Details

sample39.0ms

Algorithm

intervals

Results

17.0ms	62×	body	1280	valid
6.0ms	35×	body	640	valid
5.0ms	138×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	8×	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

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: 28.2b

Counts

2 → 1

localize6.0ms

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))))
3.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite26.0ms

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)

series134.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
39.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
80.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (37.0ms)

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

prune215.0ms

Filtered

150 candidates to 86 candidates (57.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	2	151

Merged error: 0.0b

Counts

151 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.2b	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
92×	`times-frac`
70×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
27×	`distribute-lft-out`
24×	`swap-sqr`
18×	`add-exp-log` `fma-def` `associate-r` `associate-l` `add-cbrt-cube`
12×	`associate-/r/`
11×	`pow1`
8×	`add-log-exp`
7×	`flip3-+` `flip-+`
6×	`div-inv` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `unswap-sqr`
2×	`flip3--` `flip--` `associate-/l/`
1×	`+-commutative` `pow2` `frac-times` `sub-neg` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 182

Calls

4 calls:

22.0ms	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
17.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
11.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
12.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series374.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
45.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
53.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
83.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify126.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	759	2637
1	3926	2326
2	5001	2303

prune375.0ms

Filtered

194 candidates to 135 candidates (69.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	2	196

Merged error: 0.0b

Counts

196 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
0.0b	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.1b	(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

64×	`prod-diff`
55×	`*-un-lft-identity`
47×	`add-sqr-sqrt`
44×	`unpow-prod-down`
39×	`add-cube-cbrt`
27×	`sqr-pow`
26×	`cube-prod`
24×	`times-frac`
20×	`add-exp-log`
18×	`cube-mult` `fma-def` `unpow3`
17×	`add-cbrt-cube`
16×	`difference-of-squares`
13×	`pow1`
8×	`fma-neg` `add-log-exp`
7×	`pow-pow` `pow-exp` `distribute-lft-out`
6×	`pow-unpow`
5×	`div-exp` `rem-cube-cbrt`
4×	`cbrt-undiv` `expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u`
3×	`cube-div` `flip3-+` `flip-+`
2×	`pow-to-exp` `div-inv`
1×	`difference-cubes` `+-commutative` `pow2` `frac-times` `sub-neg` `flip3--` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out--`

Counts

4 → 208

Calls

4 calls:

13.0ms	(pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3)
7.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
10.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
14.0ms	(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

series315.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3)
56.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
54.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
131.0ms	(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

simplify115.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	771	2792
1	2727	1933
2	5001	1911

prune649.0ms

Filtered

220 candidates to 113 candidates (51.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	219	3	222

Merged error: 0.0b

Counts

222 → 3

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
3.1b	(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`prod-diff`
32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod` `sqr-pow`
24×	`add-cube-cbrt`
17×	`cube-mult` `unpow3`
16×	`difference-of-squares`
9×	`cbrt-prod`
8×	`fma-neg`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 143

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
14.0ms	(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

series124.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
124.0ms	(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	397	2200
1	1311	1429
2	5002	1405

prune478.0ms

Filtered

149 candidates to 66 candidates (44.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	149	3	152

Merged error: 0.0b

Counts

152 → 3

regimes196.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	92
1	63	92

end0.0ms

sample1.0s

Algorithm

intervals

Results

416.0ms	1734×	body	1280	valid
204.0ms	1256×	body	640	valid
138.0ms	4042×	body	80	valid
72.0ms	645×	body	320	valid
29.0ms	323×	body	160	valid