Details

sample53.0ms

Algorithm

intervals

Results

22.0ms	57×	body	1280	valid
7.0ms	39×	body	640	valid
5.0ms	130×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	17×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	15	10
2	22	10
3	31	10
4	55	10
5	120	10
6	278	10
7	819	10
8	3019	10
done	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
4.3b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite201.0ms

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:

25.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms	(+ 1.0 (exp (* -2.0 x)))
150.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series176.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
20.0ms	(+ 1.0 (exp (* -2.0 x)))
109.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.6s

Counts

150 → 150

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	180	3092
1	400	2501
2	858	2219
3	2411	1982
done	5001	1796

prune382.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
0.1b	(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
4.3b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-log-exp`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`expm1-log1p-u` `div-inv`
4×	`pow1` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `log1p-udef` `flip3--` `frac-2neg` `diff-log` `log1p-expm1` `div-exp` `clear-num` `sum-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

16.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
9.0ms	(+ 1.0 (exp (* -2.0 x)))
1.0ms	(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
148.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series475.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
21.0ms	(+ 1.0 (exp (* -2.0 x)))
261.0ms	(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
127.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.8s

Counts

164 → 164

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	197	3281
1	431	2687
2	922	2383
3	2571	2036
done	5001	1958

prune573.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (fma (pow x 4) 0.08333333333333327 (* x (- 1.0 (* 0.5 x)))))
0.0b	(* x (- 1.0 (* 0.5 x)))
13.4b	(fma (pow x 4) 0.08333333333333327 (* x (- 1.0 (* 0.5 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`prod-diff`
5×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
4×	`log1p-expm1-u`
3×	`expm1-log1p-u` `associate-r` `associate-l` `add-log-exp`
2×	`sub-neg` `associate-*r/`
1×	`expm1-log1p` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `expm1-udef` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(expm1 (fma (pow x 4) 0.08333333333333327 (* x (- 1.0 (* 0.5 x)))))
20.0ms	(* x (- 1.0 (* 0.5 x)))
0.0ms	(fma (pow x 4) 0.08333333333333327 (* x (- 1.0 (* 0.5 x))))

series286.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(expm1 (fma (pow x 4) 0.08333333333333327 (* x (- 1.0 (* 0.5 x)))))
134.0ms	(* x (- 1.0 (* 0.5 x)))
72.0ms	(fma (pow x 4) 0.08333333333333327 (* x (- 1.0 (* 0.5 x))))

simplify1.7s

Counts

62 → 62

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	105	843
1	209	828
2	542	722
3	2000	713
done	5000	677

prune267.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (fma (pow x 4) 0.08333333333333327 (/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x)))))))
0.0b	(* x (- (pow 1.0 3) (pow (* 0.5 x) 3)))
13.4b	(fma (pow x 4) 0.08333333333333327 (/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x))))))
24.4b	(/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x)))))

rewrite450.0ms

Algorithm

rewrite-expression-head

Rules

192×	`prod-diff`
98×	`distribute-rgt-in` `distribute-lft-in`
92×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
80×	`add-cube-cbrt`
74×	`unpow-prod-down` `cube-prod`
46×	`sqr-pow`
40×	`cube-mult` `unpow3`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-*r/` `add-log-exp`
3×	`times-frac` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/`
1×	`difference-cubes` `expm1-log1p` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `-commutative` `flip-+` `fma-udef` `div-inv` `associate-/l` `distribute-lft-out--` `expm1-udef` `unswap-sqr`

Counts

4 → 276

Calls

4 calls:

1.0ms	(expm1 (fma (pow x 4) 0.08333333333333327 (/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x)))))))
136.0ms	(* x (- (pow 1.0 3) (pow (* 0.5 x) 3)))
1.0ms	(fma (pow x 4) 0.08333333333333327 (/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x))))))
281.0ms	(/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x)))))

series860.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(expm1 (fma (pow x 4) 0.08333333333333327 (/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x)))))))
186.0ms	(* x (- (pow 1.0 3) (pow (* 0.5 x) 3)))
159.0ms	(fma (pow x 4) 0.08333333333333327 (/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x))))))
352.0ms	(/ (* x (- (pow 1.0 3) (pow (* 0.5 x) 3))) (+ (* 1.0 1.0) (+ (* (* 0.5 x) (* 0.5 x)) (* 1.0 (* 0.5 x)))))

simplify2.7s

Counts

288 → 288

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	421	12067
1	841	7420
2	2692	5779
done	5001	4627

prune594.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes415.0ms

Accuracy

95.8% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	29	52
1	36	41
done	36	41

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	1726×	body	1280	valid
314.0ms	1263×	body	640	valid
282.0ms	4060×	body	80	valid
139.0ms	641×	body	320	valid
39.0ms	310×	body	160	valid