Details

sample389.0ms

Algorithm

intervals

Results

158.0ms	76×	body	10240	exit
70.0ms	333×	body	80	valid
68.0ms	48×	body	1280	valid
41.0ms	42×	body	640	valid
22.0ms	32×	body	320	valid
2.0ms	5×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	2873
4	824
3	298
2	122
1	48
0	19

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.7b

localize80.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1 eps) x)
0.0b	(exp (- (* (+ 1 eps) x)))
0.0b	(exp (- (* (- 1 eps) x)))
2.4b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
18×	`un-div-inv`
13×	`add-sqr-sqrt`
12×	`exp-prod`
11×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`insert-posit16` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

16.0ms	(* (- 1 eps) x)
5.0ms	(exp (- (* (+ 1 eps) x)))
7.0ms	(exp (- (* (- 1 eps) x)))
46.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (- 1 eps) x)
24.0ms	(exp (- (* (+ 1 eps) x)))
18.0ms	(exp (- (* (- 1 eps) x)))
152.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify2.3s

Counts

166 → 166

Iterations

Iter	Nodes
2	3104
1	1142
0	371

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 2/3)
4.8b	(- (* (* (* x x) x) 2/3) (* x x))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `pow-plus` `associate-r` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`insert-posit16`
2×	`pow2` `associate-l` `pow-sqr` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `flip--` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

15.0ms	(* (* x x) x)
65.0ms	(* (* (* x x) x) 2/3)
92.0ms	(- (* (* (* x x) x) 2/3) (* x x))

series264.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (* x x) x)
66.0ms	(* (* (* x x) x) 2/3)
150.0ms	(- (* (* (* x x) x) 2/3) (* x x))

simplify5.1s

Counts

73 → 73

Iterations

Iter	Nodes
4	7619
3	1942
2	571
1	199
0	83

prune732.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 2/3)
0.8b	(log (exp (* (* (* x x) x) 2/3)))
4.8b	(- (log (exp (* (* (* x x) x) 2/3))) (* x x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`log-prod` `pow-plus` `associate-r` `pow-prod-up` `add-log-exp`
4×	`insert-posit16`
3×	`associate--l+` `log-pow`
2×	`pow2` `associate-l` `pow-sqr` `*-commutative`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `rem-log-exp` `pow3` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

25.0ms	(* (* x x) x)
57.0ms	(* (* (* x x) x) 2/3)
4.0ms	(log (exp (* (* (* x x) x) 2/3)))
10.0ms	(- (log (exp (* (* (* x x) x) 2/3))) (* x x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* x x) x)
75.0ms	(* (* (* x x) x) 2/3)
47.0ms	(log (exp (* (* (* x x) x) 2/3)))
160.0ms	(- (log (exp (* (* (* x x) x) 2/3))) (* x x))

simplify821.0ms

Counts

95 → 95

Iterations

Iter	Nodes
3	2206
2	639
1	230
0	104

prune902.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x x) x) 2/3)
0.9b	(log (* (cbrt (exp (* (* (* x x) x) 2/3))) (cbrt (exp (* (* (* x x) x) 2/3)))))
0.9b	(log (cbrt (exp (* (* (* x x) x) 2/3))))
4.8b	(- (log (cbrt (exp (* (* (* x x) x) 2/3)))) (* x x))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
17×	`add-exp-log`
13×	`log-prod` `add-cbrt-cube`
11×	`log-pow`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow-prod-down`
7×	`pow1/3` `prod-exp`
6×	`cbrt-prod` `associate--l+` `cbrt-unprod`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`rem-log-exp` `associate-r`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `associate-l` `*-commutative` `flip--` `difference-of-squares`

Counts

4 → 79

Calls

4 calls:

51.0ms	(* (* (* x x) x) 2/3)
20.0ms	(log (* (cbrt (exp (* (* (* x x) x) 2/3))) (cbrt (exp (* (* (* x x) x) 2/3)))))
10.0ms	(log (cbrt (exp (* (* (* x x) x) 2/3))))
24.0ms	(- (log (cbrt (exp (* (* (* x x) x) 2/3)))) (* x x))

series3.1s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* (* x x) x) 2/3)
968.0ms	(log (* (cbrt (exp (* (* (* x x) x) 2/3))) (cbrt (exp (* (* (* x x) x) 2/3)))))
1.0s	(log (cbrt (exp (* (* (* x x) x) 2/3))))
1.1s	(- (log (cbrt (exp (* (* (* x x) x) 2/3)))) (* x x))

simplify3.7s

Counts

91 → 91

Iterations

Iter	Nodes
3	4899
2	900
1	260
0	117

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes157.0ms

Accuracy

96.6% (0.5b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.6b

bsearch437.0ms

Steps

Iters	Range		Point
11	2.3824489835354504e-16	446233850.42817044	7.315544741537903

simplify29.0ms

Iterations

Iter	Nodes
4	63
3	63
2	61
1	52
0	34

end0.0ms

sample12.1s

Algorithm

intervals

Results

3.7s	1950×	body	10240	exit
3.3s	10087×	body	80	valid
2.9s	1789×	body	1280	valid
1.2s	1259×	body	640	valid
459.0ms	628×	body	320	valid
111.0ms	291×	body	160	valid