Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	46×	body	1280	valid
7.0ms	40×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	17×	body	160	valid

simplify64.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.0b

Counts

2 → 1

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))))
4.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite28.0ms

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:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
12.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series140.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
40.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
84.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (38.0ms)

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

prune226.0ms

Filtered

150 candidates to 86 candidates (57.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	3	151

Merged error: 0b

Counts

151 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
4.6b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

1732×	`times-frac`
1496×	`*-un-lft-identity`
1023×	`add-sqr-sqrt`
1001×	`sqrt-prod`
996×	`add-cube-cbrt`
585×	`prod-diff`
249×	`distribute-lft-out`
195×	`fma-neg`
86×	`sqrt-div`
84×	`associate-/r/`
43×	`flip3-+` `flip-+`
42×	`div-inv`
30×	`associate-/l*`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `hypot-def` `associate-/l/` `distribute-lft-out--`

Counts

4 → 1110

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
21.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
89.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
44.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
73.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
87.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify235.0ms

Algorithm

egg-herbie

Counts

1122 → 1122

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1613	25952
1	5001	17156

prune1.0s

Filtered

1122 candidates to 310 candidates (27.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1122	0	1122
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	1122	3	1125

Merged error: 0b

Counts

1125 → 3

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))
8.4b	(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:

1.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
6.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
37.0ms	(* 0.33333333333333337 (pow x 3))
103.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify196.0ms

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

prune143.0ms

Filtered

62 candidates to 43 candidates (69.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	62	3	65

Merged error: 0b

Counts

65 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (* -2.0 x)) 3)
0.0b	(* (exp (* -2.0 x)) (exp (* -2.0 x)))
4.6b	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
4.9b	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
13×	`add-sqr-sqrt` `exp-prod` `exp-to-pow`
12×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`add-exp-log` `expm1-log1p-u` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `pow-pow` `cube-prod` `swap-sqr` `associate-r` `associate-l`
1×	`pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-plus` `fma-neg` `diff-log` `unpow3` `prod-diff` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

3.0ms	(pow (exp (* -2.0 x)) 3)
6.0ms	(* (exp (* -2.0 x)) (exp (* -2.0 x)))
6.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
1.0ms	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (- 1.0))

series408.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (exp (* -2.0 x)) 3)
30.0ms	(* (exp (* -2.0 x)) (exp (* -2.0 x)))
75.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
266.0ms	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	370	778
1	1878	666
2	5002	648

prune234.0ms

Filtered

105 candidates to 63 candidates (60.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	105	3	108

Merged error: 0b

Counts

108 → 3

regimes223.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	38
1	44	38

end0.0ms

sample999.0ms

Algorithm

intervals

Results

423.0ms	1750×	body	1280	valid
198.0ms	1186×	body	640	valid
129.0ms	4110×	body	80	valid
70.0ms	621×	body	320	valid
24.0ms	333×	body	160	valid