Details

sample53.0ms

Algorithm

intervals

Results

21.0ms	67×	body	1280	valid
7.0ms	31×	body	640	valid
6.0ms	135×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5012
8	2654
7	760
6	224
5	98
4	49
3	28
2	20
1	15
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize12.0ms

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))))
2.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite154.0ms

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-cbrt-cube` `add-exp-log` `div-inv`
4×	`associate-/r*`
3×	`expm1-log1p-u` `pow1` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `flip--` `distribute-lft-out--`

Counts

3 → 141

Calls

3 calls:

13.0ms	(+ 1.0 (exp (* -2.0 x)))
17.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
113.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series215.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(+ 1.0 (exp (* -2.0 x)))
44.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
154.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
3	3749
2	1082
1	419
0	180

prune554.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.2b	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite656.0ms

Algorithm

rewrite-expression-head

Rules

551×	`sqrt-prod`
463×	`*-un-lft-identity`
378×	`prod-diff`
351×	`add-sqr-sqrt`
321×	`add-cube-cbrt`
256×	`times-frac`
128×	`distribute-rgt-in` `distribute-lft-in`
67×	`distribute-lft-out`
42×	`associate-/r/`
24×	`flip3-+` `flip-+`
21×	`fma-neg` `div-inv`
12×	`difference-of-squares`
11×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `flip3--` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`sub-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-l/` `associate-r/`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 533

Calls

4 calls:

23.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
13.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
429.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
110.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series740.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
48.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
467.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
156.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify2.7s

Counts

545 → 545

Iterations

Iter	Nodes
done	5000
1	1651
0	503

prune2.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
2.6b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite911.0ms

Algorithm

rewrite-expression-head

Rules

596×	`sqrt-prod`
462×	`*-un-lft-identity`
378×	`prod-diff`
363×	`add-sqr-sqrt`
320×	`add-cube-cbrt`
258×	`times-frac`
65×	`distribute-lft-out`
63×	`fma-neg`
48×	`flip3-+` `flip-+`
42×	`associate-/r/`
28×	`frac-times`
23×	`pow1`
21×	`div-inv`
18×	`difference-of-squares`
14×	`associate-*l/`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`associate-*r/`
6×	`pow-plus` `pow-prod-up` `distribute-lft-out--`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`pow2` `pow-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 567

Calls

4 calls:

537.0ms	(* (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
93.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
102.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
129.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series784.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(* (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
129.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
161.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
160.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify2.9s

Counts

579 → 579

Iterations

Iter	Nodes
done	5000
2	4262
1	998
0	360

prune2.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x 1.0) (fma (* (* x x) x) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x)))))
0.1b	(* (* x x) x)
0.1b	(* (* x x) (* x x))
11.5b	(fma (* (* x x) x) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

134×	`pow1`
42×	`pow-prod-up`
26×	`pow-prod-down`
24×	`pow-plus` `pow-sqr`
21×	`add-cbrt-cube` `add-exp-log`
15×	`pow2`
11×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`prod-diff`
2×	`associate-l` `*-commutative` `fma-udef` `unswap-sqr`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `swap-sqr` `pow3` `flip--` `associate--r+`

Counts

4 → 124

Calls

4 calls:

11.0ms	(- (* x 1.0) (fma (* (* x x) x) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x)))))
17.0ms	(* (* x x) x)
25.0ms	(* (* x x) (* x x))
0.0ms	(fma (* (* x x) x) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* x 1.0) (fma (* (* x x) x) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x)))))
43.0ms	(* (* x x) x)
40.0ms	(* (* x x) (* x x))
144.0ms	(fma (* (* x x) x) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

simplify3.0s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
3	4142
2	929
1	330
0	126

prune417.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes289.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 29.3b

bsearch2.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	45
1	45
0	33

end0.0ms

sample2.0s

Algorithm

intervals

Results

882.0ms	1668×	body	1280	valid
421.0ms	1307×	body	640	valid
175.0ms	4107×	body	80	valid
128.0ms	617×	body	320	valid
58.0ms	301×	body	160	valid