Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	64×	body	1280	valid
6.0ms	40×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	15×	body	320	valid
0.0ms	7×	body	160	valid

simplify63.0ms

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: 29.7b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
54×	`prod-diff`
51×	`add-cube-cbrt`
49×	`times-frac`
18×	`fma-neg`
12×	`distribute-lft-out`
8×	`associate-/r/`
4×	`flip3-+` `flip-+` `div-inv`
3×	`add-log-exp`
2×	`difference-of-squares`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--`

Counts

1 → 89

Calls

1 calls:

12.0ms

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

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

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

simplify143.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	324	1294
1	894	902
2	4072	815
3	5001	754

prune127.0ms

Filtered

92 candidates to 39 candidates (42.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Merged error: 0.0b

Counts

93 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

142×	`*-un-lft-identity`
108×	`prod-diff`
106×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
86×	`times-frac`
59×	`log-prod`
56×	`exp-sum`
21×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `log-pow` `flip-+` `div-inv`
6×	`exp-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1`
2×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 166

Calls

2 calls:

19.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
13.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series158.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify166.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	463	2588
1	1133	1796
2	4498	1385
3	5001	1385

prune219.0ms

Filtered

172 candidates to 66 candidates (38.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	172	3	175

Merged error: 0.0b

Counts

175 → 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)))))
0.0b	(* 0.33333333333333337 (pow x 3))
8.9b	(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)))

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)))))
39.0ms	(* 0.33333333333333337 (pow x 3))
96.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify204.0ms

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

prune162.0ms

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: 0.0b

Counts

65 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (* -2.0 x)) 3)
0.0b	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
2.4b	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
2.5b	(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))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
27×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`distribute-lft-out`
19×	`unpow-prod-down` `cube-prod`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u`
3×	`pow-unpow` `pow-pow` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `distribute-rgt-out--` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow (exp (* -2.0 x)) 3)
12.0ms	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
8.0ms	(- (* (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))

series437.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (exp (* -2.0 x)) 3)
77.0ms	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
76.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
248.0ms	(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))

simplify81.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	454	1170
1	2072	1040
2	5001	1015

prune316.0ms

Filtered

121 candidates to 76 candidates (62.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	121	3	124

Merged error: 0.0b

Counts

124 → 3

regimes234.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample868.0ms

Algorithm

intervals

Results

369.0ms	1761×	body	1280	valid
166.0ms	1171×	body	640	valid
109.0ms	4134×	body	80	valid
57.0ms	603×	body	320	valid
20.0ms	331×	body	160	valid