6666666666666667) (* x x) (- 2.0 (* 1.0 (* x x))))

simplify1.6s

Counts

13 → 13

Iterations

Iter	Nodes
done	5002
3	1287
2	196
1	55
0	27

prune75.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- eps 1.0))
0.0b	(* x (- eps 1.0))
0.0b	(/ (exp (* x (- eps 1.0))) eps)
2.0b	(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
184×	`prod-diff`
179×	`add-sqr-sqrt`
166×	`add-cube-cbrt`
136×	`times-frac`
112×	`exp-sum`
78×	`distribute-rgt-in` `distribute-lft-in`
25×	`associate-/l*`
24×	`distribute-neg-in`
21×	`distribute-lft-out`
13×	`sub-neg`
10×	`add-cbrt-cube` `associate-r`
9×	`add-exp-log` `add-log-exp`
8×	`pow1`
6×	`associate-l`
5×	`div-inv`
4×	`expm1-log1p-u` `fma-neg` `associate-*r/` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/r*` `flip3--` `flip--`
2×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-exp` `associate--l+` `flip-+`

Counts

4 → 311

Calls

4 calls:

18.0ms	(* x (- eps 1.0))
24.0ms	(* x (- eps 1.0))
44.0ms	(/ (exp (* x (- eps 1.0))) eps)
1.9s	(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

series255.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* x (- eps 1.0))
37.0ms	(* x (- eps 1.0))
37.0ms	(/ (exp (* x (- eps 1.0))) eps)
126.0ms	(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

simplify3.0s

Counts

323 → 323

Iterations

Iter	Nodes
done	5000
2	4467
1	1186
0	523

prune2.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes111.0ms

Accuracy

0% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 0.9b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.2s	10200×	body	80	valid
2.2s	1964×	body	10240	exit
1.9s	1723×	body	1280	valid
716.0ms	1223×	body	640	valid
320.0ms	607×	body	320	valid
68.0ms	333×	body	160	valid