Details

sample51.0ms

Algorithm

intervals

Results

14.0ms	51×	body	1280	valid
9.0ms	41×	body	640	valid
7.0ms	132×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4085
11	1745
10	535
9	183
8	79
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

9.0ms	(/ x (+ x 1.0))
27.0ms	(/ (+ x 1.0) (- x 1.0))
120.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ x (+ x 1.0))
55.0ms	(/ (+ x 1.0) (- x 1.0))
178.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.6s

Counts

605 → 605

Iterations

Iter	Nodes
done	5000
2	4599
1	1252
0	523

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
29.5b	(fma x (/ 1 (+ x 1.0)) (- (* (/ 1 (- x 1.0)) (+ x 1.0))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
49×	`times-frac`
34×	`add-cube-cbrt`
21×	`associate-l`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`distribute-lft-out`
9×	`associate-/r*`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `associate-/l*`
6×	`associate-/r/`
5×	`div-exp`
4×	`expm1-log1p-u` `flip3-+` `associate-r` `prod-exp` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `clear-num` `frac-2neg` `flip3--` `1-exp` `associate-*r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 148

Calls

4 calls:

27.0ms	(/ (+ x 1.0) (- x 1.0))
16.0ms	(/ 1 (+ x 1.0))
42.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (- (* (/ 1 (- x 1.0)) (+ x 1.0))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (+ x 1.0) (- x 1.0))
26.0ms	(/ 1 (+ x 1.0))
56.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
190.0ms	(fma x (/ 1 (+ x 1.0)) (- (* (/ 1 (- x 1.0)) (+ x 1.0))))

simplify592.0ms

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
1	654
0	227

prune752.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
0.5b	(expm1 (* (/ 1 (- x 1.0)) (+ x 1.0)))
29.5b	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`associate-l`
17×	`times-frac`
14×	`add-cube-cbrt`
13×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-r` `prod-exp` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`frac-times` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `log1p-udef` `expm1-log1p` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `log1p-expm1` `-commutative` `fma-udef` `div-inv` `flip--` `distribute-lft-out` `expm1-udef`

Counts

4 → 84

Calls

4 calls:

1.0ms	(log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))
78.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
1.0ms	(expm1 (* (/ 1 (- x 1.0)) (+ x 1.0)))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))
42.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
105.0ms	(expm1 (* (/ 1 (- x 1.0)) (+ x 1.0)))
418.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))))

simplify2.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	3894
1	565
0	181

prune575.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1.0)) (sqrt (+ x 1.0)))
0.1b	(* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
0.3b	(expm1 (* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0))))
15.7b	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`sqrt-div` `add-exp-log`
22×	`associate-l`
19×	`times-frac`
18×	`frac-times` `add-cbrt-cube`
17×	`add-cube-cbrt`
14×	`flip3-+` `associate-r` `flip-+`
13×	`prod-exp`
11×	`pow1` `sqrt-prod`
10×	`associate-*r/`
9×	`associate-*l/`
7×	`cbrt-unprod`
6×	`unswap-sqr`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r/` `*-commutative` `distribute-lft-out`
1×	`expm1-log1p` `flip3--` `fma-udef` `div-inv` `flip--` `expm1-udef`

Counts

4 → 122

Calls

4 calls:

60.0ms	(* (/ 1 (- x 1.0)) (sqrt (+ x 1.0)))
118.0ms	(* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
1.0ms	(expm1 (* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0))))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (/ 1 (- x 1.0)) (sqrt (+ x 1.0)))
53.0ms	(* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
106.0ms	(expm1 (* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0))))
318.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (* (/ 1 (- x 1.0)) (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))))))

simplify2.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	4173
1	695
0	254

prune717.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.1b

bsearch129.0ms

Steps

Iters	Range		Point
8	160.65039477392645	261980.93535209994	9433.186745037076
10	-83422883652835.42	-0.9341403346610884	-0.9906799218317324

simplify9.0ms

Iterations

Iter	Nodes
done	46
1	46
0	33

end0.0ms

sample1.5s

Algorithm

intervals

Results

523.0ms	1320×	body	640	valid
313.0ms	1667×	body	1280	valid
267.0ms	4096×	body	80	valid
115.0ms	330×	body	160	valid
67.0ms	587×	body	320	valid