Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	40×	body	1280	valid
5.0ms	39×	body	640	valid
3.0ms	135×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	14×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize11.0ms

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))))
3.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite107.0ms

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)))
14.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
80.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series127.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1.0 (exp (* -2.0 x)))
38.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
74.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

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

prune259.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* -2.0 x)) 1.0)
0.0b	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
0.2b	(log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
3.6b	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

125×	`*-un-lft-identity`
96×	`log-pow`
90×	`exp-prod`
84×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
72×	`times-frac`
66×	`prod-diff`
22×	`fma-neg`
20×	`distribute-lft-out`
12×	`associate-/r/`
10×	`pow1`
7×	`flip3-+` `flip-+` `add-log-exp`
6×	`add-exp-log` `log-prod` `add-cbrt-cube` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate--l+` `associate-/l*`
2×	`distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log` `flip--` `difference-of-squares`

Counts

4 → 192

Calls

4 calls:

10.0ms	(+ (exp (* -2.0 x)) 1.0)
16.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
33.0ms	(log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
303.0ms	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

series161.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp (* -2.0 x)) 1.0)
33.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
40.0ms	(log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
74.0ms	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	466	2262
1	1376	1479
2	5001	1432

prune362.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

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))
9.8b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite17.0ms

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)))))
12.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
32.0ms	(* 0.33333333333333337 (pow x 3))
91.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify199.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

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

prune147.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes105.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample894.0ms

Algorithm

intervals

Results

350.0ms	1712×	body	1280	valid
162.0ms	1209×	body	640	valid
107.0ms	4133×	body	80	valid
61.0ms	659×	body	320	valid
16.0ms	287×	body	160	valid