Details

sample159.0ms

Algorithm

intervals

Results

102.0ms	92×	body	10240	exit
22.0ms	272×	body	80	valid
4.0ms	4×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	19	9
3	23	9
done	23	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.8b	(log (+ 1.0 (exp x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 62

Calls

3 calls:

14.0ms	(- (log (+ 1.0 (exp x))) (* x y))
7.0ms	(+ 1.0 (exp x))
6.0ms	(log (+ 1.0 (exp x)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(- (log (+ 1.0 (exp x))) (* x y))
15.0ms	(+ 1.0 (exp x))
93.0ms	(log (+ 1.0 (exp x)))

simplify3.5s

Counts

71 → 71

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	105	724
1	237	686
2	579	635
3	1595	618
4	3745	590
done	5000	589

prune205.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x (- y) (log (+ 1.0 (exp x))))
0.0b	(+ 1.0 (exp x))
0.8b	(log (+ 1.0 (exp x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow` `fma-udef`

Counts

3 → 44

Calls

3 calls:

0.0ms	(fma x (- y) (log (+ 1.0 (exp x))))
7.0ms	(+ 1.0 (exp x))
6.0ms	(log (+ 1.0 (exp x)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(fma x (- y) (log (+ 1.0 (exp x))))
9.0ms	(+ 1.0 (exp x))
74.0ms	(log (+ 1.0 (exp x)))

simplify2.3s

Counts

53 → 53

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	84	468
1	169	450
2	376	410
3	910	406
4	2269	401
done	5001	400

prune262.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(exp (log (log (+ 1.0 (exp x)))))
0.0b	(log (log (+ 1.0 (exp x))))
0.8b	(log (+ 1.0 (exp x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`log-prod`
9×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
6×	`add-exp-log` `add-log-exp`
5×	`log-pow`
4×	`expm1-log1p-u` `exp-prod` `exp-sum` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`log-div` `flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`+-commutative` `sum-log` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

7.0ms	(+ 1.0 (exp x))
3.0ms	(exp (log (log (+ 1.0 (exp x)))))
6.0ms	(log (log (+ 1.0 (exp x))))
8.0ms	(log (+ 1.0 (exp x)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (exp x))
108.0ms	(exp (log (log (+ 1.0 (exp x)))))
192.0ms	(log (log (+ 1.0 (exp x))))
96.0ms	(log (+ 1.0 (exp x)))

simplify3.2s

Counts

79 → 79

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	110	725
1	217	657
2	508	598
3	1367	589
4	4516	572
done	5000	572

prune340.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (/ x (log 2.0)))
0.2b	(* (* x (/ x (log 2.0))) (- 0.25 (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2)))))
0.2b	(/ x (log 2.0))
0.2b	(/ x (log 2.0))

rewrite662.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
61×	`times-frac`
57×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
36×	`prod-diff`
28×	`pow1`
22×	`add-exp-log` `associate-r` `add-cbrt-cube`
20×	`distribute-rgt-in` `distribute-lft-in`
19×	`distribute-lft-out`
17×	`log-pow`
8×	`associate-/r*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-r/` `associate-/l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-times` `sub-neg` `flip3--` `frac-2neg` `clear-num` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`associate-*l/` `difference-of-squares`

Counts

4 → 173

Calls

4 calls:

19.0ms	(* x (/ x (log 2.0)))
609.0ms	(* (* x (/ x (log 2.0))) (- 0.25 (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2)))))
6.0ms	(/ x (log 2.0))
14.0ms	(/ x (log 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

267.0ms	(* x (/ x (log 2.0)))
616.0ms	(* (* x (/ x (log 2.0))) (- 0.25 (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2)))))
286.0ms	(/ x (log 2.0))
292.0ms	(/ x (log 2.0))

simplify1.6s

Counts

185 → 185

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	212	4624
1	513	3731
2	1720	3011
done	5000	2555

prune730.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes61.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	11	11
done	11	11

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.7s	2410×	body	10240	exit
709.0ms	8459×	body	80	valid
355.0ms	99×	body	160	valid
101.0ms	255×	body	640	valid
91.0ms	136×	body	1280	valid
88.0ms	178×	body	320	valid