Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	56×	body	1280	valid
8.0ms	45×	body	640	valid
6.0ms	124×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	11×	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: 30.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite61.0ms

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:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
45.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series130.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(+ 1.0 (exp (* -2.0 x)))
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

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

prune255.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))
7.8b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite9.0ms

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)))))
7.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
38.0ms	(* 0.33333333333333337 (pow x 3))
95.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify200.0ms

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

prune156.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
2.8b	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

164×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
98×	`times-frac`
59×	`log-prod`
56×	`exp-sum`
26×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `difference-of-squares`
3×	`fma-def` `associate-/l*`
2×	`sub-neg` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `log-div` `flip3--` `frac-2neg` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log` `flip--`

Counts

4 → 218

Calls

4 calls:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
89.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
45.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series220.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(+ 1.0 (exp (* -2.0 x)))
82.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
80.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	537	2939
1	1511	2129
2	5001	1740

prune360.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 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)))))
31.5b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
7.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
8.0ms	(/ 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))

series389.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
72.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
45.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
225.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	382	1272
1	1331	1133
2	5002	1081

prune281.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes249.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.1b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

426.0ms	1693×	body	1280	valid
213.0ms	1244×	body	640	valid
194.0ms	4112×	body	80	valid
81.0ms	649×	body	320	valid
26.0ms	302×	body	160	valid