Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	56×	body	1280	valid
6.0ms	42×	body	640	valid
4.0ms	126×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	12×	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	1637	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: 30.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
4.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 124

Calls

2 calls:

7.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
18.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series123.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
85.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify171.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	370	1556
1	1140	1155
2	4951	1067
3	5001	1067

prune160.0ms

Filtered

130 candidates to 69 candidates (53.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	3	131

Merged error: 0.0b

Counts

131 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
9.8b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

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

series141.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* 0.33333333333333337 (pow x 3))
100.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify97.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	135	180
1	523	163
2	2591	163
3	5001	160

prune103.0ms

Filtered

45 candidates to 32 candidates (71.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	3	48

Merged error: 0.0b

Counts

48 → 3

localize11.0ms

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)))))
31.4b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite26.0ms

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))))
8.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
8.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series399.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
73.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
52.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
231.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	377	1270
1	1297	1133
2	5001	1081

prune251.0ms

Filtered

141 candidates to 85 candidates (60.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	141	3	144

Merged error: 0.0b

Counts

144 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp (* -2.0 x)) (exp (* -2.0 x)))
4.4b	(- (* 1.0 1.0) (* (exp (* -2.0 x)) (exp (* -2.0 x))))
4.4b	(- 1.0 (exp (* -2.0 x)))
4.6b	(fma (/ 2.0 (- (* 1.0 1.0) (* (exp (* -2.0 x)) (exp (* -2.0 x))))) (- 1.0 (exp (* -2.0 x))) (- 1.0))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

316×	`add-sqr-sqrt`
234×	`prod-diff`
218×	`*-un-lft-identity`
188×	`add-cube-cbrt`
124×	`associate-l`
118×	`associate-r`
108×	`swap-sqr`
96×	`exp-prod`
48×	`*-commutative` `unswap-sqr`
26×	`difference-of-squares`
22×	`pow-prod-down` `add-log-exp`
18×	`fma-neg` `pow-sqr` `pow-prod-up`
14×	`exp-to-pow`
11×	`pow1`
8×	`add-exp-log`
6×	`add-cbrt-cube` `distribute-lft-out--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow2` `pow-plus` `cbrt-unprod` `fma-udef`

Counts

4 → 407

Calls

4 calls:

20.0ms	(* (exp (* -2.0 x)) (exp (* -2.0 x)))
28.0ms	(- (* 1.0 1.0) (* (exp (* -2.0 x)) (exp (* -2.0 x))))
5.0ms	(- 1.0 (exp (* -2.0 x)))
1.0ms	(fma (/ 2.0 (- (* 1.0 1.0) (* (exp (* -2.0 x)) (exp (* -2.0 x))))) (- 1.0 (exp (* -2.0 x))) (- 1.0))

series294.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (exp (* -2.0 x)) (exp (* -2.0 x)))
48.0ms	(- (* 1.0 1.0) (* (exp (* -2.0 x)) (exp (* -2.0 x))))
27.0ms	(- 1.0 (exp (* -2.0 x)))
193.0ms	(fma (/ 2.0 (- (* 1.0 1.0) (* (exp (* -2.0 x)) (exp (* -2.0 x))))) (- 1.0 (exp (* -2.0 x))) (- 1.0))

simplify131.0ms

Algorithm

egg-herbie

Counts

419 → 419

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	917	8201
1	2488	3730
2	5002	3576

prune294.0ms

Filtered

419 candidates to 102 candidates (24.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	417	2	419
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	418	4	422

Merged error: 0.0b

Counts

422 → 4

regimes245.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	64
1	44	64

end0.0ms

sample903.0ms

Algorithm

intervals

Results

368.0ms	1664×	body	1280	valid
184.0ms	1273×	body	640	valid
119.0ms	4065×	body	80	valid
62.0ms	655×	body	320	valid
22.0ms	343×	body	160	valid