Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	53×	body	1280	valid
7.0ms	48×	body	640	valid
4.0ms	129×	body	80	valid
2.0ms	18×	body	320	valid
0.0ms	8×	body	160	valid

simplify60.0ms

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
done	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

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

rewrite107.0ms

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:

7.0ms	(+ 1.0 (exp (* -2.0 x)))
14.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
79.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series137.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
37.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

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

prune273.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
0.0b	(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
3.0b	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

580×	`*-un-lft-identity`
504×	`prod-diff`
437×	`add-sqr-sqrt`
396×	`unpow-prod-down` `cube-prod`
386×	`add-cube-cbrt`
369×	`times-frac`
92×	`distribute-lft-out`
66×	`sqr-pow`
60×	`associate-/r/`
56×	`cube-mult` `unpow3`
42×	`fma-neg`
32×	`flip3-+` `flip-+`
30×	`div-inv`
24×	`difference-of-squares`
18×	`associate-l`
14×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-r` `associate-/r*` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/l*`
2×	`frac-times` `associate-*r/` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
1×	`difference-cubes` `cube-div` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--`

Counts

4 → 729

Calls

4 calls:

16.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
166.0ms	(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
16.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
205.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series316.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
89.0ms	(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
55.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
135.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify138.0ms

Counts

741 → 741

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1377	12878
1	5002	10386
done	5002	10386

prune701.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b	(pow (+ (exp (* -2.0 x)) 1.0) 3)
3.0b	(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`times-frac`
18×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
7×	`pow1`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `associate-r` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`pow-unpow` `prod-diff` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `fma-neg` `diff-log` `unpow3` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `-commutative` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 128

Calls

4 calls:

14.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
165.0ms	(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
15.0ms	(pow (+ (exp (* -2.0 x)) 1.0) 3)
26.0ms	(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

series306.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
89.0ms	(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
46.0ms	(pow (+ (exp (* -2.0 x)) 1.0) 3)
132.0ms	(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

simplify129.0ms

Counts

140 → 140

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	738	1315
1	4424	1191
2	5001	1190
done	5001	1190

prune425.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

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)))))
3.1b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite659.0ms

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:

213.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
40.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
15.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
283.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
37.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
68.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
84.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify191.0ms

Counts

1122 → 1122

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1613	25953
1	5001	17156
done	5001	17156

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.8b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	45
1	46	45
done	46	45

end0.0ms

sample963.0ms

Algorithm

intervals

Results

367.0ms	1700×	body	1280	valid
188.0ms	1243×	body	640	valid
118.0ms	4170×	body	80	valid
60.0ms	599×	body	320	valid
18.0ms	288×	body	160	valid