Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	53×	body	1280	valid
5.0ms	38×	body	640	valid
3.0ms	135×	body	80	valid
2.0ms	23×	body	320	valid
0.0ms	7×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	31	5
3	54	5
4	119	5
5	333	5
6	1646	5
7	5001	5
done	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-exp-log` `add-cbrt-cube` `div-inv`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `distribute-lft-out--`

Counts

3 → 141

Calls

3 calls:

7.0ms	(+ 1.0 (exp (* -2.0 x)))
15.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
84.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series136.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
37.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
82.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	398	1645
1	1287	1235
2	5001	1212
done	5001	1212

prune260.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
29.1b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`sqrt-prod`
14×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `flip3-+` `div-exp` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `sum-log` `fma-udef` `inv-pow`

Counts

4 → 127

Calls

4 calls:

7.0ms	(+ 1.0 (exp (* -2.0 x)))
15.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
19.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series350.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ 1.0 (exp (* -2.0 x)))
70.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
46.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
217.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify41.0ms

Counts

139 → 139

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	378	1222
1	1335	1083
2	5001	1031
done	5001	1031

prune312.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
0.5b	(cbrt (pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3))
29.1b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)) (- 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
105×	`times-frac`
78×	`add-sqr-sqrt` `add-cube-cbrt`
64×	`sqrt-prod`
60×	`cbrt-prod`
54×	`unpow-prod-down` `cube-prod`
16×	`distribute-lft-out`
11×	`add-exp-log`
10×	`sqrt-div` `associate-/r/`
9×	`add-cbrt-cube`
7×	`pow1` `associate-/r*`
5×	`flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-flip` `div-exp` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rec-exp` `cbrt-div` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `1-exp` `clear-num` `rem-cbrt-cube` `fma-udef` `inv-pow`

Counts

4 → 211

Calls

4 calls:

19.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
19.0ms	(pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
19.0ms	(cbrt (pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3))
0.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)) (- 1.0))

series471.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
123.0ms	(pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
72.0ms	(cbrt (pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3))
224.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (pow (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)) (- 1.0))

simplify77.0ms

Counts

223 → 223

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	688	2474
1	2968	2166
2	5002	2048
done	5002	2048

prune403.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
0.1b	(* 0.33333333333333337 (pow x 3))
9.1b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`associate-r`
8×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
13.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
39.0ms	(* 0.33333333333333337 (pow x 3))
108.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify197.0ms

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	170	298
1	655	262
2	4021	262
3	5002	262
done	5002	262

prune149.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes218.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.9b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	49
1	39	49
done	39	49

end0.0ms

sample912.0ms

Algorithm

intervals

Results

347.0ms	1694×	body	1280	valid
180.0ms	1296×	body	640	valid
110.0ms	4086×	body	80	valid
54.0ms	606×	body	320	valid
18.0ms	318×	body	160	valid